https://mathimages.swarthmore.edu/api.php?action=feedcontributions&user=Tcheeseman1&feedformat=atomMath Images - User contributions [en]2022-11-30T02:46:47ZUser contributionsMediaWiki 1.31.1https://mathimages.swarthmore.edu/index.php?title=D09&diff=10040D092009-08-31T21:08:32Z<p>Tcheeseman1: /* Working On */</p>
<hr />
<div><center>'' '''Welcome to the Drexel Summer 09 Entry to [[Image:TmipClear.png|275px]]''' ''!</center><br />
<br />
'''IMPORTANT NOTE: Please put up contact information on Drexel-Swat Partnering page: [[Drexel-Swat_Partnering]]'''<br />
<br />
[[Getting Started]] --- [[A Brief Tour of What's Been Done So Far]]<br />
<br />
----<br />
<br />
'''Things to do:''' <br />
* browse around, leaving comments on the Math Images discussion page and the Swarthmore student's discussion page, looking around for interesting possibilities for interaction on the latter<br />
* look through the Helper Pages in the left navbar and the [http://wikis.swarthmore.edu/miwiki/index.php/Hard_Math Hard Math] page to see if you can find anything you'd like to work on--if there's anything you've struggled with that isn't there, add it!<br />
<br />
----<br />
<br />
'''[[Math for Computer Graphics and Computer Vision]]'''<br />
<br />
'''Resources:'''<br />
:* [http://www.kirupa.com/developer/flash/index.htm Flash/ActionScript Tutorials]<br />
:* [http://hgbook.red-bean.com/read/ Mercurial Book] (Online)<br />
:* [http://java.sun.com/developer/onlineTraining/java3d/ Java 3D Tutorials]<br />
:* [http://javaview.de/ JavaView]<br />
:* [http://javaview.de/vgp/tutor/index.html JavaView Applet Examples]<br />
:* [http://javaview.de/doc/reference/index.html JavaView API Documentation (JavaDoc)]<br />
<br />
__TOC__<br />
<br />
''' ''Check out the [[Drexel-Swat Partnering]] page to see who's paired up with whom and keep track of what they're working on...'' '''<br />
<br />
==Possible Applets/Animations for Drexel Students To Do==<br />
:* [[Parametric Equations]] Page- demonstrate the parametric construction of a circle. Perhaps the user can increase the value of the parameter in the parametric equations of a circle, and see the resulting circle be drawn in real time. The same type of applet would be cool for the butterfly curve, although I already have an animation for this curve (from wikipedia) and making another one would be more difficult than a circle.<br />
<br />
:*[[Henon Attractor]] Page - an applet allowing the users to pick values of ''a'' and ''b'' to create different Henon Attractor (Mike is now done this applet)<br />
<br />
:*[[Blue Fern]] Page - my ideas for this are pretty vague. Perhaps some sort of an animation or applet showing the different types of matrix transformations and translations involved in making the fern. Maybe showing what each matrix does to an object (rotate it, shrink it...)<br />
<br />
:*[[Brunnian Links]] - an interactive 3D model of the Borromean rings (and possibly high ring levels also) similar to this [http://video.google.com/videoplay?docid=-5851348533617330039&ei=N75DSqSJFZy8rQKG9pyNBg&q=borromean+rings&hl=en&client=firefox-a YouTube]. I was thinking about an applet that would allow users to rotate the model with their mouse to see all perspectives of the ring, as well as have an animation showing that after one ring is removed, the ring unravels.<br />
<br />
:*[[Torus]] page- The section n-torus could use an illustration of how an <math>n</math>-dimensional object can exist in <math>n+1</math> dimensions. For example a line, which is a 1D object can exist in 2D when it is bent into a circle. Similarly, in 3D, a cube wraps to form a 3-torus. Illustrations could really help explain this section. I've tried searching for images online but could not get one that specifically shows this.<br />
<br />
==[[User:Tcheeseman1|Tim]]==<br />
<br />
Click on my name above for things that I've finished<br />
<br />
===Working On===<br />
<br />
:* Applet for [[Inversion|Point and Shape Inversion]] in 3D to demonstrate creating [[Dual Polyhedron|Dual Polyhedrons]]): [http://www.cs.drexel.edu/~twc24/mathimages/inversion/ShapeInversion3D.html Release Candidate] - Need to fix trig on dodecahedron, waiting for some feedback from MaeBeth<br />
:* [[Planar Projection]] page for [[Math for Computer Graphics and Computer Vision]] and Planar Projection applet [http://www.cs.drexel.edu/~twc24/mathimages/projection/PlanarProjection.html Early Preview]<br />
<br />
==[[User:Egoldberg1|Emily G.]]==<br />
===Projects In Progress:===<br />
:*Line Drawing (manipulating alpha in parametric equations)<br />
::*Status- In progress<br />
:*[[Implicit Equations]] page<br />
::*Status- Researching<br />
<br />
===Projects for the Future:===<br />
:*Rhodonea ([[Cardioid]], Rose Petals, Limacons, etc.)- interactive graphing<br />
:*[[Torus]] & [[Volume_of_Revolution]]- interactive graphing<br />
<br />
==[[User:Slombardi1|Steve]]==<br />
Click on my name to see my project list<br />
<br />
==[[User:Asobti1|Ayush]]==<br />
<br />
I'm a Computer Science sophomore at Drexel University. This Summer term (Summer 09) is my first term working on the Math Images project.<br />
<br />
===Past Work:===<br />
:For my past work, click on my name to see my user page.<br />
<br />
===Work in Progress:===<br />
:Matrix calculator<br />
:Writing a Math and Computer Graphics page<br />
<br />
==[[User:Jdicristo1|Josh]]==<br />
<br />
I just completed my freshman year at Drexel, going for a BS in Computer Science<br />
<br />
===Projects:===<br />
:Working with Ayush and Alan to add interactivity in the pages previously created by Alan.<br />
:Working mainly with Java<br />
<br />
===Progress After Week 1===<br />
Because I am really working on this project part-time I did not make any major strides this week but I did get a few things accomplished<br />
: I learned the basics of writing Java Applets<br />
: I'm about 1/3 of the way done a program that segments a rectangle into thirds and then illustrates the Golden Spiral<br />
<br />
==[[User:Mhershey1|Mhershey1]]==<br />
test:<br />
What I have so far: http://www.pages.drexel.edu/~smh86/index.html<br />
<br />
==[[User:Mhinkle1|Matt]]==<br />
===Projects===<br />
:[http://www.pages.drexel.edu/~mjh96/java/Xformations/XformApp.html Current Project]<br />
<br />
===Week 1 Progress===<br />
:After getting comfortable with writing Java applets, I began to read the Java 3D tutorial provided by Sun. After getting down some of the basics, I began to work on the Change of Coordinates applet. So far I have created a 3D graph that has the ability to graphically display a point in 3-space as specified by the user. This point may then be displayed with a rectangular/cartesian, cylindrical, or spherical representation. As of now, the points are input via the console, yet in the finished version, the user will be able to click any location in 3-space to select a point. The user will also be able to navigate the space with a mouse or keyboard.</div>Tcheeseman1https://mathimages.swarthmore.edu/index.php?title=Planar_Projection&diff=9673Planar Projection2009-08-17T17:06:33Z<p>Tcheeseman1: /* Orthographic Projection */</p>
<hr />
<div>Summary<br />
<br />
=== Projection Parameters ===<br />
<br />
<br />
Each of the parameters uses either the ''world-coordinate'' (WC) or ''viewing reference-coordinate'' (VRC) system. The WC system uses the standard ''x'', ''y'', and ''z'' axes, while the VRC system uses the ''u'', ''v'', and ''n'' axes.<br />
<br />
:* The '''View Reference Point''' (VRP) is the point (WC) from which the camera is viewing the 3D geometry.<br />
:* The '''View Plane Normal''' (VPN) is the normal (WC) which, once projected, defines the ''n'' axis.<br />
:* The '''View Up Vector''' (VUP) is the vector (WC) that defines the orientation of the camera (i.e. which way is up) and, once projected, defines the ''v'' axis.<br />
:* The '''Projection Reference Point''' (PRP) is the point (VRC) ...<br />
:* The '''Viewing Window''' is the rectangle (VRC) that defines the size of the 2D window upon which the 3D geometry will be projected. It is defined by u<sub>min</sub>, u<sub>max</sub>, v<sub>min</sub>, and v<sub>max</sub>.<br />
:* The '''projection type''' can be either parallel or perspective.<br />
<br />
== Parallel Projection ==<br />
<br />
Summary<br />
<br />
=== Orthographic Projection ===<br />
<br />
The first step is to translate the VRP to the origin, which can be achieved by multiplying its complement with the following matrix '''T''':<br />
<br />
<math>T = \left[ \begin{array}{cccc}<br />
1 & 0 & 0 & -vrp_{x} \\<br />
0 & 1 & 0 & -vrp_{y} \\<br />
0 & 0 & 1 & -vrp_{z} \\<br />
0 & 0 & 0 & 1<br />
\end{array} \right]<br />
</math><br />
<br />
The second step is to then rotate VPN to the ''z'' axis and VUP to the ''y'' axis. To do this we will calculate the following vectors:<br />
<br />
:* <math>R_{z} = \frac{VPN}{|VPN|}</math><br />
:* <math>R_{x} = \frac{VUP \times R_{z}}{|VUP \times R_{z}|}</math><br />
:* <math>R_{y} = R_{z} \times R_{x}</math><br />
<br />
The components of these vectors (e.g. R<sub>x</sub> = < r<sub>x1</sub>, r<sub>x2</sub>, r<sub>x3</sub> >) then form the rotation matrix R:<br />
<br />
<math>R = \left[ \begin{array}{cccc}<br />
r_{x_{1}} & r_{x_{2}} & r_{x_{3}} & 0 \\<br />
r_{y_{1}} & r_{y_{2}} & r_{y_{3}} & 0 \\<br />
r_{z_{1}} & r_{z_{2}} & r_{z_{3}} & 0 \\<br />
0 & 0 & 0 & 1<br />
\end{array} \right]<br />
</math><br />
<br />
The third step is to shear the geometry so the the direction of projection (DOP) is parallel to the VPN (now aligned with the z axis). The DOP is defines as follows:<br />
<br />
<math>DOP = \left[ \begin{array}{c}<br />
\frac{u_{max} + u_{min}}{2} - prp_{u} \\<br />
\frac{v_{max} + v_{min}}{2} - prp_{v} \\<br />
-prp_{n} \\<br />
1<br />
\end{array} \right]<br />
</math><br />
<br />
To shear the DOP, we need to align it with the ''z'' axis.<br />
<br />
TODO: define shx and shy<br />
<br />
<math>SH_{par} = \left[ \begin{array}{cccc}<br />
1 & 0 & sh_{x} & 0 \\<br />
0 & 1 & sh_{y} & 0 \\<br />
0 & 0 & 1 & 0 \\<br />
0 & 0 & 0 & 1<br />
\end{array} \right]<br />
</math><br />
<br />
TODO: add translate (Tpar) and scale (Spar)<br />
<br />
The final transformation matrix for orthographic projection is then the result of the following multiplication:<br />
<br />
<math>N_{par} = (S_{par} \cdot (T_{par} \cdot (SH_{par} \cdot (R \cdot T \cdot (-VRP)))))</math><br />
<br />
=== Oblique Projection ===<br />
<br />
== Perspective Projection ==<br />
<br />
Summary</div>Tcheeseman1https://mathimages.swarthmore.edu/index.php?title=Planar_Projection&diff=9671Planar Projection2009-08-17T16:57:24Z<p>Tcheeseman1: /* Projection Parameters */</p>
<hr />
<div>Summary<br />
<br />
=== Projection Parameters ===<br />
<br />
<br />
Each of the parameters uses either the ''world-coordinate'' (WC) or ''viewing reference-coordinate'' (VRC) system. The WC system uses the standard ''x'', ''y'', and ''z'' axes, while the VRC system uses the ''u'', ''v'', and ''n'' axes.<br />
<br />
:* The '''View Reference Point''' (VRP) is the point (WC) from which the camera is viewing the 3D geometry.<br />
:* The '''View Plane Normal''' (VPN) is the normal (WC) which, once projected, defines the ''n'' axis.<br />
:* The '''View Up Vector''' (VUP) is the vector (WC) that defines the orientation of the camera (i.e. which way is up) and, once projected, defines the ''v'' axis.<br />
:* The '''Projection Reference Point''' (PRP) is the point (VRC) ...<br />
:* The '''Viewing Window''' is the rectangle (VRC) that defines the size of the 2D window upon which the 3D geometry will be projected. It is defined by u<sub>min</sub>, u<sub>max</sub>, v<sub>min</sub>, and v<sub>max</sub>.<br />
:* The '''projection type''' can be either parallel or perspective.<br />
<br />
== Parallel Projection ==<br />
<br />
Summary<br />
<br />
=== Orthographic Projection ===<br />
<br />
The first step is to translate the VRP to the origin, which can be achieved by multiplying its complement with the following matrix '''T''':<br />
<br />
<math>T = \left[ \begin{array}{cccc}<br />
1 & 0 & 0 & -vrp_{x} \\<br />
0 & 1 & 0 & -vrp_{y} \\<br />
0 & 0 & 1 & -vrp_{z} \\<br />
0 & 0 & 0 & 1<br />
\end{array} \right]<br />
</math><br />
<br />
The second step is to then rotate VPN to the ''z'' axis and VUP to the ''y'' axis. To do this we will calculate the following vectors:<br />
<br />
:* <math>R_{z} = \frac{VPN}{|VPN|}</math><br />
:* <math>R_{x} = \frac{VUP \times R_{z}}{|VUP \times R_{z}|}</math><br />
:* <math>R_{y} = R_{z} \times R_{x}</math><br />
<br />
The components of these vectors (e.g. <math>R_{x} = <r_{x_{1}}, r_{x_{2}}, r_{x_{3}}></math>) then form the rotation matrix R:<br />
<br />
<math>R = \left[ \begin{array}{cccc}<br />
r_{x_{1}} & r_{x_{2}} & r_{x_{3}} & 0 \\<br />
r_{y_{1}} & r_{y_{2}} & r_{y_{3}} & 0 \\<br />
r_{z_{1}} & r_{z_{2}} & r_{z_{3}} & 0 \\<br />
0 & 0 & 0 & 1<br />
\end{array} \right]<br />
</math><br />
<br />
The third step is to shear the geometry so the the direction of projection (DOP) is parallel to the VPN.<br />
<br />
The final transformation matrix for orthographic projection is then the result of the following multiplication:<br />
<br />
<math>N_{par} = (S_{par} \cdot (T_{par} \cdot (SH_{par} \cdot (R \cdot T \cdot (-VRP)))))</math><br />
<br />
=== Oblique Projection ===<br />
<br />
== Perspective Projection ==<br />
<br />
Summary</div>Tcheeseman1https://mathimages.swarthmore.edu/index.php?title=Planar_Projection&diff=9668Planar Projection2009-08-17T16:49:12Z<p>Tcheeseman1: /* Orthographic Projection */</p>
<hr />
<div>Summary<br />
<br />
=== Projection Parameters ===<br />
<br />
<br />
Each of the parameters uses either the ''world-coordinate'' (WC) or ''viewing reference-coordinate'' (VRC) system.<br />
<br />
:* The '''View Reference Point''' (VRP) is the point (WC) from which the camera is viewing the 3D geometry.<br />
:* The '''View Plane Normal''' (VPN) is the normal (WC) ...<br />
:* The '''View Up Vector''' (VUP) is the vector (WC) that defines the orientation of the camera (i.e. which way is up)<br />
:* The '''Projection Reference Point''' (PRP) is the point (VRC) ...<br />
:* The '''Viewing Window''' is the rectangle (VRC) that defines the size of the 2D window upon which the 3D geometry will be projected.<br />
:* The '''projection type''' can be either parallel or perspective<br />
<br />
== Parallel Projection ==<br />
<br />
Summary<br />
<br />
=== Orthographic Projection ===<br />
<br />
The first step is to translate the VRP to the origin, which can be achieved by multiplying its complement with the following matrix '''T''':<br />
<br />
<math>T = \left[ \begin{array}{cccc}<br />
1 & 0 & 0 & -vrp_{x} \\<br />
0 & 1 & 0 & -vrp_{y} \\<br />
0 & 0 & 1 & -vrp_{z} \\<br />
0 & 0 & 0 & 1<br />
\end{array} \right]<br />
</math><br />
<br />
The second step is to then rotate VPN to the ''z'' axis and VUP to the ''y'' axis. To do this we will calculate the following vectors:<br />
<br />
:* <math>R_{z} = \frac{VPN}{|VPN|}</math><br />
:* <math>R_{x} = \frac{VUP \times R_{z}}{|VUP \times R_{z}|}</math><br />
:* <math>R_{y} = R_{z} \times R_{x}</math><br />
<br />
The components of these vectors (e.g. <math>R_{x} = <r_{x_{1}}, r_{x_{2}}, r_{x_{3}}></math>) then form the rotation matrix R:<br />
<br />
<math>R = \left[ \begin{array}{cccc}<br />
r_{x_{1}} & r_{x_{2}} & r_{x_{3}} & 0 \\<br />
r_{y_{1}} & r_{y_{2}} & r_{y_{3}} & 0 \\<br />
r_{z_{1}} & r_{z_{2}} & r_{z_{3}} & 0 \\<br />
0 & 0 & 0 & 1<br />
\end{array} \right]<br />
</math><br />
<br />
The third step is to shear the geometry so the the direction of projection (DOP) is parallel to the VPN.<br />
<br />
The final transformation matrix for orthographic projection is then the result of the following multiplication:<br />
<br />
<math>N_{par} = (S_{par} \cdot (T_{par} \cdot (SH_{par} \cdot (R \cdot T \cdot (-VRP)))))</math><br />
<br />
=== Oblique Projection ===<br />
<br />
== Perspective Projection ==<br />
<br />
Summary</div>Tcheeseman1https://mathimages.swarthmore.edu/index.php?title=Planar_Projection&diff=9663Planar Projection2009-08-17T16:42:33Z<p>Tcheeseman1: /* Orthographic Projection */</p>
<hr />
<div>Summary<br />
<br />
=== Projection Parameters ===<br />
<br />
<br />
Each of the parameters uses either the ''world-coordinate'' (WC) or ''viewing reference-coordinate'' (VRC) system.<br />
<br />
:* The '''View Reference Point''' (VRP) is the point (WC) from which the camera is viewing the 3D geometry.<br />
:* The '''View Plane Normal''' (VPN) is the normal (WC) ...<br />
:* The '''View Up Vector''' (VUP) is the vector (WC) that defines the orientation of the camera (i.e. which way is up)<br />
:* The '''Projection Reference Point''' (PRP) is the point (VRC) ...<br />
:* The '''Viewing Window''' is the rectangle (VRC) that defines the size of the 2D window upon which the 3D geometry will be projected.<br />
:* The '''projection type''' can be either parallel or perspective<br />
<br />
== Parallel Projection ==<br />
<br />
Summary<br />
<br />
=== Orthographic Projection ===<br />
<br />
The first step is to translate the VRP to the origin, which can be achieved by multiplying its complement with the following matrix '''T''':<br />
<br />
<math>T = \left[ \begin{array}{cccc}<br />
1 & 0 & 0 & -vrp_{x} \\<br />
0 & 1 & 0 & -vrp_{y} \\<br />
0 & 0 & 1 & -vrp_{z} \\<br />
0 & 0 & 0 & 1<br />
\end{array} \right]<br />
</math><br />
<br />
The second step is to then rotate VPN to the ''z'' axis and VUP to the ''y'' axis. To do this we will calculate the following vectors:<br />
<br />
:* <math>R_{z} = \frac{VPN}{|VPN|}</math><br />
:* <math>R_{x} = \frac{VUP \times R_{z}}{|VUP \times R_{z}|}</math><br />
:* <math>R_{y} = R_{z} \times R_{x}</math><br />
<br />
The components of these vectors (e.g. <math>R_{x} = <r_{x_{1}}, r_{x_{2}}, r_{x_{3}}></math>) then form the rotation matrix R:<br />
<br />
<math>R = \left[ \begin{array}{cccc}<br />
r_{x_{1}} & r_{x_{2}} & r_{x_{3}} & 0 \\<br />
r_{y_{1}} & r_{y_{2}} & r_{y_{3}} & 0 \\<br />
r_{z_{1}} & r_{z_{2}} & r_{z_{3}} & 0 \\<br />
0 & 0 & 0 & 1<br />
\end{array} \right]<br />
</math><br />
<br />
The final transformation matrix for orthographic projection is then the result of the following multiplication:<br />
<br />
<math>N_{par} = (S_{par} \cdot (T_{par} \cdot (SH_{par} \cdot (R \cdot T \cdot (-VRP)))))</math><br />
<br />
=== Oblique Projection ===<br />
<br />
== Perspective Projection ==<br />
<br />
Summary</div>Tcheeseman1https://mathimages.swarthmore.edu/index.php?title=Planar_Projection&diff=9633Planar Projection2009-08-13T16:50:53Z<p>Tcheeseman1: New page: Summary === Projection Parameters === Each of the parameters uses either the ''world-coordinate'' (WC) or ''viewing reference-coordinate'' (VRC) system. :* The '''View Reference Point'...</p>
<hr />
<div>Summary<br />
<br />
=== Projection Parameters ===<br />
<br />
<br />
Each of the parameters uses either the ''world-coordinate'' (WC) or ''viewing reference-coordinate'' (VRC) system.<br />
<br />
:* The '''View Reference Point''' (VRP) is the point (WC) from which the camera is viewing the 3D geometry.<br />
:* The '''View Plane Normal''' (VPN) is the normal (WC) ...<br />
:* The '''View Up Vector''' (VUP) is the vector (WC) that defines the orientation of the camera (i.e. which way is up)<br />
:* The '''Projection Reference Point''' (PRP) is the point (VRC) ...<br />
:* The '''Viewing Window''' is the rectangle (VRC) that defines the size of the 2D window upon which the 3D geometry will be projected.<br />
:* The '''projection type''' can be either parallel or perspective<br />
<br />
== Parallel Projection ==<br />
<br />
Summary<br />
<br />
=== Orthographic Projection ===<br />
<br />
=== Oblique Projection ===<br />
<br />
== Perspective Projection ==<br />
<br />
Summary</div>Tcheeseman1https://mathimages.swarthmore.edu/index.php?title=D09&diff=9632D092009-08-13T16:24:50Z<p>Tcheeseman1: /* Working On */</p>
<hr />
<div><center>'' '''Welcome to the Drexel Summer 09 Entry to [[Image:TmipClear.png|275px]]''' ''!</center><br />
<br />
'''IMPORTANT NOTE: Please put up contact information on Drexel-Swat Partnering page: [[Drexel-Swat_Partnering]]'''<br />
<br />
[[Getting Started]] --- [[A Brief Tour of What's Been Done So Far]]<br />
<br />
----<br />
<br />
'''Things to do:''' <br />
* browse around, leaving comments on the Math Images discussion page and the Swarthmore student's discussion page, looking around for interesting possibilities for interaction on the latter<br />
* look through the Helper Pages in the left navbar and the [http://wikis.swarthmore.edu/miwiki/index.php/Hard_Math Hard Math] page to see if you can find anything you'd like to work on--if there's anything you've struggled with that isn't there, add it!<br />
<br />
----<br />
<br />
'''[[Math for Computer Graphics and Computer Vision]]'''<br />
<br />
'''Resources:'''<br />
:* [http://www.kirupa.com/developer/flash/index.htm Flash/ActionScript Tutorials]<br />
:* [http://hgbook.red-bean.com/read/ Mercurial Book] (Online)<br />
:* [http://java.sun.com/developer/onlineTraining/java3d/ Java 3D Tutorials]<br />
:* [http://javaview.de/ JavaView]<br />
:* [http://javaview.de/vgp/tutor/index.html JavaView Applet Examples]<br />
:* [http://javaview.de/doc/reference/index.html JavaView API Documentation (JavaDoc)]<br />
<br />
__TOC__<br />
<br />
''' ''Check out the [[Drexel-Swat Partnering]] page to see who's paired up with whom and keep track of what they're working on...'' '''<br />
<br />
==Possible Applets/Animations for Drexel Students To Do==<br />
:* [[Parametric Equations]] Page- demonstrate the parametric construction of a circle. Perhaps the user can increase the value of the parameter in the parametric equations of a circle, and see the resulting circle be drawn in real time. The same type of applet would be cool for the butterfly curve, although I already have an animation for this curve (from wikipedia) and making another one would be more difficult than a circle.<br />
<br />
:*[[Henon Attractor]] Page - an applet allowing the users to pick values of ''a'' and ''b'' to create different Henon Attractor (Mike is now done this applet)<br />
<br />
:*[[Blue Fern]] Page - my ideas for this are pretty vague. Perhaps some sort of an animation or applet showing the different types of matrix transformations and translations involved in making the fern. Maybe showing what each matrix does to an object (rotate it, shrink it...)<br />
<br />
:*[[Brunnian Links]] - an interactive 3D model of the Borromean rings (and possibly high ring levels also) similar to this [http://video.google.com/videoplay?docid=-5851348533617330039&ei=N75DSqSJFZy8rQKG9pyNBg&q=borromean+rings&hl=en&client=firefox-a YouTube]. I was thinking about an applet that would allow users to rotate the model with their mouse to see all perspectives of the ring, as well as have an animation showing that after one ring is removed, the ring unravels.<br />
<br />
:*[[Torus]] page- The section n-torus could use an illustration of how an <math>n</math>-dimensional object can exist in <math>n+1</math> dimensions. For example a line, which is a 1D object can exist in 2D when it is bent into a circle. Similarly, in 3D, a cube wraps to form a 3-torus. Illustrations could really help explain this section. I've tried searching for images online but could not get one that specifically shows this.<br />
<br />
==[[User:Tcheeseman1|Tim]]==<br />
<br />
Click on my name above for things that I've finished<br />
<br />
===Working On===<br />
<br />
:* Applet for [[Inversion|Point and Shape Inversion]] in 3D to demonstrate creating [[Dual Polyhedron|Dual Polyhedrons]]): [http://www.cs.drexel.edu/~twc24/mathimages/inversion/ShapeInversion3D.html Release Candidate] - Need to fix trig on dodecahedron, waiting for some feedback from MaeBeth<br />
:* [[Planar Projection]] page for [[Math for Computer Graphics and Computer Vision]]<br />
<br />
==[[User:Egoldberg1|Emily G.]]==<br />
===Projects In Progress:===<br />
:*Line Drawing (manipulating alpha in parametric equation of a line)<br />
::*Status- In progress<br />
:*[[Tessellations]] Image Gallery<br />
::*Status- Mostly done<br />
<br />
===Projects for the Future:===<br />
:*Rhodonea ([[Cardioid]], Rose Petals, Limacons, etc.)- interactive graphing<br />
::*Status- Investigating the possibility of using a webMathematica applet to accomplish this<br />
:*[[Torus]] & [[Volume_of_Revolution]]- interactive graphing<br />
::*Status- Investigating the possibility of using a webMathematica applet to accomplish this<br />
<br />
==[[User:Slombardi1|Steve]]==<br />
Click on my name to see my project list<br />
<br />
pages todo:<br />
:fourier transform<br />
:[[Bump Mapping|Bump Mapping]]<br />
:[[Gaussian Pyramid|Gaussian Pyramid]]<br />
:Image Convolution<br />
<br />
==[[User:Asobti1|Ayush]]==<br />
<br />
I'm a Computer Science sophomore at Drexel University. This Summer term (Summer 09) is my first term working on the Math Images project.<br />
<br />
===Past Work:===<br />
:For my past work, click on my name to see my user page.<br />
<br />
===Work in Progress:===<br />
:Matrix calculator<br />
:Writing a Math and Computer Graphics page<br />
<br />
==[[User:Jdicristo1|Josh]]==<br />
<br />
I just completed my freshman year at Drexel, going for a BS in Computer Science<br />
<br />
===Projects:===<br />
:Working with Ayush and Alan to add interactivity in the pages previously created by Alan.<br />
:Working mainly with Java<br />
<br />
===Progress After Week 1===<br />
Because I am really working on this project part-time I did not make any major strides this week but I did get a few things accomplished<br />
: I learned the basics of writing Java Applets<br />
: I'm about 1/3 of the way done a program that segments a rectangle into thirds and then illustrates the Golden Spiral<br />
<br />
==[[User:Mhershey1|Mhershey1]]==<br />
test:<br />
<java_applet code="Bluewashrecursive.class" width="500" height="400"/><br />
What I have so far: http://www.pages.drexel.edu/~smh86/index.html<br />
:*[[Blue Wash]], applet changing ''k'' (in '''Inclined Recursive Method''') & animation drawing the basic no ''k'' method (in '''Basic Recursive Method''') <br />
:*[[Blue Fern]], [[Henon Attractor]], redo the animations with small points<br />
:*[[Hyperbolic Tilings]], applet where users input Schläfli symbol to create a tiling<br />
:**This would take too long for me to do. Maybe someone else can do this one, or we could just use the already made applet?<br />
:*[[Newton's Basin]], redo the animation (maybe users input the equations)<br />
:*[[Logarithms]], interactive quiz with exponential and logarithmic equations<br />
:*[[Harter-Heighway Dragon]], animating the curve at each iteration stage<br />
<br />
==[[User:Mhinkle1|Matt]]==<br />
If you see the green box below, you have Java installed. All Java 3D applets were tested using version 1.6.0_14. If it still does not work, please let me know!<br />
<java_applet code="JavaVersionDisplayApplet.class" width="400" height="50" archive="http://www.pages.drexel.edu/~mjh96/java/JavaTest/JavaVersionTestApp.jar" /><br />
:[http://www.javatester.org/index.htm Click here] to learn more about the Java Tester Applet.<br />
<br />
===Projects===<br />
:Current Project:<br />
:<b>Subdivision Surfaces Applet</b><br />
:*Description: An applet which allows the user to display a selection of geometry primitives and manipulate the number of subdivisions<br />
:[[User:Mhinkle1|Click here]] for a full listing of my work.<br />
<br />
===Week 1 Progress===<br />
:After getting comfortable with writing Java applets, I began to read the Java 3D tutorial provided by Sun. After getting down some of the basics, I began to work on the Change of Coordinates applet. So far I have created a 3D graph that has the ability to graphically display a point in 3-space as specified by the user. This point may then be displayed with a rectangular/cartesian, cylindrical, or spherical representation. As of now, the points are input via the console, yet in the finished version, the user will be able to click any location in 3-space to select a point. The user will also be able to navigate the space with a mouse or keyboard.</div>Tcheeseman1https://mathimages.swarthmore.edu/index.php?title=D09&diff=9534D092009-08-04T19:48:10Z<p>Tcheeseman1: /* Working On */</p>
<hr />
<div><center>'' '''Welcome to the Drexel Summer 09 Entry to [[Image:TmipClear.png|275px]]''' ''!</center><br />
<br />
'''IMPORTANT NOTE: Please put up contact information on Drexel-Swat Partnering page: [[Drexel-Swat_Partnering]]'''<br />
<br />
[[Getting Started]] --- [[A Brief Tour of What's Been Done So Far]]<br />
<br />
----<br />
<br />
'''Things to do:''' <br />
* browse around, leaving comments on the Math Images discussion page and the Swarthmore student's discussion page, looking around for interesting possibilities for interaction on the latter<br />
* look through the Helper Pages in the left navbar and the [http://wikis.swarthmore.edu/miwiki/index.php/Hard_Math Hard Math] page to see if you can find anything you'd like to work on--if there's anything you've struggled with that isn't there, add it!<br />
<br />
----<br />
<br />
'''[[Math for Computer Graphics and Computer Vision]]'''<br />
<br />
'''Resources:'''<br />
:* [http://www.kirupa.com/developer/flash/index.htm Flash/ActionScript Tutorials]<br />
:* [http://hgbook.red-bean.com/read/ Mercurial Book] (Online)<br />
:* [http://java.sun.com/developer/onlineTraining/java3d/ Java 3D Tutorials]<br />
:* [http://javaview.de/ JavaView]<br />
:* [http://javaview.de/vgp/tutor/index.html JavaView Applet Examples]<br />
:* [http://javaview.de/doc/reference/index.html JavaView API Documentation (JavaDoc)]<br />
<br />
__TOC__<br />
<br />
''' ''Check out the [[Drexel-Swat Partnering]] page to see who's paired up with whom and keep track of what they're working on...'' '''<br />
<br />
==Possible Applets/Animations for Drexel Students To Do==<br />
:* [[Parametric Equations]] Page- demonstrate the parametric construction of a circle. Perhaps the user can increase the value of the parameter in the parametric equations of a circle, and see the resulting circle be drawn in real time. The same type of applet would be cool for the butterfly curve, although I already have an animation for this curve (from wikipedia) and making another one would be more difficult than a circle.<br />
<br />
:*[[Henon Attractor]] Page - an applet allowing the users to pick values of ''a'' and ''b'' to create different Henon Attractor (Mike is now done this applet)<br />
<br />
:*[[Blue Fern]] Page - my ideas for this are pretty vague. Perhaps some sort of an animation or applet showing the different types of matrix transformations and translations involved in making the fern. Maybe showing what each matrix does to an object (rotate it, shrink it...)<br />
<br />
:*[[Brunnian Links]] - an interactive 3D model of the Borromean rings (and possibly high ring levels also) similar to this [http://video.google.com/videoplay?docid=-5851348533617330039&ei=N75DSqSJFZy8rQKG9pyNBg&q=borromean+rings&hl=en&client=firefox-a YouTube]. I was thinking about an applet that would allow users to rotate the model with their mouse to see all perspectives of the ring, as well as have an animation showing that after one ring is removed, the ring unravels.<br />
<br />
:*[[Torus]] page- The section n-torus could use an illustration of how an <math>n</math>-dimensional object can exist in <math>n+1</math> dimensions. For example a line, which is a 1D object can exist in 2D when it is bent into a circle. Similarly, in 3D, a cube wraps to form a 3-torus. Illustrations could really help explain this section. I've tried searching for images online but could not get one that specifically shows this.<br />
<br />
==[[User:Tcheeseman1|Tim]]==<br />
<br />
Click on my name above for things that I've finished<br />
<br />
===Working On===<br />
<br />
:* Applet for [[Inversion|Point and Shape Inversion]] in 3D to demonstrate creating [[Dual Polyhedron|Dual Polyhedrons]]): [http://www.cs.drexel.edu/~twc24/mathimages/inversion/ShapeInversion3D.html Early Preview] - Re-working the inversion algorithm to be more general (i.e. same function call for ALL polyhedra, irregular or not), need to fix trig on dodecahedron<br />
<br />
==[[User:Egoldberg1|Emily G.]]==<br />
===Projects In Progress:===<br />
:*Line Drawing (manipulating alpha in parametric equation of a line)<br />
::*Status- In progress<br />
:*[[Tessellations]] Image Gallery<br />
::*Status- Mostly done<br />
<br />
===Projects for the Future:===<br />
:*[[Cantor_Set]] zooming flash loop<br />
::*Status- On hold. Does anyone have any experience with this kind of thing? Mine keep turning out to be more confusing than helpful to the viewer.<br />
:*Rhodonea ([[Cardioid]], Rose Petals, Limacons, etc.)- interactive graphing<br />
::*Status- Investigating the possibility of using a webMathematica applet to accomplish this<br />
:*[[Torus]] & [[Volume_of_Revolution]]- interactive graphing<br />
::*Status- Investigating the possibility of using a webMathematica applet to accomplish this<br />
<br />
==[[User:Slombardi1|Steve]]==<br />
Click on my name to see my project list<br />
<br />
==[[User:Asobti1|Ayush]]==<br />
<br />
I'm a Computer Science sophomore at Drexel University. This Summer term (Summer 09) is my first term working on the Math Images project.<br />
<br />
===The Plan:===<br />
:Working with Josh and Alan to add interactivity in the pages previously created by Alan.<br />
:I plan to concentrate on Flash animation while Josh explores the Java.<br />
<br />
<br />
===Work Progress:===<br />
:'''Week 1:'''<br />
::Surfed around the MathImages website. Familiarized myself with the many different pages and projects.<br />
::Spoke with Alan and Josh and made a tentative plan of what is to be achieved in the duration of the research project.<br />
::Installed and set up Adobe Flash CS4. Started reading tutorials and watching videos to learn using Flash.<br />
::Learned basic wiki tags and wiki usage and embedding flash .swf files into wiki<br />
:::<flash>file=Test_anim.swf|width=280|height=200|</flash><br />
::Created a simple flash animation to show matrix multiplication of two 2x2 matrices. May be incorporated in the Matrix helper page.<br />
::<flash>file=Matrix_multiplication_new.swf|width=500|height=300|</flash><br />
:'''Matrix Calculator:'''<br />
::Currently working on a Matrix calculator. <br />
::After making the barebones framework in week 3, I have been adding features in it this week. It now has the option to add and recall from memory, a Clear option, the calculator returns an error if the user does not select any operator, it does not accept non-numeric values etc.<br />
::You can see the beta ver. here : [http://megaswf.com/view/4af984ebc5d7de995d57aeb531251c28.html]<br />
<br />
:: Some features I am currently working on:<br />
:::*Allowing user to select dimensions of Matrix<br />
:::*Calculation of Invert, Adjoint and Determinant of Matrix<br />
:::*Show tutorials for all operations<br />
<br />
==[[User:Jdicristo1|Josh]]==<br />
<br />
I just completed my freshman year at Drexel, going for a BS in Computer Science<br />
<br />
===Projects:===<br />
:Working with Ayush and Alan to add interactivity in the pages previously created by Alan.<br />
:Working mainly with Java<br />
<br />
===Progress After Week 1===<br />
Because I am really working on this project part-time I did not make any major strides this week but I did get a few things accomplished<br />
: I learned the basics of writing Java Applets<br />
: I'm about 1/3 of the way done a program that segments a rectangle into thirds and then illustrates the Golden Spiral<br />
<br />
==[[User:Mhershey1|Mhershey1]]==<br />
test:<br />
<java_applet code="Bluewashrecursive.class" width="500" height="400"/><br />
What I have so far: http://www.pages.drexel.edu/~smh86/index.html<br />
:*[[Blue Wash]], applet changing ''k'' (in '''Inclined Recursive Method''') & animation drawing the basic no ''k'' method (in '''Basic Recursive Method''') <br />
:*[[Blue Fern]], [[Henon Attractor]], redo the animations with small points<br />
:*[[Hyperbolic Tilings]], applet where users input Schläfli symbol to create a tiling<br />
:**This would take too long for me to do. Maybe someone else can do this one, or we could just use the already made applet?<br />
:*[[Newton's Basin]], redo the animation (maybe users input the equations)<br />
:*[[Logarithms]], interactive quiz with exponential and logarithmic equations<br />
:*[[Harter-Heighway Dragon]], animating the curve at each iteration stage<br />
<br />
==[[User:Mhinkle1|Matt]]==<br />
If you see the green box below, you have Java installed. All Java 3D applets were tested using version 1.6.0_14. If it still does not work, please let me know!<br />
<java_applet code="JavaVersionDisplayApplet.class" width="400" height="50" archive="http://www.pages.drexel.edu/~mjh96/java/JavaTest/JavaVersionTestApp.jar" /><br />
:[http://www.javatester.org/index.htm Click here] to learn more about the Java Tester Applet.<br />
<br />
===Projects===<br />
:[[User:Mhinkle1|Click here]] for a full listing of my work.<br />
<br />
===Week 1 Progress===<br />
:After getting comfortable with writing Java applets, I began to read the Java 3D tutorial provided by Sun. After getting down some of the basics, I began to work on the Change of Coordinates applet. So far I have created a 3D graph that has the ability to graphically display a point in 3-space as specified by the user. This point may then be displayed with a rectangular/cartesian, cylindrical, or spherical representation. As of now, the points are input via the console, yet in the finished version, the user will be able to click any location in 3-space to select a point. The user will also be able to navigate the space with a mouse or keyboard.</div>Tcheeseman1https://mathimages.swarthmore.edu/index.php?title=D09&diff=8959D092009-07-23T20:05:46Z<p>Tcheeseman1: /* Working On */</p>
<hr />
<div><center>'' '''Welcome to the Drexel Summer 09 Entry to [[Image:TmipClear.png|275px]]''' ''!</center><br />
<br />
'''IMPORTANT NOTE: Please put up contact information on Drexel-Swat Partnering page: [[Drexel-Swat_Partnering]]'''<br />
<br />
[[Getting Started]] --- [[A Brief Tour of What's Been Done So Far]]<br />
<br />
----<br />
<br />
'''Things to do:''' <br />
* browse around, leaving comments on the Math Images discussion page and the Swarthmore student's discussion page, looking around for interesting possibilities for interaction on the latter<br />
* look through the Helper Pages in the left navbar and the [http://wikis.swarthmore.edu/miwiki/index.php/Hard_Math Hard Math] page to see if you can find anything you'd like to work on--if there's anything you've struggled with that isn't there, add it!<br />
<br />
----<br />
<br />
'''[[Math for Computer Graphics and Computer Vision]]'''<br />
<br />
'''Resources:'''<br />
:* [http://www.kirupa.com/developer/flash/index.htm Flash/ActionScript Tutorials]<br />
:* [http://hgbook.red-bean.com/read/ Mercurial Book] (Online)<br />
:* [http://java.sun.com/developer/onlineTraining/java3d/ Java 3D Tutorials]<br />
:* [http://javaview.de/ JavaView]<br />
:* [http://javaview.de/vgp/tutor/index.html JavaView Applet Examples]<br />
:* [http://javaview.de/doc/reference/index.html JavaView API Documentation (JavaDoc)]<br />
<br />
__TOC__<br />
<br />
''' ''Check out the [[Drexel-Swat Partnering]] page to see who's paired up with whom and keep track of what they're working on...'' '''<br />
<br />
==Possible Applets/Animations for Drexel Students To Do==<br />
:* [[Parametric Equations]] Page- demonstrate the parametric construction of a circle. Perhaps the user can increase the value of the parameter in the parametric equations of a circle, and see the resulting circle be drawn in real time. The same type of applet would be cool for the butterfly curve, although I already have an animation for this curve (from wikipedia) and making another one would be more difficult than a circle.<br />
<br />
:*[[Henon Attractor]] Page - an applet allowing the users to pick values of ''a'' and ''b'' to create different Henon Attractor (Mike is now done this applet)<br />
<br />
:*[[Blue Fern]] Page - my ideas for this are pretty vague. Perhaps some sort of an animation or applet showing the different types of matrix transformations and translations involved in making the fern. Maybe showing what each matrix does to an object (rotate it, shrink it...)<br />
<br />
:*[[Brunnian Links]] - an interactive 3D model of the Borromean rings (and possibly high ring levels also) similar to this [http://video.google.com/videoplay?docid=-5851348533617330039&ei=N75DSqSJFZy8rQKG9pyNBg&q=borromean+rings&hl=en&client=firefox-a YouTube]. I was thinking about an applet that would allow users to rotate the model with their mouse to see all perspectives of the ring, as well as have an animation showing that after one ring is removed, the ring unravels.<br />
<br />
:*[[Torus]] page- The section n-torus could use an illustration of how an <math>n</math>-dimensional object can exist in <math>n+1</math> dimensions. For example a line, which is a 1D object can exist in 2D when it is bent into a circle. Similarly, in 3D, a cube wraps to form a 3-torus. Illustrations could really help explain this section. I've tried searching for images online but could not get one that specifically shows this.<br />
<br />
==[[User:Tcheeseman1|Tim]]==<br />
<br />
Click on my name above for things that I've finished<br />
<br />
===Working On===<br />
<br />
:* Applet for [[Inversion|Point and Shape Inversion]] in 3D to demonstrate creating [[Dual Polyhedron|Dual Polyhedrons]]): [http://www.cs.drexel.edu/~twc24/mathimages/inversion/ShapeInversion3D.html Early Preview] - Just has Platonic Solids for now, need to add a few irregular polygons.<br />
<br />
==[[User:Egoldberg1|Emily G.]]==<br />
===Projects In Progress:===<br />
:*Line Drawing (manipulating alpha in parametric equation of a line)<br />
::*Status- In progress<br />
:*[[Tessellations]] Image Gallery<br />
::*Status- Mostly done<br />
<br />
===Projects for the Future:===<br />
:*[[Cantor_Set]] zooming flash loop<br />
::*Status- On hold. Does anyone have any experience with this kind of thing? Mine keep turning out to be more confusing than helpful to the viewer.<br />
:*[[Transformations ]] java applet which allows user to change values in transformational matrices and then see the changes that it makes on the image.<br />
::*Status-Not Started<br />
:*Rhodonea ([[Cardioid]], Rose Petals, Limacons, etc.)- interactive graphing<br />
::*Status- Investigating the possibility of using a webMathematica applet to accomplish this<br />
:*[[Torus]] & [[Volume_of_Revolution]]- interactive graphing<br />
::*Status- Investigating the possibility of using a webMathematica applet to accomplish this<br />
<br />
==[[User:Slombardi1|Steve]]==<br />
:Stereographic Projection applet: [http://www.tcnj.edu/~lombar26/StereoProj/StereoProj.html Stereographic Projection]<br />
:Hypotrochoid applet: [http://www.tcnj.edu/~lombar26/Hypotrochoid/Hypotrochoid.html Hypotrochoid]<br />
:Metaballs applet: [http://www.tcnj.edu/~lombar26/ImplicitSurf/ImplicitSurf.html Metaballs]<br />
:Mandelbrot applet: [http://www.tcnj.edu/~lombar26/Mandelbrot/Mandelbrot.html Mandelbrot]<br />
:Koch Snowflake applet: [http://www.tcnj.edu/~lombar26/KochSnowflake/KochSnowflake.html Koch Snowflake]<br />
:Catenary applet: [http://www.tcnj.edu/~lombar26/Catenary/Catenary.html Catenary]<br />
:Julia set applet: [http://www.tcnj.edu/~lombar26/Julia/Julia.html Julia set]<br />
::Hi Steve,<br />
::I've seen this applet, and I've like it--it's just very similar to most Julia Set applets out there at only deal with Julia Sets of functions of the form <math> f(x)=x^2+a+bi</math>. I'd think it would be *really* cool to have an applet where someone could plug in any old rational function and get a Julia Set, though I know that might be too hard. <br />
::As an aside, what computational method did you use (an escape criterion, like my short program on that page, or something else)?<br />
::Thanks, and keep up the great work.<br />
:::~Anna<br />
::: There's a cool applet showing the relationship between Julia and Mendelbrot sets [http://javaview.de/vgp/tutor/fractal/PaFractalImage.html here]. -Tim<br />
:Chryzode applet: [http://www.tcnj.edu/~lombar26/Chryzode/Chryzode.html Chryzode]<br />
:Conic Section applet: [http://www.tcnj.edu/~lombar26/ConicSection/ConicSection.html Conic Section]<br />
:Procedural Images applet: [http://www.tcnj.edu/~lombar26/ProcImages/ProcImages.html Procedural Images]<br />
:Julia applet, version 2: [http://www.tcnj.edu/~lombar26/Julia2/Julia.html Julia set 2.0]<br />
::Thanks for the idea, lemme know if you find any bugs (there's plenty i'm sure) -Steve<br />
:Self Organizing Primitives: [http://www.tcnj.edu/~lombar26/SelfOrganize/SelfOrganize.html Self Organize]<br />
:Image Rectification [http://www.tcnj.edu/~lombar26/ImageRectify/ImageRectify.html Image Rectification]<br />
<br />
Test:<br />
<java_applet code="Mandelbrot.class" width="200" height="200" archive="Mandelbrot.jar" /><br />
<br />
==[[User:Asobti1|Ayush]]==<br />
<br />
I'm a Computer Science sophomore at Drexel University. This Summer term (Summer 09) is my first term working on the Math Images project.<br />
<br />
===The Plan:===<br />
:Working with Josh and Alan to add interactivity in the pages previously created by Alan.<br />
:I plan to concentrate on Flash animation while Josh explores the Java.<br />
<br />
<br />
===Work Progress:===<br />
:'''Week 1:'''<br />
::Surfed around the MathImages website. Familiarized myself with the many different pages and projects.<br />
::Spoke with Alan and Josh and made a tentative plan of what is to be achieved in the duration of the research project.<br />
::Installed and set up Adobe Flash CS4. Started reading tutorials and watching videos to learn using Flash.<br />
::Learned basic wiki tags and wiki usage and embedding flash .swf files into wiki<br />
:::<flash>file=Test_anim.swf|width=280|height=200|</flash><br />
::Created a simple flash animation to show matrix multiplication of two 2x2 matrices. May be incorporated in the Matrix helper page.<br />
::<flash>file=Matrix_multiplication_new.swf|width=500|height=300|</flash><br />
:'''Matrix Calculator:'''<br />
::Currently working on a Matrix calculator. <br />
::After making the barebones framework in week 3, I have been adding features in it this week. It now has the option to add and recall from memory, a Clear option, the calculator returns an error if the user does not select any operator, it does not accept non-numeric values etc.<br />
::You can see the beta ver. here : [http://megaswf.com/view/4af984ebc5d7de995d57aeb531251c28.html]<br />
<br />
:: Some features I am currently working on:<br />
:::*Allowing user to select dimensions of Matrix<br />
:::*Calculation of Invert, Adjoint and Determinant of Matrix<br />
:::*Show tutorials for all operations<br />
<br />
==[[User:Jdicristo1|Josh]]==<br />
<br />
I just completed my freshman year at Drexel, going for a BS in Computer Science<br />
<br />
===Projects:===<br />
:Working with Ayush and Alan to add interactivity in the pages previously created by Alan.<br />
:Working mainly with Java<br />
<br />
===Progress After Week 1===<br />
Because I am really working on this project part-time I did not make any major strides this week but I did get a few things accomplished<br />
: I learned the basics of writing Java Applets<br />
: I'm about 1/3 of the way done a program that segments a rectangle into thirds and then illustrates the Golden Spiral<br />
<br />
==[[User:Mhershey1|Mhershey1]]==<br />
test:<br />
<java_applet code="Bluewashrecursive.class" width="500" height="400"/><br />
What I have so far: http://www.pages.drexel.edu/~smh86/index.html<br />
:*[[Blue Wash]], applet changing ''k'' (in '''Inclined Recursive Method''') & animation drawing the basic no ''k'' method (in '''Basic Recursive Method''') <br />
:*[[Blue Fern]], [[Henon Attractor]], redo the animations with small points<br />
:*[[Hyperbolic Tilings]], applet where users input Schläfli symbol to create a tiling<br />
:**This would take too long for me to do. Maybe someone else can do this one, or we could just use the already made applet?<br />
:*[[Newton's Basin]], redo the animation (maybe users input the equations)<br />
:*[[Logarithms]], interactive quiz with exponential and logarithmic equations<br />
:*[[Harter-Heighway Dragon]], animating the curve at each iteration stage<br />
<br />
==[[User:Mhinkle1|Matt]]==<br />
If you see the green box below, you have Java installed. To view the [http://www.pages.drexel.edu/~mjh96/java/ChangeOfCoords/ChangeOfCoordsApp.html Change of Coordinate Systems Applet], your version number should at least be 1.6.0_14. If it still does not work, please let me know!<br />
<java_applet code="JavaVersionDisplayApplet.class" width="400" height="50" archive="http://www.pages.drexel.edu/~mjh96/java/JavaTest/JavaVersionTestApp.jar" /><br />
:[http://www.javatester.org/index.htm Click here] to learn more about the Java Tester Applet.<br />
===Projects:===<br />
:*[[Change of Coordinate Systems]]<br />
::*Status: Finished<br />
::*Description: An applet which allows for a visual representation of user defined points in 3-space<br />
::*Link: [http://www.pages.drexel.edu/~mjh96/java/ChangeOfCoords/ChangeOfCoordsApp.html Change of Coordinate Systems Applet]<br />
::*Notes: Finished applet, if you find any bugs, please let me know! email: mjh96@drexel.edu<br />
:*[[Gradients and Directional Derivatives]]<br />
::*Status: Not Started<br />
::*Description:An applet or animation that displays the gradient at different points on a surface<br />
:*[[Vector]]<br />
::*Status: Finished<br />
::*Description: An applet allowing for an interactive representation of 2D vector algebra, mainly consisting of: addition and subtraction. Scalar multiplication was not included as it would be a detriment to the applet's simple point and click interface. However, if anyone feels this feature should be added, I can certainly do so.<br />
::*Link: [http://www.pages.drexel.edu/~mjh96/java/Vector2D/VectorAlgebra2D.html 2D Vector Applet]<br />
::*Notes: If you find any bugs, please let me know! email: mjh96@drexel.edu. Also, I am aware of the annoying tendency of vectors clipping with the bounds of the graph when the addition procedure is carried out.<br />
:*[[Probability Distributions]]<br />
::*Status: Finished<br />
::*Description: An applet allowing the user to simulate rolling a six-sided dice, and graphically keep track of the outcome distribution.<br />
::*Link: [http://www.pages.drexel.edu/~mjh96/java/Prob/DiceProbApp.html Dice Probability Applet]<br />
::*Notes: Let me know if you have any suggestions. email: mjh96@drexel.edu<br />
:*[[Vector | Vector Cross Product]]<br />
::*Status: Finished<br />
::*Description: An applet allowing the user to enter the components of 2 vectors and display a graphical representation of a vector cross product. This consists of representing the two vectors and the cross product in which they create, which is normalized.<br />
::*Link: [http://www.pages.drexel.edu/~mjh96/java/CrossProduct/CrossProductApp.html Vector Cross Product Applet]<br />
::*Notes: Please let me know if you have any suggestions or find any bugs. email: mjh96@drexel.edu<br />
:*[[Arithmetic Sequence]]<br />
::*Status: Finished<br />
::*Description: An applet that generates a random arithmetic sequence and allows the user to fill in missing spots.<br />
::*Link: [http://www.pages.drexel.edu/~mjh96/java/ASeq/ASeqApp.html Arithmetic Sequence Applet]<br />
::*Notes: Please let me know if you have any suggestions or find any bugs. email: mjh96@drexel.edu<br />
<br />
:''Note: If a project is listed as "Not Started," feel free to pick it up if you wish''<br />
<br />
===Week 1 Progress===<br />
:After getting comfortable with writing Java applets, I began to read the Java 3D tutorial provided by Sun. After getting down some of the basics, I began to work on the Change of Coordinates applet. So far I have created a 3D graph that has the ability to graphically display a point in 3-space as specified by the user. This point may then be displayed with a rectangular/cartesian, cylindrical, or spherical representation. As of now, the points are input via the console, yet in the finished version, the user will be able to click any location in 3-space to select a point. The user will also be able to navigate the space with a mouse or keyboard.</div>Tcheeseman1https://mathimages.swarthmore.edu/index.php?title=D09&diff=8853D092009-07-22T20:10:07Z<p>Tcheeseman1: /* Working On */</p>
<hr />
<div><center>'' '''Welcome to the Drexel Summer 09 Entry to [[Image:TmipClear.png|275px]]''' ''!</center><br />
<br />
'''IMPORTANT NOTE: Please put up contact information on Drexel-Swat Partnering page: [[Drexel-Swat_Partnering]]'''<br />
<br />
[[Getting Started]] --- [[A Brief Tour of What's Been Done So Far]]<br />
<br />
----<br />
<br />
'''Things to do:''' <br />
* browse around, leaving comments on the Math Images discussion page and the Swarthmore student's discussion page, looking around for interesting possibilities for interaction on the latter<br />
* look through the Helper Pages in the left navbar and the [http://wikis.swarthmore.edu/miwiki/index.php/Hard_Math Hard Math] page to see if you can find anything you'd like to work on--if there's anything you've struggled with that isn't there, add it!<br />
<br />
----<br />
<br />
'''[[Math for Computer Graphics and Computer Vision]]'''<br />
<br />
'''Resources:'''<br />
:* [http://www.kirupa.com/developer/flash/index.htm Flash/ActionScript Tutorials]<br />
:* [http://hgbook.red-bean.com/read/ Mercurial Book] (Online)<br />
:* [http://java.sun.com/developer/onlineTraining/java3d/ Java 3D Tutorials]<br />
:* [http://javaview.de/ JavaView]<br />
:* [http://javaview.de/vgp/tutor/index.html JavaView Applet Examples]<br />
:* [http://javaview.de/doc/reference/index.html JavaView API Documentation (JavaDoc)]<br />
<br />
__TOC__<br />
<br />
''' ''Check out the [[Drexel-Swat Partnering]] page to see who's paired up with whom and keep track of what they're working on...'' '''<br />
<br />
==Possible Applets/Animations for Drexel Students To Do==<br />
:* [[Parametric Equations]] Page- demonstrate the parametric construction of a circle. Perhaps the user can increase the value of the parameter in the parametric equations of a circle, and see the resulting circle be drawn in real time. The same type of applet would be cool for the butterfly curve, although I already have an animation for this curve (from wikipedia) and making another one would be more difficult than a circle.<br />
<br />
:*[[Henon Attractor]] Page - an applet allowing the users to pick values of ''a'' and ''b'' to create different Henon Attractor (Mike is now done this applet)<br />
<br />
:*[[Blue Fern]] Page - my ideas for this are pretty vague. Perhaps some sort of an animation or applet showing the different types of matrix transformations and translations involved in making the fern. Maybe showing what each matrix does to an object (rotate it, shrink it...)<br />
<br />
:*[[Brunnian Links]] - an interactive 3D model of the Borromean rings (and possibly high ring levels also) similar to this [http://video.google.com/videoplay?docid=-5851348533617330039&ei=N75DSqSJFZy8rQKG9pyNBg&q=borromean+rings&hl=en&client=firefox-a YouTube]. I was thinking about an applet that would allow users to rotate the model with their mouse to see all perspectives of the ring, as well as have an animation showing that after one ring is removed, the ring unravels.<br />
<br />
:*[[Torus]] page- The section n-torus could use an illustration of how an <math>n</math>-dimensional object can exist in <math>n+1</math> dimensions. For example a line, which is a 1D object can exist in 2D when it is bent into a circle. Similarly, in 3D, a cube wraps to form a 3-torus. Illustrations could really help explain this section. I've tried searching for images online but could not get one that specifically shows this.<br />
<br />
==[[User:Tcheeseman1|Tim]]==<br />
<br />
Click on my name above for things that I've finished<br />
<br />
===Working On===<br />
<br />
:* Applet for [[Inversion|Point and Shape Inversion]] in 3D to demonstrate creating [[Dual Polyhedron|Dual Polyhedrons]]): [http://www.cs.drexel.edu/~twc24/mathimages/inversion/ShapeInversion3D.html Early Preview] - Just shows inverted vertices for now, still need to add faces. Need to add a few irregular polygons.<br />
<br />
==[[User:Egoldberg1|Emily G.]]==<br />
===Projects In Progress:===<br />
:*Line Drawing (manipulating alpha in parametric equation of a line)<br />
::*Status- In progress<br />
:*[[Tessellations]] Image Gallery<br />
::*Status- Mostly done<br />
<br />
===Projects for the Future:===<br />
:*[[Cantor_Set]] zooming flash loop<br />
::*Status- On hold. Does anyone have any experience with this kind of thing? Mine keep turning out to be more confusing than helpful to the viewer.<br />
:*[[Transformations ]] java applet which allows user to change values in transformational matrices and then see the changes that it makes on the image.<br />
::*Status-Not Started<br />
:*Rhodonea ([[Cardioid]], Rose Petals, Limacons, etc.)- interactive graphing<br />
::*Status- Investigating the possibility of using a webMathematica applet to accomplish this<br />
:*[[Torus]] & [[Volume_of_Revolution]]- interactive graphing<br />
::*Status- Investigating the possibility of using a webMathematica applet to accomplish this<br />
<br />
==[[User:Slombardi1|Steve]]==<br />
:Stereographic Projection applet: [http://www.tcnj.edu/~lombar26/StereoProj/StereoProj.html Stereographic Projection]<br />
:Hypotrochoid applet: [http://www.tcnj.edu/~lombar26/Hypotrochoid/Hypotrochoid.html Hypotrochoid]<br />
:Metaballs applet: [http://www.tcnj.edu/~lombar26/ImplicitSurf/ImplicitSurf.html Metaballs]<br />
:Mandelbrot applet: [http://www.tcnj.edu/~lombar26/Mandelbrot/Mandelbrot.html Mandelbrot]<br />
:Koch Snowflake applet: [http://www.tcnj.edu/~lombar26/KochSnowflake/KochSnowflake.html Koch Snowflake]<br />
:Catenary applet: [http://www.tcnj.edu/~lombar26/Catenary/Catenary.html Catenary]<br />
:Julia set applet: [http://www.tcnj.edu/~lombar26/Julia/Julia.html Julia set]<br />
::Hi Steve,<br />
::I've seen this applet, and I've like it--it's just very similar to most Julia Set applets out there at only deal with Julia Sets of functions of the form <math> f(x)=x^2+a+bi</math>. I'd think it would be *really* cool to have an applet where someone could plug in any old rational function and get a Julia Set, though I know that might be too hard. <br />
::As an aside, what computational method did you use (an escape criterion, like my short program on that page, or something else)?<br />
::Thanks, and keep up the great work.<br />
:::~Anna<br />
::: There's a cool applet showing the relationship between Julia and Mendelbrot sets [http://javaview.de/vgp/tutor/fractal/PaFractalImage.html here]. -Tim<br />
:Chryzode applet: [http://www.tcnj.edu/~lombar26/Chryzode/Chryzode.html Chryzode]<br />
:Conic Section applet: [http://www.tcnj.edu/~lombar26/ConicSection/ConicSection.html Conic Section]<br />
:Procedural Images applet: [http://www.tcnj.edu/~lombar26/ProcImages/ProcImages.html Procedural Images]<br />
:Julia applet, version 2: [http://www.tcnj.edu/~lombar26/Julia2/Julia.html Julia set 2.0]<br />
::Thanks for the idea, lemme know if you find any bugs (there's plenty i'm sure) -Steve<br />
:Self Organizing Primitives: [http://www.tcnj.edu/~lombar26/SelfOrganize/SelfOrganize.html Self Organize]<br />
:Image Rectification [http://www.tcnj.edu/~lombar26/ImageRectify/ImageRectify.html Image Rectification]<br />
<br />
Test:<br />
<java_applet code="Mandelbrot.class" width="200" height="200" archive="Mandelbrot.jar" /><br />
<br />
==[[User:Asobti1|Ayush]]==<br />
<br />
I'm a Computer Science sophomore at Drexel University. This Summer term (Summer 09) is my first term working on the Math Images project.<br />
<br />
===The Plan:===<br />
:Working with Josh and Alan to add interactivity in the pages previously created by Alan.<br />
:I plan to concentrate on Flash animation while Josh explores the Java.<br />
<br />
<br />
===Work Progress:===<br />
:'''Week 1:'''<br />
::Surfed around the MathImages website. Familiarized myself with the many different pages and projects.<br />
::Spoke with Alan and Josh and made a tentative plan of what is to be achieved in the duration of the research project.<br />
::Installed and set up Adobe Flash CS4. Started reading tutorials and watching videos to learn using Flash.<br />
::Learned basic wiki tags and wiki usage and embedding flash .swf files into wiki<br />
:::<flash>file=Test_anim.swf|width=280|height=200|</flash><br />
::Created a simple flash animation to show matrix multiplication of two 2x2 matrices. May be incorporated in the Matrix helper page.<br />
::<flash>file=Matrix_multiplication_new.swf|width=500|height=300|</flash><br />
:'''Matrix Calculator:'''<br />
::Currently working on a Matrix calculator. <br />
::After making the barebones framework in week 3, I have been adding features in it this week. It now has the option to add and recall from memory, a Clear option, the calculator returns an error if the user does not select any operator, it does not accept non-numeric values etc.<br />
::You can see the beta ver. here : [http://megaswf.com/view/4af984ebc5d7de995d57aeb531251c28.html]<br />
<br />
:: Some features I am currently working on:<br />
:::*Allowing user to select dimensions of Matrix<br />
:::*Calculation of Invert, Adjoint and Determinant of Matrix<br />
:::*Show tutorials for all operations<br />
<br />
==[[User:Jdicristo1|Josh]]==<br />
<br />
I just completed my freshman year at Drexel, going for a BS in Computer Science<br />
<br />
===Projects:===<br />
:Working with Ayush and Alan to add interactivity in the pages previously created by Alan.<br />
:Working mainly with Java<br />
<br />
===Progress After Week 1===<br />
Because I am really working on this project part-time I did not make any major strides this week but I did get a few things accomplished<br />
: I learned the basics of writing Java Applets<br />
: I'm about 1/3 of the way done a program that segments a rectangle into thirds and then illustrates the Golden Spiral<br />
<br />
==[[User:Mhershey1|Mhershey1]]==<br />
test:<br />
<java_applet code="Bluewashrecursive.class" width="500" height="400"/><br />
What I have so far: http://www.pages.drexel.edu/~smh86/index.html<br />
:*[[Blue Wash]], applet changing ''k'' (in '''Inclined Recursive Method''') & animation drawing the basic no ''k'' method (in '''Basic Recursive Method''') <br />
:*[[Blue Fern]], [[Henon Attractor]], redo the animations with small points<br />
:*[[Hyperbolic Tilings]], applet where users input Schläfli symbol to create a tiling<br />
:**This would take too long for me to do. Maybe someone else can do this one, or we could just use the already made applet?<br />
:*[[Newton's Basin]], redo the animation (maybe users input the equations)<br />
:*[[Logarithms]], interactive quiz with exponential and logarithmic equations<br />
:*[[Harter-Heighway Dragon]], animating the curve at each iteration stage<br />
<br />
==[[User:Mhinkle1|Matt]]==<br />
If you see the green box below, you have Java installed. To view the [http://www.pages.drexel.edu/~mjh96/java/ChangeOfCoords/ChangeOfCoordsApp.html Change of Coordinate Systems Applet], your version number should at least be 1.6.0_14. If it still does not work, please let me know!<br />
<java_applet code="JavaVersionDisplayApplet.class" width="400" height="50" archive="http://www.pages.drexel.edu/~mjh96/java/JavaTest/JavaVersionTestApp.jar" /><br />
:[http://www.javatester.org/index.htm Click here] to learn more about the Java Tester Applet.<br />
===Projects:===<br />
:*[[Change of Coordinate Systems]]<br />
::*Status: Finished<br />
::*Description: An applet which allows for a visual representation of user defined points in 3-space<br />
::*Link: [http://www.pages.drexel.edu/~mjh96/java/ChangeOfCoords/ChangeOfCoordsApp.html Change of Coordinate Systems Applet]<br />
::*Notes: Finished applet, if you find any bugs, please let me know! email: mjh96@drexel.edu<br />
:*[[Gradients and Directional Derivatives]]<br />
::*Status: Not Started<br />
::*Description:An applet or animation that displays the gradient at different points on a surface<br />
:*[[Vector]]<br />
::*Status: Finished<br />
::*Description: An applet allowing for an interactive representation of 2D vector algebra, mainly consisting of: addition and subtraction. Scalar multiplication was not included as it would be a detriment to the applet's simple point and click interface. However, if anyone feels this feature should be added, I can certainly do so.<br />
::*Link: [http://www.pages.drexel.edu/~mjh96/java/Vector2D/VectorAlgebra2D.html 2D Vector Applet]<br />
::*Notes: If you find any bugs, please let me know! email: mjh96@drexel.edu. Also, I am aware of the annoying tendency of vectors clipping with the bounds of the graph when the addition procedure is carried out.<br />
:*[[Probability Distributions]]<br />
::*Status: Finished<br />
::*Description: An applet allowing the user to simulate rolling a six-sided dice, and graphically keep track of the outcome distribution.<br />
::*Link: [http://www.pages.drexel.edu/~mjh96/java/Prob/DiceProbApp.html Dice Probability Applet]<br />
::*Notes: Let me know if you have any suggestions. email: mjh96@drexel.edu<br />
:*[[Vector | Vector Cross Product]]<br />
::*Status: Finished<br />
::*Description: An applet allowing the user to enter the components of 2 vectors and display a graphical representation of a vector cross product. This consists of representing the two vectors and the cross product in which they create, which is normalized.<br />
::*Link: [http://www.pages.drexel.edu/~mjh96/java/CrossProduct/CrossProductApp.html Vector Cross Product Applet]<br />
::*Notes: Please let me know if you have any suggestions or find any bugs. email: mjh96@drexel.edu<br />
:*[[Arithmetic Sequence]]<br />
::*Status: Finished<br />
::*Description: An applet that generates a random arithmetic sequence and allows the user to fill in missing spots.<br />
::*Link: [http://www.pages.drexel.edu/~mjh96/java/ASeq/ASeqApp.html Arithmetic Sequence Applet]<br />
::*Notes: Please let me know if you have any suggestions or find any bugs. email: mjh96@drexel.edu<br />
<br />
:''Note: If a project is listed as "Not Started," feel free to pick it up if you wish''<br />
<br />
===Week 1 Progress===<br />
:After getting comfortable with writing Java applets, I began to read the Java 3D tutorial provided by Sun. After getting down some of the basics, I began to work on the Change of Coordinates applet. So far I have created a 3D graph that has the ability to graphically display a point in 3-space as specified by the user. This point may then be displayed with a rectangular/cartesian, cylindrical, or spherical representation. As of now, the points are input via the console, yet in the finished version, the user will be able to click any location in 3-space to select a point. The user will also be able to navigate the space with a mouse or keyboard.</div>Tcheeseman1https://mathimages.swarthmore.edu/index.php?title=D09&diff=8579D092009-07-20T16:39:07Z<p>Tcheeseman1: /* Working On */</p>
<hr />
<div><center>'' '''Welcome to the Drexel Summer 09 Entry to [[Image:TmipClear.png|275px]]''' ''!</center><br />
<br />
'''IMPORTANT NOTE: Please put up contact information on Drexel-Swat Partnering page: [[Drexel-Swat_Partnering]]'''<br />
<br />
[[Getting Started]] --- [[A Brief Tour of What's Been Done So Far]]<br />
<br />
----<br />
<br />
'''Things to do:''' <br />
* browse around, leaving comments on the Math Images discussion page and the Swarthmore student's discussion page, looking around for interesting possibilities for interaction on the latter<br />
* look through the Helper Pages in the left navbar and the [http://wikis.swarthmore.edu/miwiki/index.php/Hard_Math Hard Math] page to see if you can find anything you'd like to work on--if there's anything you've struggled with that isn't there, add it!<br />
<br />
----<br />
<br />
'''[[Math for Computer Graphics and Computer Vision]]'''<br />
<br />
'''Resources:'''<br />
:* [http://www.kirupa.com/developer/flash/index.htm Flash/ActionScript Tutorials]<br />
:* [http://hgbook.red-bean.com/read/ Mercurial Book] (Online)<br />
:* [http://java.sun.com/developer/onlineTraining/java3d/ Java 3D Tutorials]<br />
:* [http://javaview.de/ JavaView]<br />
:* [http://javaview.de/vgp/tutor/index.html JavaView Applet Examples]<br />
:* [http://javaview.de/doc/reference/index.html JavaView API Documentation (JavaDoc)]<br />
<br />
__TOC__<br />
<br />
''' ''Check out the [[Drexel-Swat Partnering]] page to see who's paired up with whom and keep track of what they're working on...'' '''<br />
<br />
==Possible Applets/Animations for Drexel Students To Do==<br />
:* [[Parametric Equations]] Page- demonstrate the parametric construction of a circle. Perhaps the user can increase the value of the parameter in the parametric equations of a circle, and see the resulting circle be drawn in real time. The same type of applet would be cool for the butterfly curve, although I already have an animation for this curve (from wikipedia) and making another one would be more difficult than a circle.<br />
<br />
:*[[Henon Attractor]] Page - an applet allowing the users to pick values of ''a'' and ''b'' to create different Henon Attractor (Mike is now done this applet)<br />
<br />
:*[[Blue Fern]] Page - my ideas for this are pretty vague. Perhaps some sort of an animation or applet showing the different types of matrix transformations and translations involved in making the fern. Maybe showing what each matrix does to an object (rotate it, shrink it...)<br />
<br />
:*[[Brunnian Links]] - an interactive 3D model of the Borromean rings (and possibly high ring levels also) similar to this [http://video.google.com/videoplay?docid=-5851348533617330039&ei=N75DSqSJFZy8rQKG9pyNBg&q=borromean+rings&hl=en&client=firefox-a YouTube]. I was thinking about an applet that would allow users to rotate the model with their mouse to see all perspectives of the ring, as well as have an animation showing that after one ring is removed, the ring unravels.<br />
<br />
:*[[Torus]] page- The section n-torus could use an illustration of how an <math>n</math>-dimensional object can exist in <math>n+1</math> dimensions. For example a line, which is a 1D object can exist in 2D when it is bent into a circle. Similarly, in 3D, a cube wraps to form a 3-torus. Illustrations could really help explain this section. I've tried searching for images online but could not get one that specifically shows this.<br />
<br />
==[[User:Tcheeseman1|Tim]]==<br />
<br />
Click on my name above for things that I've finished<br />
<br />
===Working On===<br />
<br />
:* Applet for [[Inversion|Point and Shape Inversion]] in 3D to demonstrate creating [[Dual Polyhedron|Dual Polyhedrons]]): [http://www.cs.drexel.edu/~twc24/mathimages/inversion/ShapeInversion3D.html Early Preview] - Just shows inverted vertices for now, still need to add faces. Also need to add the other platonic solids (only cube and octahedron at the moment)<br />
<br />
==[[User:Egoldberg1|Emily G.]]==<br />
===Projects In Progress:===<br />
:*Line Drawing (manipulating alpha in parametric equation of a line)<br />
::*Status- In progress<br />
:*[[Tessellations]] Image Gallery<br />
::*Status- Mostly done<br />
<br />
===Projects for the Future:===<br />
:*[[Cantor_Set]] zooming flash loop<br />
::*Status- On hold. Does anyone have any experience with this kind of thing? Mine keep turning out to be more confusing than helpful to the viewer.<br />
:*[[Transformations ]] java applet which allows user to change values in transformational matrices and then see the changes that it makes on the image.<br />
::*Status-Not Started<br />
:*Rhodonea ([[Cardioid]], Rose Petals, Limacons, etc.)- interactive graphing<br />
::*Status- Investigating the possibility of using a webMathematica applet to accomplish this<br />
:*[[Torus]] & [[Volume_of_Revolution]]- interactive graphing<br />
::*Status- Investigating the possibility of using a webMathematica applet to accomplish this<br />
<br />
==[[User:Slombardi1|Steve]]==<br />
:Stereographic Projection applet: [http://www.tcnj.edu/~lombar26/StereoProj/StereoProj.html Stereographic Projection]<br />
:Hypotrochoid applet: [http://www.tcnj.edu/~lombar26/Hypotrochoid/Hypotrochoid.html Hypotrochoid]<br />
:Metaballs applet: [http://www.tcnj.edu/~lombar26/ImplicitSurf/ImplicitSurf.html Metaballs]<br />
:Mandelbrot applet: [http://www.tcnj.edu/~lombar26/Mandelbrot/Mandelbrot.html Mandelbrot]<br />
:Koch Snowflake applet: [http://www.tcnj.edu/~lombar26/KochSnowflake/KochSnowflake.html Koch Snowflake]<br />
:Catenary applet: [http://www.tcnj.edu/~lombar26/Catenary/Catenary.html Catenary]<br />
:Julia set applet: [http://www.tcnj.edu/~lombar26/Julia/Julia.html Julia set]<br />
::Hi Steve,<br />
::I've seen this applet, and I've like it--it's just very similar to most Julia Set applets out there at only deal with Julia Sets of functions of the form <math> f(x)=x^2+a+bi</math>. I'd think it would be *really* cool to have an applet where someone could plug in any old rational function and get a Julia Set, though I know that might be too hard. <br />
::As an aside, what computational method did you use (an escape criterion, like my short program on that page, or something else)?<br />
::Thanks, and keep up the great work.<br />
:::~Anna<br />
::: There's a cool applet showing the relationship between Julia and Mendelbrot sets [http://javaview.de/vgp/tutor/fractal/PaFractalImage.html here]. -Tim<br />
:Chryzode applet: [http://www.tcnj.edu/~lombar26/Chryzode/Chryzode.html Chryzode]<br />
:Conic Section applet: [http://www.tcnj.edu/~lombar26/ConicSection/ConicSection.html Conic Section]<br />
:Procedural Images applet: [http://www.tcnj.edu/~lombar26/ProcImages/ProcImages.html Procedural Images]<br />
<br />
Test:<br />
<java_applet code="Mandelbrot.class" width="200" height="200" archive="Mandelbrot.jar" /><br />
<br />
==[[User:Asobti1|Ayush]]==<br />
<br />
I'm a Computer Science sophomore at Drexel University. This Summer term (Summer 09) is my first term working on the Math Images project.<br />
<br />
===The Plan:===<br />
:Working with Josh and Alan to add interactivity in the pages previously created by Alan.<br />
:I plan to concentrate on Flash animation while Josh explores the Java.<br />
<br />
<br />
===Work Progress:===<br />
:'''Week 1:'''<br />
::Surfed around the MathImages website. Familiarized myself with the many different pages and projects.<br />
::Spoke with Alan and Josh and made a tentative plan of what is to be achieved in the duration of the research project.<br />
::Installed and set up Adobe Flash CS4. Started reading tutorials and watching videos to learn using Flash.<br />
::Learned basic wiki tags and wiki usage and embedding flash .swf files into wiki<br />
:::<flash>file=Test_anim.swf|width=280|height=200|</flash><br />
::Created a simple flash animation to show matrix multiplication of two 2x2 matrices. May be incorporated in the Matrix helper page.<br />
::<flash>file=Matrix_multiplication_new.swf|width=500|height=300|</flash><br />
:'''Matrix Calculator:'''<br />
::Currently working on a Matrix calculator. <br />
::After making the barebones framework in week 3, I have been adding features in it this week. It now has the option to add and recall from memory, a Clear option, the calculator returns an error if the user does not select any operator, it does not accept non-numeric values etc.<br />
::You can see the beta ver. here : [http://megaswf.com/view/4af984ebc5d7de995d57aeb531251c28.html]<br />
<br />
:: Some features I am currently working on:<br />
:::*Allowing user to select dimensions of Matrix<br />
:::*Calculation of Invert, Adjoint and Determinant of Matrix<br />
:::*Show tutorials for all operations<br />
<br />
==[[User:Jdicristo1|Josh]]==<br />
<br />
I just completed my freshman year at Drexel, going for a BS in Computer Science<br />
<br />
===Projects:===<br />
:Working with Ayush and Alan to add interactivity in the pages previously created by Alan.<br />
:Working mainly with Java<br />
<br />
===Progress After Week 1===<br />
Because I am really working on this project part-time I did not make any major strides this week but I did get a few things accomplished<br />
: I learned the basics of writing Java Applets<br />
: I'm about 1/3 of the way done a program that segments a rectangle into thirds and then illustrates the Golden Spiral<br />
<br />
==[[User:Mhershey1|Mhershey1]]==<br />
test:<br />
<java_applet code="Bluewashrecursive.class" width="500" height="400"/><br />
What I have so far: http://www.pages.drexel.edu/~smh86/index.html<br />
:*[[Blue Wash]], applet changing ''k'' (in '''Inclined Recursive Method''') & animation drawing the basic no ''k'' method (in '''Basic Recursive Method''') <br />
:*[[Blue Fern]], [[Henon Attractor]], redo the animations with small points<br />
:*[[Hyperbolic Tilings]], applet where users input Schläfli symbol to create a tiling<br />
:**This would take too long for me to do. Maybe someone else can do this one, or we could just use the already made applet?<br />
:*[[Newton's Basin]], redo the animation (maybe users input the equations)<br />
:*[[Logarithms]], interactive quiz with exponential and logarithmic equations<br />
:*[[Harter-Heighway Dragon]], animating the curve at each iteration stage<br />
<br />
==[[User:Mhinkle1|Matt]]==<br />
If you see the green box below, you have Java installed. To view the [http://www.pages.drexel.edu/~mjh96/java/ChangeOfCoords/ChangeOfCoordsApp.html Change of Coordinate Systems Applet], your version number should at least be 1.6.0_14. If it still does not work, please let me know!<br />
<java_applet code="JavaVersionDisplayApplet.class" width="400" height="50" archive="http://www.pages.drexel.edu/~mjh96/java/JavaTest/JavaVersionTestApp.jar" /><br />
:[http://www.javatester.org/index.htm Click here] to learn more about the Java Tester Applet.<br />
===Projects:===<br />
:*[[Change of Coordinate Systems]]<br />
::*Status: Finished<br />
::*Description: An applet which allows for a visual representation of user defined points in 3-space<br />
::*Link: [http://www.pages.drexel.edu/~mjh96/java/ChangeOfCoords/ChangeOfCoordsApp.html Change of Coordinate Systems Applet]<br />
::*Notes: Finished applet, if you find any bugs, please let me know! email: mjh96@drexel.edu<br />
:*[[Gradients and Directional Derivatives]]<br />
::*Status: Not Started<br />
::*Description:An applet or animation that displays the gradient at different points on a surface<br />
:*[[Vector]]<br />
::*Status: Finished<br />
::*Description: An applet allowing for an interactive representation of 2D vector algebra, mainly consisting of: addition and subtraction. Scalar multiplication was not included as it would be a detriment to the applet's simple point and click interface. However, if anyone feels this feature should be added, I can certainly do so.<br />
::*Link: [http://www.pages.drexel.edu/~mjh96/java/Vector2D/VectorAlgebra2D.html 2D Vector Applet]<br />
::*Notes: If you find any bugs, please let me know! email: mjh96@drexel.edu. Also, I am aware of the annoying tendency of vectors clipping with the bounds of the graph when the addition procedure is carried out.<br />
:*[[Probability Distributions]]<br />
::*Status: Finished<br />
::*Description: An applet allowing the user to simulate rolling a six-sided dice, and graphically keep track of the outcome distribution.<br />
::*Link: [http://www.pages.drexel.edu/~mjh96/java/Prob/DiceProbApp.html Dice Probability Applet]<br />
::*Notes: Let me know if you have any suggestions. email: mjh96@drexel.edu<br />
:*[[Vector | Vector Cross Product]]<br />
::*Status: In Progress<br />
::*Description: An applet allowing the user to enter the components of 2 vectors and display a graphical representation of a vector cross product<br />
:*[[Arithmetic Sequence]]<br />
::*Status: Finalizing<br />
::*Description: An applet that generates a random arithmetic sequence and allows the user to fill in missing spots. A geometric version is likely to follow.<br />
<br />
:''Note: If a project is listed as "Not Started," feel free to pick it up if you wish''<br />
<br />
===Week 1 Progress===<br />
:After getting comfortable with writing Java applets, I began to read the Java 3D tutorial provided by Sun. After getting down some of the basics, I began to work on the Change of Coordinates applet. So far I have created a 3D graph that has the ability to graphically display a point in 3-space as specified by the user. This point may then be displayed with a rectangular/cartesian, cylindrical, or spherical representation. As of now, the points are input via the console, yet in the finished version, the user will be able to click any location in 3-space to select a point. The user will also be able to navigate the space with a mouse or keyboard.<br />
<br />
<java_applet code="VectorAlgebra2D.class" width="600" height="350" archive="VectorAlgebra2DApp.jar" /><br />
<java_applet code="DiceProbabilityApp.class" width="800" height ="430" archive="DiceProbApp.jar" /></div>Tcheeseman1https://mathimages.swarthmore.edu/index.php?title=D09&diff=8542D092009-07-18T01:43:45Z<p>Tcheeseman1: /* Steve */</p>
<hr />
<div><center>'' '''Welcome to the Drexel Summer 09 Entry to [[Image:TmipClear.png|275px]]''' ''!</center><br />
<br />
'''IMPORTANT NOTE: Please put up contact information on Drexel-Swat Partnering page: [[Drexel-Swat_Partnering]]'''<br />
<br />
[[Getting Started]] --- [[A Brief Tour of What's Been Done So Far]]<br />
<br />
----<br />
<br />
'''Things to do:''' <br />
* browse around, leaving comments on the Math Images discussion page and the Swarthmore student's discussion page, looking around for interesting possibilities for interaction on the latter<br />
* look through the Helper Pages in the left navbar and the [http://wikis.swarthmore.edu/miwiki/index.php/Hard_Math Hard Math] page to see if you can find anything you'd like to work on--if there's anything you've struggled with that isn't there, add it!<br />
<br />
----<br />
<br />
'''[[Math for Computer Graphics and Computer Vision]]'''<br />
<br />
'''Resources:'''<br />
:* [http://www.kirupa.com/developer/flash/index.htm Flash/ActionScript Tutorials]<br />
:* [http://hgbook.red-bean.com/read/ Mercurial Book] (Online)<br />
:* [http://java.sun.com/developer/onlineTraining/java3d/ Java 3D Tutorials]<br />
:* [http://javaview.de/ JavaView]<br />
:* [http://javaview.de/vgp/tutor/index.html JavaView Applet Examples]<br />
:* [http://javaview.de/doc/reference/index.html JavaView API Documentation (JavaDoc)]<br />
<br />
__TOC__<br />
<br />
''' ''Check out the [[Drexel-Swat Partnering]] page to see who's paired up with whom and keep track of what they're working on...'' '''<br />
<br />
==Possible Applets/Animations for Drexel Students To Do==<br />
:* [[Parametric Equations]] Page- demonstrate the parametric construction of a circle. Perhaps the user can increase the value of the parameter in the parametric equations of a circle, and see the resulting circle be drawn in real time. The same type of applet would be cool for the butterfly curve, although I already have an animation for this curve (from wikipedia) and making another one would be more difficult than a circle.<br />
<br />
:*[[Henon Attractor]] Page - an applet allowing the users to pick values of ''a'' and ''b'' to create different Henon Attractor (Mike is now done this applet)<br />
<br />
:*[[Blue Fern]] Page - my ideas for this are pretty vague. Perhaps some sort of an animation or applet showing the different types of matrix transformations and translations involved in making the fern. Maybe showing what each matrix does to an object (rotate it, shrink it...)<br />
<br />
:*[[Brunnian Links]] - an interactive 3D model of the Borromean rings (and possibly high ring levels also) similar to this [http://video.google.com/videoplay?docid=-5851348533617330039&ei=N75DSqSJFZy8rQKG9pyNBg&q=borromean+rings&hl=en&client=firefox-a YouTube]. I was thinking about an applet that would allow users to rotate the model with their mouse to see all perspectives of the ring, as well as have an animation showing that after one ring is removed, the ring unravels.<br />
<br />
:*[[Torus]] page- The section n-torus could use an illustration of how an <math>n</math>-dimensional object can exist in <math>n+1</math> dimensions. For example a line, which is a 1D object can exist in 2D when it is bent into a circle. Similarly, in 3D, a cube wraps to form a 3-torus. Illustrations could really help explain this section. I've tried searching for images online but could not get one that specifically shows this.<br />
<br />
==[[User:Tcheeseman1|Tim]]==<br />
<br />
Click on my name above for things that I've finished<br />
<br />
===Working On===<br />
<br />
:* Applet for [[Inversion|Point and Shape Inversion]] in 3D to demonstrate creating [[Dual Polyhedron|Dual Polyhedrons]]): [http://www.cs.drexel.edu/~twc24/mathimages/inversion/ShapeInversion3D.html Early Preview] - Math isn't quite right but the basics are there<br />
<br />
==[[User:Egoldberg1|Emily G.]]==<br />
===Projects In Progress:===<br />
:*Line Drawing (manipulating alpha in parametric equation of a line)<br />
::*Status- In progress<br />
:*[[Tessellations]] Image Gallery<br />
::*Status- Mostly done<br />
<br />
===Projects for the Future:===<br />
:*[[Cantor_Set]] zooming flash loop<br />
::*Status- On hold. Does anyone have any experience with this kind of thing? Mine keep turning out to be more confusing than helpful to the viewer.<br />
:*[[Transformations ]] java applet which allows user to change values in transformational matrices and then see the changes that it makes on the image.<br />
::*Status-Not Started<br />
:*Rhodonea ([[Cardioid]], Rose Petals, Limacons, etc.)- interactive graphing<br />
::*Status- Investigating the possibility of using a webMathematica applet to accomplish this<br />
:*[[Torus]] & [[Volume_of_Revolution]]- interactive graphing<br />
::*Status- Investigating the possibility of using a webMathematica applet to accomplish this<br />
<br />
==[[User:Slombardi1|Steve]]==<br />
:Stereographic Projection applet: [http://www.tcnj.edu/~lombar26/StereoProj/StereoProj.html Stereographic Projection]<br />
:Hypotrochoid applet: [http://www.tcnj.edu/~lombar26/Hypotrochoid/Hypotrochoid.html Hypotrochoid]<br />
:Metaballs applet: [http://www.tcnj.edu/~lombar26/ImplicitSurf/ImplicitSurf.html Metaballs]<br />
:Mandelbrot applet: [http://www.tcnj.edu/~lombar26/Mandelbrot/Mandelbrot.html Mandelbrot]<br />
:Koch Snowflake applet: [http://www.tcnj.edu/~lombar26/KochSnowflake/KochSnowflake.html Koch Snowflake]<br />
:Catenary applet: [http://www.tcnj.edu/~lombar26/Catenary/Catenary.html Catenary]<br />
:Julia set applet: [http://www.tcnj.edu/~lombar26/Julia/Julia.html Julia set]<br />
::Hi Steve,<br />
::I've seen this applet, and I've like it--it's just very similar to most Julia Set applets out there at only deal with Julia Sets of functions of the form <math> f(x)=x^2+a+bi</math>. I'd think it would be *really* cool to have an applet where someone could plug in any old rational function and get a Julia Set, though I know that might be too hard. <br />
::As an aside, what computational method did you use (an escape criterion, like my short program on that page, or something else)?<br />
::Thanks, and keep up the great work.<br />
:::~Anna<br />
::: There's a cool applet showing the relationship between Julia and Mendelbrot sets [http://javaview.de/vgp/tutor/fractal/PaFractalImage.html here]. -Tim<br />
:Chryzode applet: [http://www.tcnj.edu/~lombar26/Chryzode/Chryzode.html Chryzode]<br />
:Conic Section applet: [http://www.tcnj.edu/~lombar26/ConicSection/ConicSection.html Conic Section]<br />
:Procedural Images applet: [http://www.tcnj.edu/~lombar26/ProcImages/ProcImages.html Procedural Images]<br />
<br />
Test:<br />
<java_applet code="Mandelbrot.class" width="200" height="200" archive="Mandelbrot.jar" /><br />
<br />
==[[User:Asobti1|Ayush]]==<br />
<br />
I'm a Computer Science sophomore at Drexel University. This Summer term (Summer 09) is my first term working on the Math Images project.<br />
<br />
===The Plan:===<br />
:Working with Josh and Alan to add interactivity in the pages previously created by Alan.<br />
:I plan to concentrate on Flash animation while Josh explores the Java.<br />
<br />
<br />
===Work Progress:===<br />
:'''Week 1:'''<br />
::Surfed around the MathImages website. Familiarized myself with the many different pages and projects.<br />
::Spoke with Alan and Josh and made a tentative plan of what is to be achieved in the duration of the research project.<br />
::Installed and set up Adobe Flash CS4. Started reading tutorials and watching videos to learn using Flash.<br />
::Learned basic wiki tags and wiki usage and embedding flash .swf files into wiki<br />
:::<flash>file=Test_anim.swf|width=280|height=200|</flash><br />
::Created a simple flash animation to show matrix multiplication of two 2x2 matrices. May be incorporated in the Matrix helper page.<br />
::<flash>file=Matrix_multiplication_new.swf|width=500|height=300|</flash><br />
:'''Matrix Calculator:'''<br />
::Currently working on a Matrix calculator. <br />
::After making the barebones framework in week 3, I have been adding features in it this week. It now has the option to add and recall from memory, a Clear option, the calculator returns an error if the user does not select any operator, it does not accept non-numeric values etc.<br />
::You can see the beta ver. here : [http://megaswf.com/view/4af984ebc5d7de995d57aeb531251c28.html]<br />
<br />
:: Some features I am currently working on:<br />
:::*Allowing user to select dimensions of Matrix<br />
:::*Calculation of Invert, Adjoint and Determinant of Matrix<br />
:::*Show tutorials for all operations<br />
<br />
==[[User:Jdicristo1|Josh]]==<br />
<br />
I just completed my freshman year at Drexel, going for a BS in Computer Science<br />
<br />
===Projects:===<br />
:Working with Ayush and Alan to add interactivity in the pages previously created by Alan.<br />
:Working mainly with Java<br />
<br />
===Progress After Week 1===<br />
Because I am really working on this project part-time I did not make any major strides this week but I did get a few things accomplished<br />
: I learned the basics of writing Java Applets<br />
: I'm about 1/3 of the way done a program that segments a rectangle into thirds and then illustrates the Golden Spiral<br />
<br />
==[[User:Mhershey1|Mhershey1]]==<br />
test:<br />
<java_applet code="Bluewashrecursive.class" width="500" height="400"/><br />
What I have so far: http://www.pages.drexel.edu/~smh86/index.html<br />
:*[[Blue Wash]], applet changing ''k'' (in '''Inclined Recursive Method''') & animation drawing the basic no ''k'' method (in '''Basic Recursive Method''') <br />
:*[[Blue Fern]], [[Henon Attractor]], redo the animations with small points<br />
:*[[Hyperbolic Tilings]], applet where users input Schläfli symbol to create a tiling<br />
:**This would take too long for me to do. Maybe someone else can do this one, or we could just use the already made applet?<br />
:*[[Newton's Basin]], redo the animation (maybe users input the equations)<br />
:*[[Logarithms]], interactive quiz with exponential and logarithmic equations<br />
:*[[Harter-Heighway Dragon]], animating the curve at each iteration stage<br />
<br />
==[[User:Mhinkle1|Matt]]==<br />
If you see the green box below, you have Java installed. To view the [http://www.pages.drexel.edu/~mjh96/java/ChangeOfCoords/ChangeOfCoordsApp.html Change of Coordinate Systems Applet], your version number should at least be 1.6.0_14. If it still does not work, please let me know!<br />
<java_applet code="JavaVersionDisplayApplet.class" width="400" height="50" archive="http://www.pages.drexel.edu/~mjh96/java/JavaTest/JavaVersionTestApp.jar" /><br />
:[http://www.javatester.org/index.htm Click here] to learn more about the Java Tester Applet.<br />
===Projects:===<br />
:*[[Change of Coordinate Systems]]<br />
::*Status: Finished<br />
::*Description: An applet which allows for a visual representation of user defined points in 3-space<br />
::*Link: [http://www.pages.drexel.edu/~mjh96/java/ChangeOfCoords/ChangeOfCoordsApp.html Change of Coordinate Systems Applet]<br />
::*Notes: Finished applet, if you find any bugs, please let me know! email: mjh96@drexel.edu<br />
:*[[Gradients and Directional Derivatives]]<br />
::*Status: Not Started<br />
::*Description:An applet or animation that displays the gradient at different points on a surface<br />
:*[[Vector]]<br />
::*Status: Finished<br />
::*Description: An applet allowing for an interactive representation of 2D vector algebra, mainly consisting of: addition and subtraction. Scalar multiplication was not included as it would be a detriment to the applet's simple point and click interface. However, if anyone feels this feature should be added, I can certainly do so.<br />
::*Link: [http://www.pages.drexel.edu/~mjh96/java/Vector2D/VectorAlgebra2D.html 2D Vector Applet]<br />
::*Notes: If you find any bugs, please let me know! email: mjh96@drexel.edu. Also, I am aware of the annoying tendency of vectors clipping with the bounds of the graph when the addition procedure is carried out.<br />
:*[[Probability Distributions]]<br />
::*Status: Finished<br />
::*Description: An applet allowing the user to simulate rolling a six-sided dice, and graphically keep track of the outcome distribution.<br />
::*Link: [http://www.pages.drexel.edu/~mjh96/java/Prob/DiceProbApp.html Dice Probability Applet]<br />
::*Notes: Let me know if you have any suggestions. email: mjh96@drexel.edu<br />
:*[[Vector | Vector Cross Product]]<br />
::*Status: Not Started (Someone else may pick it up if they wish)<br />
::*Description: An applet allowing the user to enter the components of 2 vectors and display a graphical representation of a vector cross product<br />
:*[[Arithmetic Sequence]]<br />
::*Status: In Progress<br />
::*Description: An applet that generates a random arithmetic sequence and allows the user to fill in missing spots. A geometric version is likely to follow.<br />
<br />
:''Note: If a project is listed as "Not Started," feel free to pick it up if you wish''<br />
<br />
===Week 1 Progress===<br />
:After getting comfortable with writing Java applets, I began to read the Java 3D tutorial provided by Sun. After getting down some of the basics, I began to work on the Change of Coordinates applet. So far I have created a 3D graph that has the ability to graphically display a point in 3-space as specified by the user. This point may then be displayed with a rectangular/cartesian, cylindrical, or spherical representation. As of now, the points are input via the console, yet in the finished version, the user will be able to click any location in 3-space to select a point. The user will also be able to navigate the space with a mouse or keyboard.<br />
<br />
<java_applet code="VectorAlgebra2D.class" width="600" height="350" archive="VectorAlgebra2DApp.jar" /><br />
<java_applet code="DiceProbabilityApp.class" width="800" height ="430" archive="DiceProbApp.jar" /></div>Tcheeseman1https://mathimages.swarthmore.edu/index.php?title=D09&diff=8539D092009-07-17T19:18:48Z<p>Tcheeseman1: </p>
<hr />
<div><center>'' '''Welcome to the Drexel Summer 09 Entry to [[Image:TmipClear.png|275px]]''' ''!</center><br />
<br />
'''IMPORTANT NOTE: Please put up contact information on Drexel-Swat Partnering page: [[Drexel-Swat_Partnering]]'''<br />
<br />
[[Getting Started]] --- [[A Brief Tour of What's Been Done So Far]]<br />
<br />
----<br />
<br />
'''Things to do:''' <br />
* browse around, leaving comments on the Math Images discussion page and the Swarthmore student's discussion page, looking around for interesting possibilities for interaction on the latter<br />
* look through the Helper Pages in the left navbar and the [http://wikis.swarthmore.edu/miwiki/index.php/Hard_Math Hard Math] page to see if you can find anything you'd like to work on--if there's anything you've struggled with that isn't there, add it!<br />
<br />
----<br />
'''Notes from July 6th Video Conference'''<br />
*See Rebekah's page as well as Alan's for ideas for more projects. <br />
*Gene has invited us to write pages for the math for computer graphics topics. <br />
*Also, we've been invited to Swarthmore if we wish, next week, to begin work with webMathematica while the license for Drexel is pending approval.<br />
'''Notes from July 8th VC'''<br />
*Next VC meeting tentatively scheduled for Friday (7/17)<br />
*Gene mentioned that he has acquired 5 webMathematica licenses for Drexel<br />
----<br />
<br />
'''[[Math for Computer Graphics and Computer Vision]]'''<br />
<br />
'''Resources:'''<br />
:* [http://www.kirupa.com/developer/flash/index.htm Flash/ActionScript Tutorials]<br />
:* [http://hgbook.red-bean.com/read/ Mercurial Book] (Online)<br />
:* [http://java.sun.com/developer/onlineTraining/java3d/ Java 3D Tutorials]<br />
:* [http://javaview.de/ JavaView]<br />
:* [http://javaview.de/vgp/tutor/index.html JavaView Applet Examples]<br />
:* [http://javaview.de/doc/reference/index.html JavaView API Documentation (JavaDoc)]<br />
<br />
__TOC__<br />
<br />
''' ''Check out the [[Drexel-Swat Partnering]] page to see who's paired up with whom and keep track of what they're working on...'' '''<br />
<br />
==Possible Applets/Animations for Drexel Students To Do==<br />
:* [[Parametric Equations]] Page- demonstrate the parametric construction of a circle. Perhaps the user can increase the value of the parameter in the parametric equations of a circle, and see the resulting circle be drawn in real time. The same type of applet would be cool for the butterfly curve, although I already have an animation for this curve (from wikipedia) and making another one would be more difficult than a circle.<br />
<br />
:*[[Henon Attractor]] Page - an applet allowing the users to pick values of ''a'' and ''b'' to create different Henon Attractor (Mike is now done this applet)<br />
<br />
:*[[Blue Fern]] Page - my ideas for this are pretty vague. Perhaps some sort of an animation or applet showing the different types of matrix transformations and translations involved in making the fern. Maybe showing what each matrix does to an object (rotate it, shrink it...)<br />
<br />
:*[[Brunnian Links]] - an interactive 3D model of the Borromean rings (and possibly high ring levels also) similar to this [http://video.google.com/videoplay?docid=-5851348533617330039&ei=N75DSqSJFZy8rQKG9pyNBg&q=borromean+rings&hl=en&client=firefox-a YouTube]. I was thinking about an applet that would allow users to rotate the model with their mouse to see all perspectives of the ring, as well as have an animation showing that after one ring is removed, the ring unravels.<br />
<br />
:*[[Torus]] page- The section n-torus could use an illustration of how an <math>n</math>-dimensional object can exist in <math>n+1</math> dimensions. For example a line, which is a 1D object can exist in 2D when it is bent into a circle. Similarly, in 3D, a cube wraps to form a 3-torus. Illustrations could really help explain this section. I've tried searching for images online but could not get one that specifically shows this.<br />
<br />
==[[User:Tcheeseman1|Tim]]==<br />
<br />
Click on my name above for things that I've finished<br />
<br />
===Working On===<br />
<br />
:* Applet for [[Inversion|Point and Shape Inversion]] in 3D to demonstrate creating [[Dual Polyhedron|Dual Polyhedrons]]): [http://www.cs.drexel.edu/~twc24/mathimages/inversion/ShapeInversion3D.html Early Preview] - Math isn't quite right but the basics are there<br />
<br />
==[[User:Egoldberg1|Emily G.]]==<br />
===Projects In Progress:===<br />
:*Line Drawing (manipulating alpha in parametric equation of a line)<br />
::*Status- In progress<br />
:*[[Tessellations]] Image Gallery<br />
::*Status- Mostly done<br />
<br />
===Projects for the Future:===<br />
:*[[Cantor_Set]] zooming flash loop<br />
::*Status- On hold. Does anyone have any experience with this kind of thing? Mine keep turning out to be more confusing than helpful to the viewer.<br />
:*[[Transformations ]] java applet which allows user to change values in transformational matrices and then see the changes that it makes on the image.<br />
::*Status-Not Started<br />
:*Rhodonea ([[Cardioid]], Rose Petals, Limacons, etc.)- interactive graphing<br />
::*Status- Investigating the possibility of using a webMathematica applet to accomplish this<br />
:*[[Torus]] & [[Volume_of_Revolution]]- interactive graphing<br />
::*Status- Investigating the possibility of using a webMathematica applet to accomplish this<br />
<br />
==[[User:Slombardi1|Steve]]==<br />
:Stereographic Projection applet: [http://www.tcnj.edu/~lombar26/StereoProj/StereoProj.html Stereographic Projection]<br />
:Hypotrochoid applet: [http://www.tcnj.edu/~lombar26/Hypotrochoid/Hypotrochoid.html Hypotrochoid]<br />
:Metaballs applet: [http://www.tcnj.edu/~lombar26/ImplicitSurf/ImplicitSurf.html Metaballs]<br />
:Mandelbrot applet: [http://www.tcnj.edu/~lombar26/Mandelbrot/Mandelbrot.html Mandelbrot]<br />
:Koch Snowflake applet: [http://www.tcnj.edu/~lombar26/KochSnowflake/KochSnowflake.html Koch Snowflake]<br />
:Catenary applet: [http://www.tcnj.edu/~lombar26/Catenary/Catenary.html Catenary]<br />
:Julia set applet: [http://www.tcnj.edu/~lombar26/Julia/Julia.html Julia set]<br />
:Chryzode applet: [http://www.tcnj.edu/~lombar26/Chryzode/Chryzode.html Chryzode]<br />
:Conic Section applet: [http://www.tcnj.edu/~lombar26/ConicSection/ConicSection.html Conic Section]<br />
:Procedural Images applet: [http://www.tcnj.edu/~lombar26/ProcImages/ProcImages.html Procedural Images]<br />
<br />
Test:<br />
<java_applet code="Mandelbrot.class" width="200" height="200" archive="Mandelbrot.jar" /><br />
<br />
==[[User:Asobti1|Ayush]]==<br />
<br />
I'm a Computer Science sophomore at Drexel University. This Summer term (Summer 09) is my first term working on the Math Images project.<br />
<br />
===The Plan:===<br />
:Working with Josh and Alan to add interactivity in the pages previously created by Alan.<br />
:I plan to concentrate on Flash animation while Josh explores the Java.<br />
<br />
<br />
===Work Progress:===<br />
:'''Week 1:'''<br />
::Surfed around the MathImages website. Familiarized myself with the many different pages and projects.<br />
::Spoke with Alan and Josh and made a tentative plan of what is to be achieved in the duration of the research project.<br />
::Installed and set up Adobe Flash CS4. Started reading tutorials and watching videos to learn using Flash.<br />
::Learned basic wiki tags and wiki usage and embedding flash .swf files into wiki<br />
:::<flash>file=Test_anim.swf|width=280|height=200|</flash><br />
::Created a simple flash animation to show matrix multiplication of two 2x2 matrices. May be incorporated in the Matrix helper page.<br />
::<flash>file=Matrix_multiplication_new.swf|width=500|height=300|</flash><br />
:'''Matrix Calculator:'''<br />
::Currently working on a Matrix calculator. <br />
::After making the barebones framework in week 3, I have been adding features in it this week. It now has the option to add and recall from memory, a Clear option, the calculator returns an error if the user does not select any operator, it does not accept non-numeric values etc.<br />
::You can see the beta ver. here : [http://megaswf.com/view/4af984ebc5d7de995d57aeb531251c28.html]<br />
<br />
:: Some features I am currently working on:<br />
:::*Allowing user to select dimensions of Matrix<br />
:::*Calculation of Invert, Adjoint and Determinant of Matrix<br />
:::*Show tutorials for all operations<br />
<br />
==[[User:Jdicristo1|Josh]]==<br />
<br />
I just completed my freshman year at Drexel, going for a BS in Computer Science<br />
<br />
===Projects:===<br />
:Working with Ayush and Alan to add interactivity in the pages previously created by Alan.<br />
:Working mainly with Java<br />
<br />
===Progress After Week 1===<br />
Because I am really working on this project part-time I did not make any major strides this week but I did get a few things accomplished<br />
: I learned the basics of writing Java Applets<br />
: I'm about 1/3 of the way done a program that segments a rectangle into thirds and then illustrates the Golden Spiral<br />
<br />
==[[User:Mhershey1|Mhershey1]]==<br />
test:<br />
<java_applet code="Bluewashrecursive.class" width="500" height="400"/><br />
What I have so far: http://www.pages.drexel.edu/~smh86/index.html<br />
:*[[Blue Wash]], applet changing ''k'' (in '''Inclined Recursive Method''') & animation drawing the basic no ''k'' method (in '''Basic Recursive Method''') <br />
:*[[Blue Fern]], [[Henon Attractor]], redo the animations with small points<br />
:*[[Hyperbolic Tilings]], applet where users input Schläfli symbol to create a tiling<br />
:**This would take too long for me to do. Maybe someone else can do this one, or we could just use the already made applet?<br />
:*[[Newton's Basin]], redo the animation (maybe users input the equations)<br />
:*[[Logarithms]], interactive quiz with exponential and logarithmic equations<br />
:*[[Harter-Heighway Dragon]], animating the curve at each iteration stage<br />
<br />
==[[User:Mhinkle1|Matt]]==<br />
If you see the green box below, you have Java installed. To view the [http://www.pages.drexel.edu/~mjh96/java/ChangeOfCoords/ChangeOfCoordsApp.html Change of Coordinate Systems Applet], your version number should at least be 1.6.0_14. If it still does not work, please let me know!<br />
<java_applet code="JavaVersionDisplayApplet.class" width="400" height="50" archive="http://www.pages.drexel.edu/~mjh96/java/JavaTest/JavaVersionTestApp.jar" /><br />
:[http://www.javatester.org/index.htm Click here] to learn more about the Java Tester Applet.<br />
===Projects:===<br />
:*[[Change of Coordinate Systems]]<br />
::*Status: Finished<br />
::*Description: An applet which allows for a visual representation of user defined points in 3-space<br />
::*Link: [http://www.pages.drexel.edu/~mjh96/java/ChangeOfCoords/ChangeOfCoordsApp.html Change of Coordinate Systems Applet]<br />
::*Notes: Finished applet, if you find any bugs, please let me know! email: mjh96@drexel.edu<br />
:*[[Gradients and Directional Derivatives]]<br />
::*Status: Not Started<br />
::*Description:An applet or animation that displays the gradient at different points on a surface<br />
:*[[Vector]]<br />
::*Status: Finished<br />
::*Description: An applet allowing for an interactive representation of 2D vector algebra, mainly consisting of: addition and subtraction. Scalar multiplication was not included as it would be a detriment to the applet's simple point and click interface. However, if anyone feels this feature should be added, I can certainly do so.<br />
::*Link: [http://www.pages.drexel.edu/~mjh96/java/Vector2D/VectorAlgebra2D.html 2D Vector Applet]<br />
::*Notes: If you find any bugs, please let me know! email: mjh96@drexel.edu. Also, I am aware of the annoying tendency of vectors clipping with the bounds of the graph when the addition procedure is carried out.<br />
:*[[Probability Distributions]]<br />
::*Status: Finished<br />
::*Description: An applet allowing the user to simulate rolling a six-sided dice, and graphically keep track of the outcome distribution.<br />
::*Link: [http://www.pages.drexel.edu/~mjh96/java/Prob/DiceProbApp.html Dice Probability Applet]<br />
::*Notes: Let me know if you have any suggestions. email: mjh96@drexel.edu<br />
:*[[Vector | Vector Cross Product]]<br />
::*Status: Not Started (Someone else may pick it up if they wish)<br />
::*Description: An applet allowing the user to enter the components of 2 vectors and display a graphical representation of a vector cross product<br />
:*[[Arithmetic Sequence]]<br />
::*Status: In Progress<br />
::*Description: An applet that generates a random arithmetic sequence and allows the user to fill in missing spots. A geometric version is likely to follow.<br />
<br />
:''Note: If a project is listed as "Not Started," feel free to pick it up if you wish''<br />
<br />
===Week 1 Progress===<br />
:After getting comfortable with writing Java applets, I began to read the Java 3D tutorial provided by Sun. After getting down some of the basics, I began to work on the Change of Coordinates applet. So far I have created a 3D graph that has the ability to graphically display a point in 3-space as specified by the user. This point may then be displayed with a rectangular/cartesian, cylindrical, or spherical representation. As of now, the points are input via the console, yet in the finished version, the user will be able to click any location in 3-space to select a point. The user will also be able to navigate the space with a mouse or keyboard.<br />
<br />
<java_applet code="VectorAlgebra2D.class" width="600" height="350" archive="VectorAlgebra2DApp.jar" /><br />
<java_applet code="DiceProbabilityApp.class" width="800" height ="430" archive="DiceProbApp.jar" /></div>Tcheeseman1https://mathimages.swarthmore.edu/index.php?title=D09&diff=8535D092009-07-17T18:41:09Z<p>Tcheeseman1: /* Tim */</p>
<hr />
<div><center>'' '''Welcome to the Drexel Summer 09 Entry to [[Image:TmipClear.png|275px]]''' ''!</center><br />
<br />
'''IMPORTANT NOTE: Please put up contact information on Drexel-Swat Partnering page: [[Drexel-Swat_Partnering]]'''<br />
<br />
[[Getting Started]] --- [[A Brief Tour of What's Been Done So Far]]<br />
<br />
----<br />
<br />
'''Things to do:''' <br />
* browse around, leaving comments on the Math Images discussion page and the Swarthmore student's discussion page, looking around for interesting possibilities for interaction on the latter<br />
* look through the Helper Pages in the left navbar and the [http://wikis.swarthmore.edu/miwiki/index.php/Hard_Math Hard Math] page to see if you can find anything you'd like to work on--if there's anything you've struggled with that isn't there, add it!<br />
<br />
----<br />
'''Notes from July 6th Video Conference'''<br />
*See Rebekah's page as well as Alan's for ideas for more projects. <br />
*Gene has invited us to write pages for the math for computer graphics topics. <br />
*Also, we've been invited to Swarthmore if we wish, next week, to begin work with webMathematica while the license for Drexel is pending approval.<br />
'''Notes from July 8th VC'''<br />
*Next VC meeting tentatively scheduled for Friday (7/17)<br />
*Gene mentioned that he has acquired 5 webMathematica licenses for Drexel<br />
----<br />
<br />
'''[[Math for Computer Graphics and Computer Vision]]'''<br />
<br />
'''Resources:'''<br />
:* [http://www.kirupa.com/developer/flash/index.htm Flash/ActionScript Tutorials]<br />
:* [http://hgbook.red-bean.com/read/ Mercurial Book] (Online)<br />
:* [http://java.sun.com/developer/onlineTraining/java3d/ Java 3D Tutorials]<br />
<br />
<br />
__TOC__<br />
<br />
''' ''Check out the [[Drexel-Swat Partnering]] page to see who's paired up with whom and keep track of what they're working on...'' '''<br />
<br />
==Possible Applets/Animations for Drexel Students To Do==<br />
:* [[Parametric Equations]] Page- demonstrate the parametric construction of a circle. Perhaps the user can increase the value of the parameter in the parametric equations of a circle, and see the resulting circle be drawn in real time. The same type of applet would be cool for the butterfly curve, although I already have an animation for this curve (from wikipedia) and making another one would be more difficult than a circle.<br />
<br />
:*[[Henon Attractor]] Page - an applet allowing the users to pick values of ''a'' and ''b'' to create different Henon Attractor (Mike is now done this applet)<br />
<br />
:*[[Blue Fern]] Page - my ideas for this are pretty vague. Perhaps some sort of an animation or applet showing the different types of matrix transformations and translations involved in making the fern. Maybe showing what each matrix does to an object (rotate it, shrink it...)<br />
<br />
:*[[Brunnian Links]] - an interactive 3D model of the Borromean rings (and possibly high ring levels also) similar to this [http://video.google.com/videoplay?docid=-5851348533617330039&ei=N75DSqSJFZy8rQKG9pyNBg&q=borromean+rings&hl=en&client=firefox-a YouTube]. I was thinking about an applet that would allow users to rotate the model with their mouse to see all perspectives of the ring, as well as have an animation showing that after one ring is removed, the ring unravels.<br />
<br />
:*[[Torus]] page- The section n-torus could use an illustration of how an <math>n</math>-dimensional object can exist in <math>n+1</math> dimensions. For example a line, which is a 1D object can exist in 2D when it is bent into a circle. Similarly, in 3D, a cube wraps to form a 3-torus. Illustrations could really help explain this section. I've tried searching for images online but could not get one that specifically shows this.<br />
<br />
==[[User:Tcheeseman1|Tim]]==<br />
<br />
Click on my name above for things that I've finished<br />
<br />
===Working On===<br />
<br />
:* Applet for [[Inversion|Point and Shape Inversion]] in 3D to demonstrate creating [[Dual Polyhedron|Dual Polyhedrons]]): [http://www.cs.drexel.edu/~twc24/mathimages/inversion/ShapeInversion3D.html Early Preview] - Math isn't quite right but the basics are there<br />
<br />
==[[User:Egoldberg1|Emily G.]]==<br />
===Projects:===<br />
:*[[Pascal's Triangle]]-, with input from Lizah using Flash to visualize patterns.<br />
::*Status- Finished (6/30) [http://www.pages.drexel.edu/~ecg32/mi/work.html See it here] or [[User:Egoldberg1|here]].<br />
:*[[Towers of Hanoi]]-, make an applet which allows users to play this game. <br />
::*Status- Finished (7/7)<br />
:*[[Tessellations]] Image Gallery<br />
::*Status- In progress (using Flash)<br />
:*Rhodonea ([[Cardioid]], Rose Petals, Limacons, etc.)- interactive graphing<br />
::*Status- Investigating the possibility of using a webMathematica applet to accomplish this<br />
:*[[Torus]] & [[Volume_of_Revolution]]- interactive graphing<br />
::*Status- Investigating the possibility of using a webMathematica applet to accomplish this<br />
:*[[Cantor_Set]] zooming flash loop<br />
::*Status- On hold (revision of strategy necessary).<br />
<br />
<br />
====Week One====<br />
:This week after setting up Flash CS4 on my laptop and while familiarizing myself with actionscript3, I began a flash tutorial which explains and visualizes the patterns within [[Pascal's Triangle]]. The final result will be longer than I initially realized. At this point, it almost feels like I'm creating a movie, but that's alright because I want the tutorial to be thorough and to have clear visualizations of the patterns. Without thorough animation, some of the patterns would be particularly hard to see for yourself. Animation is started but not complete for the original triangle, diagonal rows, shallow diagonal rows (Fibonacci sequence), and the even/odd pattern (Sierpenski's triangle). Descriptions are needed for all of the patterns. Animation is not started for the hockey stick pattern. With no snags, I should be able to finish this animation by next Friday.<br />
<br />
====Week Two====<br />
:The majority of the week was spent refining the [[Pascal's Triangle]] tutorial. Specifically, it was spent completing the animations within the tutorial, revising the descriptions/explanations, and debugging. In the final hours of the week, I looked into finding more projects which I can work on in the future, and began developing a flash video which is a looping zoom into a [[Cantor_Set]]. This week I also looked into the use of webMathematica for some applets. I think it will be particularly helpful in the construction of some interactive applets (like the Rhodonea graphing tool or for graphing 3d objects).<br />
<br />
==[[User:Slombardi1|Steve]]==<br />
:Stereographic Projection applet: [http://www.tcnj.edu/~lombar26/StereoProj/StereoProj.html Stereographic Projection]<br />
:Hypotrochoid applet: [http://www.tcnj.edu/~lombar26/Hypotrochoid/Hypotrochoid.html Hypotrochoid]<br />
:Metaballs applet: [http://www.tcnj.edu/~lombar26/ImplicitSurf/ImplicitSurf.html Metaballs]<br />
:Mandelbrot applet: [http://www.tcnj.edu/~lombar26/Mandelbrot/Mandelbrot.html Mandelbrot]<br />
:Koch Snowflake applet: [http://www.tcnj.edu/~lombar26/KochSnowflake/KochSnowflake.html Koch Snowflake]<br />
:Catenary applet: [http://www.tcnj.edu/~lombar26/Catenary/Catenary.html Catenary]<br />
:Julia set applet: [http://www.tcnj.edu/~lombar26/Julia/Julia.html Julia set]<br />
:Chryzode applet: [http://www.tcnj.edu/~lombar26/Chryzode/Chryzode.html Chryzode]<br />
:Conic Section applet: [http://www.tcnj.edu/~lombar26/ConicSection/ConicSection.html Conic Section]<br />
:Procedural Images applet: [http://www.tcnj.edu/~lombar26/ProcImages/ProcImages.html Procedural Images]<br />
<br />
Test:<br />
<java_applet code="Mandelbrot.class" width="200" height="200" archive="Mandelbrot.jar" /><br />
<br />
==[[User:Asobti1|Ayush]]==<br />
<br />
I'm a Computer Science sophomore at Drexel University. This Summer term (Summer 09) is my first term working on the Math Images project.<br />
<br />
===The Plan:===<br />
:Working with Josh and Alan to add interactivity in the pages previously created by Alan.<br />
:I plan to concentrate on Flash animation while Josh explores the Java.<br />
<br />
<br />
===Work Progress:===<br />
:'''Week 1:'''<br />
::Surfed around the MathImages website. Familiarized myself with the many different pages and projects.<br />
::Spoke with Alan and Josh and made a tentative plan of what is to be achieved in the duration of the research project.<br />
::Installed and set up Adobe Flash CS4. Started reading tutorials and watching videos to learn using Flash.<br />
::Learned basic wiki tags and wiki usage and embedding flash .swf files into wiki<br />
:::<flash>file=Test_anim.swf|width=280|height=200|</flash><br />
::Created a simple flash animation to show matrix multiplication of two 2x2 matrices. May be incorporated in the Matrix helper page.<br />
::<flash>file=Matrix_multiplication_new.swf|width=500|height=300|</flash><br />
:'''Matrix Calculator:'''<br />
::Currently working on a Matrix calculator. <br />
::After making the barebones framework in week 3, I have been adding features in it this week. It now has the option to add and recall from memory, a Clear option, the calculator returns an error if the user does not select any operator, it does not accept non-numeric values etc.<br />
::You can see the beta ver. here : [http://megaswf.com/view/4af984ebc5d7de995d57aeb531251c28.html]<br />
<br />
:: Some features I am currently working on:<br />
:::*Allowing user to select dimensions of Matrix<br />
:::*Calculation of Invert, Adjoint and Determinant of Matrix<br />
:::*Show tutorials for all operations<br />
<br />
==[[User:Jdicristo1|Josh]]==<br />
<br />
I just completed my freshman year at Drexel, going for a BS in Computer Science<br />
<br />
===Projects:===<br />
:Working with Ayush and Alan to add interactivity in the pages previously created by Alan.<br />
:Working mainly with Java<br />
<br />
===Progress After Week 1===<br />
Because I am really working on this project part-time I did not make any major strides this week but I did get a few things accomplished<br />
: I learned the basics of writing Java Applets<br />
: I'm about 1/3 of the way done a program that segments a rectangle into thirds and then illustrates the Golden Spiral<br />
<br />
==[[User:Mhershey1|Mhershey1]]==<br />
test:<br />
<java_applet code="Bluewashrecursive.class" width="500" height="400"/><br />
What I have so far: http://www.pages.drexel.edu/~smh86/index.html<br />
:*[[Blue Wash]], applet changing ''k'' (in '''Inclined Recursive Method''') & animation drawing the basic no ''k'' method (in '''Basic Recursive Method''') <br />
:*[[Blue Fern]], [[Henon Attractor]], redo the animations with small points<br />
:*[[Hyperbolic Tilings]], applet where users input Schläfli symbol to create a tiling<br />
:**This would take too long for me to do. Maybe someone else can do this one, or we could just use the already made applet?<br />
:*[[Newton's Basin]], redo the animation (maybe users input the equations)<br />
:*[[Logarithms]], interactive quiz with exponential and logarithmic equations<br />
:*[[Harter-Heighway Dragon]], animating the curve at each iteration stage<br />
<br />
==[[User:Mhinkle1|Matt]]==<br />
If you see the green box below, you have Java installed. To view the [http://www.pages.drexel.edu/~mjh96/java/ChangeOfCoords/ChangeOfCoordsApp.html Change of Coordinate Systems Applet], your version number should at least be 1.6.0_14. If it still does not work, please let me know!<br />
<java_applet code="JavaVersionDisplayApplet.class" width="400" height="50" archive="http://www.pages.drexel.edu/~mjh96/java/JavaTest/JavaVersionTestApp.jar" /><br />
:[http://www.javatester.org/index.htm Click here] to learn more about the Java Tester Applet.<br />
===Projects:===<br />
:*[[Change of Coordinate Systems]]<br />
::*Status: Finished<br />
::*Description: An applet which allows for a visual representation of user defined points in 3-space<br />
::*Link: [http://www.pages.drexel.edu/~mjh96/java/ChangeOfCoords/ChangeOfCoordsApp.html Change of Coordinate Systems Applet]<br />
::*Notes: Finished applet, if you find any bugs, please let me know! email: mjh96@drexel.edu<br />
:*[[Gradients and Directional Derivatives]]<br />
::*Status: Not Started<br />
::*Description:An applet or animation that displays the gradient at different points on a surface<br />
:*[[Vector]]<br />
::*Status: Finished<br />
::*Description: An applet allowing for an interactive representation of 2D vector algebra, mainly consisting of: addition and subtraction. Scalar multiplication was not included as it would be a detriment to the applet's simple point and click interface. However, if anyone feels this feature should be added, I can certainly do so.<br />
::*Link: [http://www.pages.drexel.edu/~mjh96/java/Vector2D/VectorAlgebra2D.html 2D Vector Applet]<br />
::*Notes: If you find any bugs, please let me know! email: mjh96@drexel.edu. Also, I am aware of the annoying tendency of vectors clipping with the bounds of the graph when the addition procedure is carried out.<br />
:*[[Probability Distributions]]<br />
::*Status: Finished<br />
::*Description: An applet allowing the user to simulate rolling a six-sided dice, and graphically keep track of the outcome distribution.<br />
::*Link: [http://www.pages.drexel.edu/~mjh96/java/Prob/DiceProbApp.html Dice Probability Applet]<br />
::*Notes: Let me know if you have any suggestions. email: mjh96@drexel.edu<br />
:*[[Vector | Vector Cross Product]]<br />
::*Status: Not Started (Someone else may pick it up if they wish)<br />
::*Description: An applet allowing the user to enter the components of 2 vectors and display a graphical representation of a vector cross product<br />
:*[[Arithmetic Sequence]]<br />
::*Status: In Progress<br />
::*Description: An applet that generates a random arithmetic sequence and allows the user to fill in missing spots. A geometric version is likely to follow.<br />
<br />
:''Note: If a project is listed as "Not Started," feel free to pick it up if you wish''<br />
<br />
===Week 1 Progress===<br />
:After getting comfortable with writing Java applets, I began to read the Java 3D tutorial provided by Sun. After getting down some of the basics, I began to work on the Change of Coordinates applet. So far I have created a 3D graph that has the ability to graphically display a point in 3-space as specified by the user. This point may then be displayed with a rectangular/cartesian, cylindrical, or spherical representation. As of now, the points are input via the console, yet in the finished version, the user will be able to click any location in 3-space to select a point. The user will also be able to navigate the space with a mouse or keyboard.<br />
<br />
<java_applet code="VectorAlgebra2D.class" width="600" height="350" archive="VectorAlgebra2DApp.jar" /><br />
<java_applet code="DiceProbabilityApp.class" width="800" height ="430" archive="DiceProbApp.jar" /></div>Tcheeseman1https://mathimages.swarthmore.edu/index.php?title=User:Tcheeseman1&diff=8534User:Tcheeseman12009-07-17T18:40:42Z<p>Tcheeseman1: </p>
<hr />
<div>===Done===<br />
:* Set up the [http://saturn.cs.drexel.edu/mathimages/ Code Repository]. See README's and examples for standard practice. Requires installing [http://mercurial.selenic.com/wiki/ Mercurial] ([http://sourceforge.net/project/showfiles.php?group_id=199155 Windows Installer]) ([http://www.vectrace.com/mercurialeclipse/ Eclipse Plugin])<br />
:* Re-familiarized myself with ActionScript 3<br />
:* Created an interactive 2D [[Inversion|Point Inversion]] Flash animation<br />
:* Interactive 2D [[Inversion|Shape Inversion]] Flash animation</div>Tcheeseman1https://mathimages.swarthmore.edu/index.php?title=D09&diff=8533D092009-07-17T18:40:17Z<p>Tcheeseman1: /* Tim */</p>
<hr />
<div><center>'' '''Welcome to the Drexel Summer 09 Entry to [[Image:TmipClear.png|275px]]''' ''!</center><br />
<br />
'''IMPORTANT NOTE: Please put up contact information on Drexel-Swat Partnering page: [[Drexel-Swat_Partnering]]'''<br />
<br />
[[Getting Started]] --- [[A Brief Tour of What's Been Done So Far]]<br />
<br />
----<br />
<br />
'''Things to do:''' <br />
* browse around, leaving comments on the Math Images discussion page and the Swarthmore student's discussion page, looking around for interesting possibilities for interaction on the latter<br />
* look through the Helper Pages in the left navbar and the [http://wikis.swarthmore.edu/miwiki/index.php/Hard_Math Hard Math] page to see if you can find anything you'd like to work on--if there's anything you've struggled with that isn't there, add it!<br />
<br />
----<br />
'''Notes from July 6th Video Conference'''<br />
*See Rebekah's page as well as Alan's for ideas for more projects. <br />
*Gene has invited us to write pages for the math for computer graphics topics. <br />
*Also, we've been invited to Swarthmore if we wish, next week, to begin work with webMathematica while the license for Drexel is pending approval.<br />
'''Notes from July 8th VC'''<br />
*Next VC meeting tentatively scheduled for Friday (7/17)<br />
*Gene mentioned that he has acquired 5 webMathematica licenses for Drexel<br />
----<br />
<br />
'''[[Math for Computer Graphics and Computer Vision]]'''<br />
<br />
'''Resources:'''<br />
:* [http://www.kirupa.com/developer/flash/index.htm Flash/ActionScript Tutorials]<br />
:* [http://hgbook.red-bean.com/read/ Mercurial Book] (Online)<br />
:* [http://java.sun.com/developer/onlineTraining/java3d/ Java 3D Tutorials]<br />
<br />
<br />
__TOC__<br />
<br />
''' ''Check out the [[Drexel-Swat Partnering]] page to see who's paired up with whom and keep track of what they're working on...'' '''<br />
<br />
==Possible Applets/Animations for Drexel Students To Do==<br />
:* [[Parametric Equations]] Page- demonstrate the parametric construction of a circle. Perhaps the user can increase the value of the parameter in the parametric equations of a circle, and see the resulting circle be drawn in real time. The same type of applet would be cool for the butterfly curve, although I already have an animation for this curve (from wikipedia) and making another one would be more difficult than a circle.<br />
<br />
:*[[Henon Attractor]] Page - an applet allowing the users to pick values of ''a'' and ''b'' to create different Henon Attractor (Mike is now done this applet)<br />
<br />
:*[[Blue Fern]] Page - my ideas for this are pretty vague. Perhaps some sort of an animation or applet showing the different types of matrix transformations and translations involved in making the fern. Maybe showing what each matrix does to an object (rotate it, shrink it...)<br />
<br />
:*[[Brunnian Links]] - an interactive 3D model of the Borromean rings (and possibly high ring levels also) similar to this [http://video.google.com/videoplay?docid=-5851348533617330039&ei=N75DSqSJFZy8rQKG9pyNBg&q=borromean+rings&hl=en&client=firefox-a YouTube]. I was thinking about an applet that would allow users to rotate the model with their mouse to see all perspectives of the ring, as well as have an animation showing that after one ring is removed, the ring unravels.<br />
<br />
:*[[Torus]] page- The section n-torus could use an illustration of how an <math>n</math>-dimensional object can exist in <math>n+1</math> dimensions. For example a line, which is a 1D object can exist in 2D when it is bent into a circle. Similarly, in 3D, a cube wraps to form a 3-torus. Illustrations could really help explain this section. I've tried searching for images online but could not get one that specifically shows this.<br />
<br />
==[[User:Tcheeseman1|Tim]]==<br />
<br />
===Working On===<br />
<br />
:* Applet for [[Inversion|Point and Shape Inversion]] in 3D to demonstrate creating [[Dual Polyhedron|Dual Polyhedrons]]): [http://www.cs.drexel.edu/~twc24/mathimages/inversion/ShapeInversion3D.html Early Preview] - Math isn't quite right but the basics are there<br />
<br />
==[[User:Egoldberg1|Emily G.]]==<br />
===Projects:===<br />
:*[[Pascal's Triangle]]-, with input from Lizah using Flash to visualize patterns.<br />
::*Status- Finished (6/30) [http://www.pages.drexel.edu/~ecg32/mi/work.html See it here] or [[User:Egoldberg1|here]].<br />
:*[[Towers of Hanoi]]-, make an applet which allows users to play this game. <br />
::*Status- Finished (7/7)<br />
:*[[Tessellations]] Image Gallery<br />
::*Status- In progress (using Flash)<br />
:*Rhodonea ([[Cardioid]], Rose Petals, Limacons, etc.)- interactive graphing<br />
::*Status- Investigating the possibility of using a webMathematica applet to accomplish this<br />
:*[[Torus]] & [[Volume_of_Revolution]]- interactive graphing<br />
::*Status- Investigating the possibility of using a webMathematica applet to accomplish this<br />
:*[[Cantor_Set]] zooming flash loop<br />
::*Status- On hold (revision of strategy necessary).<br />
<br />
<br />
====Week One====<br />
:This week after setting up Flash CS4 on my laptop and while familiarizing myself with actionscript3, I began a flash tutorial which explains and visualizes the patterns within [[Pascal's Triangle]]. The final result will be longer than I initially realized. At this point, it almost feels like I'm creating a movie, but that's alright because I want the tutorial to be thorough and to have clear visualizations of the patterns. Without thorough animation, some of the patterns would be particularly hard to see for yourself. Animation is started but not complete for the original triangle, diagonal rows, shallow diagonal rows (Fibonacci sequence), and the even/odd pattern (Sierpenski's triangle). Descriptions are needed for all of the patterns. Animation is not started for the hockey stick pattern. With no snags, I should be able to finish this animation by next Friday.<br />
<br />
====Week Two====<br />
:The majority of the week was spent refining the [[Pascal's Triangle]] tutorial. Specifically, it was spent completing the animations within the tutorial, revising the descriptions/explanations, and debugging. In the final hours of the week, I looked into finding more projects which I can work on in the future, and began developing a flash video which is a looping zoom into a [[Cantor_Set]]. This week I also looked into the use of webMathematica for some applets. I think it will be particularly helpful in the construction of some interactive applets (like the Rhodonea graphing tool or for graphing 3d objects).<br />
<br />
==[[User:Slombardi1|Steve]]==<br />
:Stereographic Projection applet: [http://www.tcnj.edu/~lombar26/StereoProj/StereoProj.html Stereographic Projection]<br />
:Hypotrochoid applet: [http://www.tcnj.edu/~lombar26/Hypotrochoid/Hypotrochoid.html Hypotrochoid]<br />
:Metaballs applet: [http://www.tcnj.edu/~lombar26/ImplicitSurf/ImplicitSurf.html Metaballs]<br />
:Mandelbrot applet: [http://www.tcnj.edu/~lombar26/Mandelbrot/Mandelbrot.html Mandelbrot]<br />
:Koch Snowflake applet: [http://www.tcnj.edu/~lombar26/KochSnowflake/KochSnowflake.html Koch Snowflake]<br />
:Catenary applet: [http://www.tcnj.edu/~lombar26/Catenary/Catenary.html Catenary]<br />
:Julia set applet: [http://www.tcnj.edu/~lombar26/Julia/Julia.html Julia set]<br />
:Chryzode applet: [http://www.tcnj.edu/~lombar26/Chryzode/Chryzode.html Chryzode]<br />
:Conic Section applet: [http://www.tcnj.edu/~lombar26/ConicSection/ConicSection.html Conic Section]<br />
:Procedural Images applet: [http://www.tcnj.edu/~lombar26/ProcImages/ProcImages.html Procedural Images]<br />
<br />
Test:<br />
<java_applet code="Mandelbrot.class" width="200" height="200" archive="Mandelbrot.jar" /><br />
<br />
==[[User:Asobti1|Ayush]]==<br />
<br />
I'm a Computer Science sophomore at Drexel University. This Summer term (Summer 09) is my first term working on the Math Images project.<br />
<br />
===The Plan:===<br />
:Working with Josh and Alan to add interactivity in the pages previously created by Alan.<br />
:I plan to concentrate on Flash animation while Josh explores the Java.<br />
<br />
<br />
===Work Progress:===<br />
:'''Week 1:'''<br />
::Surfed around the MathImages website. Familiarized myself with the many different pages and projects.<br />
::Spoke with Alan and Josh and made a tentative plan of what is to be achieved in the duration of the research project.<br />
::Installed and set up Adobe Flash CS4. Started reading tutorials and watching videos to learn using Flash.<br />
::Learned basic wiki tags and wiki usage and embedding flash .swf files into wiki<br />
:::<flash>file=Test_anim.swf|width=280|height=200|</flash><br />
::Created a simple flash animation to show matrix multiplication of two 2x2 matrices. May be incorporated in the Matrix helper page.<br />
::<flash>file=Matrix_multiplication_new.swf|width=500|height=300|</flash><br />
:'''Matrix Calculator:'''<br />
::Currently working on a Matrix calculator. <br />
::After making the barebones framework in week 3, I have been adding features in it this week. It now has the option to add and recall from memory, a Clear option, the calculator returns an error if the user does not select any operator, it does not accept non-numeric values etc.<br />
::You can see the beta ver. here : [http://megaswf.com/view/4af984ebc5d7de995d57aeb531251c28.html]<br />
<br />
:: Some features I am currently working on:<br />
:::*Allowing user to select dimensions of Matrix<br />
:::*Calculation of Invert, Adjoint and Determinant of Matrix<br />
:::*Show tutorials for all operations<br />
<br />
==[[User:Jdicristo1|Josh]]==<br />
<br />
I just completed my freshman year at Drexel, going for a BS in Computer Science<br />
<br />
===Projects:===<br />
:Working with Ayush and Alan to add interactivity in the pages previously created by Alan.<br />
:Working mainly with Java<br />
<br />
===Progress After Week 1===<br />
Because I am really working on this project part-time I did not make any major strides this week but I did get a few things accomplished<br />
: I learned the basics of writing Java Applets<br />
: I'm about 1/3 of the way done a program that segments a rectangle into thirds and then illustrates the Golden Spiral<br />
<br />
==[[User:Mhershey1|Mhershey1]]==<br />
test:<br />
<java_applet code="Bluewashrecursive.class" width="500" height="400"/><br />
What I have so far: http://www.pages.drexel.edu/~smh86/index.html<br />
:*[[Blue Wash]], applet changing ''k'' (in '''Inclined Recursive Method''') & animation drawing the basic no ''k'' method (in '''Basic Recursive Method''') <br />
:*[[Blue Fern]], [[Henon Attractor]], redo the animations with small points<br />
:*[[Hyperbolic Tilings]], applet where users input Schläfli symbol to create a tiling<br />
:**This would take too long for me to do. Maybe someone else can do this one, or we could just use the already made applet?<br />
:*[[Newton's Basin]], redo the animation (maybe users input the equations)<br />
:*[[Logarithms]], interactive quiz with exponential and logarithmic equations<br />
:*[[Harter-Heighway Dragon]], animating the curve at each iteration stage<br />
<br />
==[[User:Mhinkle1|Matt]]==<br />
If you see the green box below, you have Java installed. To view the [http://www.pages.drexel.edu/~mjh96/java/ChangeOfCoords/ChangeOfCoordsApp.html Change of Coordinate Systems Applet], your version number should at least be 1.6.0_14. If it still does not work, please let me know!<br />
<java_applet code="JavaVersionDisplayApplet.class" width="400" height="50" archive="http://www.pages.drexel.edu/~mjh96/java/JavaTest/JavaVersionTestApp.jar" /><br />
:[http://www.javatester.org/index.htm Click here] to learn more about the Java Tester Applet.<br />
===Projects:===<br />
:*[[Change of Coordinate Systems]]<br />
::*Status: Finished<br />
::*Description: An applet which allows for a visual representation of user defined points in 3-space<br />
::*Link: [http://www.pages.drexel.edu/~mjh96/java/ChangeOfCoords/ChangeOfCoordsApp.html Change of Coordinate Systems Applet]<br />
::*Notes: Finished applet, if you find any bugs, please let me know! email: mjh96@drexel.edu<br />
:*[[Gradients and Directional Derivatives]]<br />
::*Status: Not Started<br />
::*Description:An applet or animation that displays the gradient at different points on a surface<br />
:*[[Vector]]<br />
::*Status: Finished<br />
::*Description: An applet allowing for an interactive representation of 2D vector algebra, mainly consisting of: addition and subtraction. Scalar multiplication was not included as it would be a detriment to the applet's simple point and click interface. However, if anyone feels this feature should be added, I can certainly do so.<br />
::*Link: [http://www.pages.drexel.edu/~mjh96/java/Vector2D/VectorAlgebra2D.html 2D Vector Applet]<br />
::*Notes: If you find any bugs, please let me know! email: mjh96@drexel.edu. Also, I am aware of the annoying tendency of vectors clipping with the bounds of the graph when the addition procedure is carried out.<br />
:*[[Probability Distributions]]<br />
::*Status: Finished<br />
::*Description: An applet allowing the user to simulate rolling a six-sided dice, and graphically keep track of the outcome distribution.<br />
::*Link: [http://www.pages.drexel.edu/~mjh96/java/Prob/DiceProbApp.html Dice Probability Applet]<br />
::*Notes: Let me know if you have any suggestions. email: mjh96@drexel.edu<br />
:*[[Vector | Vector Cross Product]]<br />
::*Status: Not Started (Someone else may pick it up if they wish)<br />
::*Description: An applet allowing the user to enter the components of 2 vectors and display a graphical representation of a vector cross product<br />
:*[[Arithmetic Sequence]]<br />
::*Status: In Progress<br />
::*Description: An applet that generates a random arithmetic sequence and allows the user to fill in missing spots. A geometric version is likely to follow.<br />
<br />
:''Note: If a project is listed as "Not Started," feel free to pick it up if you wish''<br />
<br />
===Week 1 Progress===<br />
:After getting comfortable with writing Java applets, I began to read the Java 3D tutorial provided by Sun. After getting down some of the basics, I began to work on the Change of Coordinates applet. So far I have created a 3D graph that has the ability to graphically display a point in 3-space as specified by the user. This point may then be displayed with a rectangular/cartesian, cylindrical, or spherical representation. As of now, the points are input via the console, yet in the finished version, the user will be able to click any location in 3-space to select a point. The user will also be able to navigate the space with a mouse or keyboard.<br />
<br />
<java_applet code="VectorAlgebra2D.class" width="600" height="350" archive="VectorAlgebra2DApp.jar" /><br />
<java_applet code="DiceProbabilityApp.class" width="800" height ="430" archive="DiceProbApp.jar" /></div>Tcheeseman1https://mathimages.swarthmore.edu/index.php?title=Pascal%27s_Triangle2&diff=7734Pascal's Triangle22009-07-08T17:28:41Z<p>Tcheeseman1: </p>
<hr />
<div>{{Image Description<br />
|ImageName=Pascal's Triangle<br />
|Image=Pascal2.gif<br />
|ImageIntro=Pascal's Triangle<br />
|ImageDescElem=Pascal's triangle is a triangular arrangement of specific numbers which have interesting patterns. We start out with 1 and 1, 1, for the first two rows. To construct each entry in the next row, we sum the two numbers immediately above it to the right and to the left. If there's only one number diagonally above the entry to the left and to the right, then we enter just that number. We can continue doing this endlessly. This pattern is just one of the many patterns within the triangle.<br />
|ImageDesc=Each entry in a Pascal's triangle is identified by a row and a place. The rows are labeled starting from zero, so the first row would be row 0, the second one would be row 1, the third, row 2 and so forth. Places are given to each entry starting from the first number after 1, from the left to the right. 70 for example would be identified as row 8, place 4. <br />
<br />
===Properties===<br />
*The triangle is bordered by 1's on the right and left edges.<br />
*The next line of numbers in diagonal order after the edge numbers are natural numbers 1,2,3,4...<br />
*The next set of numbers inwards after the natural numbers are triangular numbers 1,3,6,10,15...<br />
*After the triangular numbers we have tetrahedral numbers in order 1,4,10,20...<br />
*The next d-diagonal contains the next higher dimensional "d-[http://en.wikipedia.org/wiki/Simplex simplex]" numbers.<br />
*The first number after 1 in each row divides all the other numbers in that row if and only if it is prime.<br />
<br />
===Patterns within Pascal's triangle===<br />
Pascal's triangle contains a number of smaller patterns within it. Some of these patterns include:<br />
<br />
<br />
====Magic 11's====<br />
If a row is made into a single number (omitting the spaces), the resulting number is equal to 11 raised to the <math>n^th</math> power, where <math>n</math> is the row number. For example:<br />
<br />
<table border="2" cellpadding="12"><br />
<th WIDTH="80">Row #</th><br />
<th WIDTH="150">Actual Row</th><br />
<th WIDTH="100">Single Number </th><br />
<th WIDTH="80">Formula</th><br />
<tr><br />
<td>0</td><br />
<td align="center">1</td><br />
<td>1</td><br />
<td><math>11^0</math></td></tr><br />
<tr><br />
<td>1</td><br />
<td align="center">1 1</td><br />
<td>11</td><br />
<td><math>11^1</math></td></tr><br />
<tr><br />
<td>2</td><br />
<td align="center">1 2 1</td><br />
<td>121</td><br />
<td><math>11^2</math></td></tr><br />
<tr><br />
<td>3</td><br />
<td align="center">1 3 3 1</td><br />
<td>1,331</td><br />
<td><math>11^3</math></td></tr><br />
<tr><br />
<td>4</td><br />
<td align="center">1 4 6 4 1</td><br />
<td>14,641</td><br />
<td><math>11^4</math></td></tr><br />
<tr><br />
<td>5</td><br />
<td align="center">1 5 10 10 5 1</td><br />
<td>15,101,051</td><br />
<td><math>11^5</math></td></tr><br />
<tr><br />
<td>6</td><br />
<td align="center">1 6 15 20 15 9 1</td><br />
<td>1,615,201,561</td><br />
<td><math>11^6</math></td></tr></table><br />
<br />
====Hockey Stick Pattern==== <br />
[[Image:hockey.gif|right|thumb|Hockey stick pattern http://ptri1.tripod.com/]]<br />
If we select entries diagonally starting from 1 on the edge up to any point in the triangle, the sum of the numbers selected is equal to the number below the selection that is not on the diagonal. To understand this better, please refer to the tutorial on the below.<br />
<br />
<h4>Fibonacci Sequence</h4><br />
[[Image:pascal4.gif|left|thumb|300px| http://mathforum.org/dr.math/faq/faq.pascal.triangle.html]]<br />
The Fibonacci sequence is a list of Fibonacci numbers. Each Fibonacci number is generated by adding the previous two consecutive terms in the sequence. The first two Fibonacci numbers are 0 and 1. This pattern can be located in Pascal's triangle. The sum of the entries in each row, as shown in the tutorial gives a Fibonacci number.<br />
This creates the sequence 1,1,2,3,5,8,13,21,34,...which is the Fibonacci sequence.<br />
<br><br><br><br><br><br><br><br><br><br><br />
<h4>Sierpenski Triangle</h4>[[Image:pascal.png|right|thumb|Sierpenski triangle generated by coloring odd and even numbers with Pascal's triangle with two different colors http://en.wikipedia.org/wiki/Pascal's_triangle]]<br />
If we are to color the odd and even numbers in Pascal's triangle with two distinct colors, we would observe an interesting recursive pattern seen in the [[Sierpinski's Triangle|Sierpinski triangle]]. You could try this out in the tutorial and see what happens.<br />
<br />
These are just a few of the patterns observed in Pascal's triangle. Other patterns include:<br />
<br />
:*[[Pascal's triangle and points on a circle]]<br />
:*[[Pascal's Triangle and Lozanic's triangle]]<br />
:*[[Pascal's triangle and Catalan Numbers]]<br />
:*[[Pascal's Petals]]<br />
<br />
====Animation Demonstrating Patterns====<br />
The Flash animation below allows you to explore some of the patterns present in Pascal's Triangle:<br />
<br />
<center><flash>file=Pascal3.swf|height=400|width=400</flash></center><br />
<br />
===Applications of Pascal's Triangle===<br />
<br />
====In Algebra====<br />
<br />
Pascal's triangle can be used to determine binomial coefficients in binomial expansions. For example<br />
<br />
<math>(x + y)^2 = x^2 + 2xy + y^2 =1{x^2}{y^0} + {2x^1}{y^1} +{1x^0}{y^2} <br />
</math><br />
<br />
In the above example, notice that the coefficients in the expansion are exactly the same as the entries in row two in Pascal's triangle.<br />
<br />
This is summarized in the [http://en.wikipedia.org/wiki/Binomial_theorem binomial theorem] which states that in general, <br />
<br />
<math>(x + y)^n</math> = <math>{a_0}{x^n}</math> <math>+</math> <math>{a_1}{x^{n-1}}</math> <math>+</math> <math>{a_2}{x^{n-2}}{y^2}</math><math>+</math> … <math>+</math> <math>{a_{n-1}}{xy^{n-1}}</math> <math>+</math> <math>{a_n}{y^n}</math><br />
<br />
<br />
where <math>a_i</math> are the entries in row <math>n</math> in Pascal's triangle.<br />
<br />
<h3>In [http://en.wikipedia.org/wiki/Combinatorics Combinatorics]</h3><br />
<br />
<br />
|AuthorName=Math Forum<br />
|SiteName=Mathforum.org<br />
|SiteURL=http://mathforum.org/workshops/usi/pascal/images/fill.comb.gif<br />
|Field=Algebra<br />
|InProgress=No<br />
}}</div>Tcheeseman1https://mathimages.swarthmore.edu/index.php?title=D09&diff=7097D092009-07-06T16:32:20Z<p>Tcheeseman1: /* Tim */</p>
<hr />
<div><center>'' '''Welcome to the Drexel Summer 09 Entry to [[Image:TmipClear.png|275px]]''' ''!</center><br />
<br />
'''IMPORTANT NOTE: Please put up contact information on Drexel-Swat Partnering page: [[Drexel-Swat_Partnering]]'''<br />
<br />
[[Getting Started]] --- [[A Brief Tour of What's Been Done So Far]]<br />
<br />
----<br />
<br />
'''Things to do:''' <br />
* browse around, leaving comments on the Math Images discussion page and the Swarthmore student's discussion page, looking around for interesting possibilities for interaction on the latter<br />
* look through the Helper Pages in the left navbar and the [http://wikis.swarthmore.edu/miwiki/index.php/Hard_Math Hard Math] page to see if you can find anything you'd like to work on--if there's anything you've struggled with that isn't there, add it!<br />
<br />
----<br />
<br />
<br />
'''[[Math for Computer Graphics and Computer Vision]]'''<br />
<br />
'''Resources:'''<br />
:* [http://www.kirupa.com/developer/flash/index.htm Flash/ActionScript Tutorials]<br />
:* [http://hgbook.red-bean.com/read/ Mercurial Book] (Online)<br />
:* [http://java.sun.com/developer/onlineTraining/java3d/ Java 3D Tutorials]<br />
<br />
<br />
__TOC__<br />
<br />
''' ''Check out the [[Drexel-Swat Partnering]] page to see who's paired up with whom and keep track of what they're working on...'' '''<br />
<br />
==[[User:Tcheeseman1|Tim]]==<br />
===Done===<br />
:* Set up the [http://saturn.cs.drexel.edu/mathimages/ Code Repository]. See README's and examples for standard practice. Requires installing [http://mercurial.selenic.com/wiki/ Mercurial] ([http://sourceforge.net/project/showfiles.php?group_id=199155 Windows Installer]) ([http://www.vectrace.com/mercurialeclipse/ Eclipse Plugin])<br />
:* Re-familiarized myself with ActionScript 3<br />
:* Created an interactive 2D [[Inversion|Point Inversion]] Flash animation<br />
:* Interactive 2D [[Inversion|Shape Inversion]] Flash animation<br />
<br />
===To Do===<br />
:* Learn more Java3D<br />
:* Applet for [[Inversion|Point Inversion]] in 3D<br />
:* Applet for 3D polyhedra Inversion 3D about a sphere to demonstrate creating [[Dual Polyhedron|Dual Polyhedrons]])<br />
<br />
==[[User:Egoldberg1|Emily G.]]==<br />
===Projects:===<br />
:*[[Pascal's Triangle]]-, with input from Lizah using Flash to visualize patterns.<br />
::*Status- Finished & Open for Revision (6/30) [http://www.pages.drexel.edu/~ecg32/mi/work.html See it here] or [[User:Egoldberg1|here]].<br />
:*Rhodonea ([[Cardioid]], Rose Petals, Limacons, etc.)- interactive graphing<br />
::*Status- Investigating the possibility of using a webMathematica applet to accomplish this<br />
:*[[Cantor_Set]] zooming flash loop<br />
::*Status- On hold (revision of strategy necessary).<br />
:*[[Tessellations]] Image Gallery<br />
::*Status- Not Started<br />
:*[[Torus]]- interactive graphing<br />
::*Status- Investigating the possibility of using a webMathematica applet to accomplish this<br />
<br />
====Week One====<br />
:This week after setting up Flash CS4 on my laptop and while familiarizing myself with actionscript3, I began a flash tutorial which explains and visualizes the patterns within [[Pascal's Triangle]]. The final result will be longer than I initially realized. At this point, it almost feels like I'm creating a movie, but that's alright because I want the tutorial to be thorough and to have clear visualizations of the patterns. Without thorough animation, some of the patterns would be particularly hard to see for yourself. Animation is started but not complete for the original triangle, diagonal rows, shallow diagonal rows (Fibonacci sequence), and the even/odd pattern (Sierpenski's triangle). Descriptions are needed for all of the patterns. Animation is not started for the hockey stick pattern. With no snags, I should be able to finish this animation by next Friday.<br />
<br />
====Week Two====<br />
:The majority of the week was spent refining the [[Pascal's Triangle]] tutorial. Specifically, it was spent completing the animations within the tutorial, revising the descriptions/explanations, and debugging. In the final hours of the week, I looked into finding more projects which I can work on in the future, and began developing a flash video which is a looping zoom into a [[Cantor_Set]]. This week I also looked into the use of webMathematica for some applets. I think it will be particularly helpful in the construction of some interactive applets (like the Rhodonea graphing tool or for graphing 3d objects).<br />
<br />
==[[User:Slombardi1|Steve]]==<br />
:Stereographic Projection applet: [http://www.tcnj.edu/~lombar26/StereoProj/StereoProj.html Stereographic Projection]<br />
:Hypotrochoid applet: [http://www.tcnj.edu/~lombar26/Hypotrochoid/Hypotrochoid.html Hypotrochoid]<br />
:Metaballs applet: [http://www.tcnj.edu/~lombar26/ImplicitSurf/ImplicitSurf.html Metaballs]<br />
:Mandelbrot applet: [http://www.tcnj.edu/~lombar26/Mandelbrot/Mandelbrot.html Mandelbrot]<br />
:Koch Snowflake applet: [http://www.tcnj.edu/~lombar26/KochSnowflake/KochSnowflake.html Koch Snowflake]<br />
:Catenary applet: [http://www.tcnj.edu/~lombar26/Catenary/Catenary.html Catenary]<br />
:Julia set applet: [http://www.tcnj.edu/~lombar26/Julia/Julia.html Julia set]<br />
<br />
Test:<br />
<java_applet code="Mandelbrot.class" width="200" height="200" archive="Mandelbrot.jar" /><br />
<br />
==[[User:Asobti1|Ayush]]==<br />
<br />
I'm a Computer Science sophomore at Drexel University. This Summer term (Summer 09) is my first term working on the Math Images project.<br />
<br />
===The Plan:===<br />
:Working with Josh and Alan to add interactivity in the pages previously created by Alan.<br />
:I plan to concentrate on Flash animation while Josh explores the Java.<br />
<br />
<br />
===Work Progress:===<br />
:'''Week 1:'''<br />
::Surfed around the MathImages website. Familiarized myself with the many different pages and projects.<br />
::Spoke with Alan and Josh and made a tentative plan of what is to be achieved in the duration of the research project.<br />
::Installed and set up Adobe Flash CS4. Started reading tutorials and watching videos to learn using Flash.<br />
::Learned basic wiki tags and wiki usage and embedding flash .swf files into wiki<br />
:::<flash>file=Test_anim.swf|width=280|height=200|</flash><br />
::Created a simple flash animation to show matrix multiplication of two 2x2 matrices. May be incorporated in the Matrix helper page.<br />
::<flash>file=Matrix_multiplication_new.swf|width=500|height=300|</flash><br />
<br />
==[[User:Jdicristo1|Josh]]==<br />
<br />
I just completed my freshman year at Drexel, going for a BS in Computer Science<br />
<br />
===Projects:===<br />
:Working with Ayush and Alan to add interactivity in the pages previously created by Alan.<br />
:Working mainly with Java<br />
<br />
===Progress After Week 1===<br />
Because I am really working on this project part-time I did not make any major strides this week but I did get a few things accomplished<br />
: I learned the basics of writing Java Applets<br />
: I'm about 1/3 of the way done a program that segments a rectangle into thirds and then illustrates the Golden Spiral<br />
<br />
==[[User:Mhershey1|Mhershey1]]==<br />
What I have so far: http://www.pages.drexel.edu/~smh86/index.html<br />
:*[[Blue Wash]], applet changing ''k'' (in '''Inclined Recursive Method''') & animation drawing the basic no ''k'' method (in '''Basic Recursive Method''') <br />
:*[[Blue Fern]], [[Henon Attractor]], redo the animations with small points<br />
:*[[Hyperbolic Tilings]], applet where users input Schläfli symbol to create a tiling<br />
:**This is far too hard for me to do. I took the applet someone made from http://aleph0.clarku.edu/~djoyce/poincare/PoincareApplet.html and decompiled it, but I still didn't understand the math they were using. Maybe someone else can do this one, or we could just use the already made applet?<br />
:*[[Newton's Basin]], redo the animation (maybe users input the equations)<br />
:*[[Logarithms]], interactive quiz with exponential and logarithmic equations<br />
:*[[Harter-Heighway Dragon]], animating the curve at each iteration stage<br />
<br />
==[[User:Mhinkle1|Matt]]==<br />
===Projects:===<br />
:*[[Change of Coordinate Systems]]::An applet which allows for a visual representation of user defined points in 2-space and 3-space<br />
::*[http://www.pages.drexel.edu/~mjh96/java/coordsapp.html Change of Coordinate Systems Applet -- Java 3D not installed] (Click the area labeled "Coordinate System Display" if nothing appears after loading to display the graph)<br />
::*[http://www.pages.drexel.edu/~mjh96/java/coordsapp_alt.html Change of Coordinate Systems Applet -- Java 3D installed]<br />
::A demo version of the Change of Coordinate Systems Applet. It's nearly finished, I just need to place some restrictions on what the user can do and fix some other bugs. To navigate the view pane, simply use the right and left arrow keys to rotate around the Z-axis and use the up and down keys to zoom in and out.<br />
::I was unable to implement the "mouse click point selection" as the requirements for such an input system turned out to be impractical. It was also decided that such input behavior would be confusing for the user as well. As of now, the user inputs a point by simply entering its parameters and clicking a button to update the view pane.<br />
:*[[Gradients and Directional Derivatives]]::An applet or animation that displays the gradient at different points on a surface<br />
<br />
===Week 1 Progress===<br />
:After getting comfortable with writing Java applets, I began to read the Java 3D tutorial provided by Sun. After getting down some of the basics, I began to work on the Change of Coordinates applet. So far I have created a 3D graph that has the ability to graphically display a point in 3-space as specified by the user. This point may then be displayed with a rectangular/cartesian, cylindrical, or spherical representation. As of now, the points are input via the console, yet in the finished version, the user will be able to click any location in 3-space to select a point. The user will also be able to navigate the space with a mouse or keyboard.</div>Tcheeseman1https://mathimages.swarthmore.edu/index.php?title=File:ShapeInversion2D.swf&diff=7095File:ShapeInversion2D.swf2009-07-06T16:29:33Z<p>Tcheeseman1: uploaded a new version of "Image:ShapeInversion2D.swf"</p>
<hr />
<div></div>Tcheeseman1https://mathimages.swarthmore.edu/index.php?title=D09&diff=6947D092009-07-02T18:48:59Z<p>Tcheeseman1: /* Tim */</p>
<hr />
<div><center>'' '''Welcome to the Drexel Summer 09 Entry to [[Image:TmipClear.png|275px]]''' ''!</center><br />
<br />
'''IMPORTANT NOTE: Please put up contact information on Drexel-Swat Partnering page: [[Drexel-Swat_Partnering]]'''<br />
<br />
[[Getting Started]] --- [[A Brief Tour of What's Been Done So Far]]<br />
<br />
----<br />
<br />
'''Things to do:''' <br />
* browse around, leaving comments on the Math Images discussion page and the Swarthmore student's discussion page, looking around for interesting possibilities for interaction on the latter<br />
* look through the Helper Pages in the left navbar and the [http://wikis.swarthmore.edu/miwiki/index.php/Hard_Math Hard Math] page to see if you can find anything you'd like to work on--if there's anything you've struggled with that isn't there, add it!<br />
<br />
----<br />
<br />
<br />
'''[[Math for Computer Graphics and Computer Vision]]'''<br />
<br />
'''Resources:'''<br />
:* [http://www.kirupa.com/developer/flash/index.htm Flash/ActionScript Tutorials]<br />
:* [http://hgbook.red-bean.com/read/ Mercurial Book] (Online)<br />
:* [http://java.sun.com/developer/onlineTraining/java3d/ Java 3D Tutorials]<br />
<br />
<br />
__TOC__<br />
<br />
''' ''Check out the [[Drexel-Swat Partnering]] page to see who's paired up with whom and keep track of what they're working on...'' '''<br />
<br />
==[[User:Tcheeseman1|Tim]]==<br />
===Week 1===<br />
:* Set up the [http://saturn.cs.drexel.edu/mathimages/ Code Repository]. See README's and examples for standard practice. Requires installing [http://mercurial.selenic.com/wiki/ Mercurial] ([http://sourceforge.net/project/showfiles.php?group_id=199155 Windows Installer]) ([http://www.vectrace.com/mercurialeclipse/ Eclipse Plugin])<br />
:* Re-familiarize myself with ActionScript 3 and created an interactive 2D [[Inversion|Point Inversion]] Flash animation:<br />
<flash>file=PointInversion2D.swf|width=500|height=500|</flash><br />
<br />
===Week 2===<br />
:* Interactive 2D [[Inversion|Shape Inversion]] Flash animation:<br />
<flash>file=ShapeInversion2D.swf|width=500|height=500|</flash><br />
<br />
===To Do List===<br />
:* Applet for [[Inversion|Point Inversion]] in 3D<br />
:* Applet for 3D polyhedra Inversion 3D about a sphere to demonstrate creating [[Dual Polyhedron|Dual Polyhedrons]])<br />
<br />
==[[User:Egoldberg1|Emily G.]]==<br />
===Projects:===<br />
:*[[Pascal's Triangle]]-, with input from Lizah using Flash to visualize patterns.<br />
::*Status- Finished & Open for Revision (6/30) [http://www.pages.drexel.edu/~ecg32/mi/work.html See it here] or [[User:Egoldberg1|here]].<br />
:*Rhodonea ([[Cardioid]], Rose Petals, Limacons, etc.)- interactive graphing<br />
::*Status- Investigating the possibility of using a webMathematica applet to accomplish this<br />
:*[[Tessellations]] Image Gallery<br />
::*Status- Not Started<br />
<br />
====Week One====<br />
:This week after setting up Flash CS4 on my laptop and while familiarizing myself with actionscript3, I began a flash tutorial which explains and visualizes the patterns within Pascal's Triangle. The final result will be longer than I initially realized. At this point, it almost feels like I'm creating a movie, but that's alright because I want the tutorial to be thorough and to have clear visualizations of the patterns. Without thorough animation, some of the patterns would be particularly hard to see for yourself. Animation is started but not complete for the original triangle, diagonal rows, shallow diagonal rows (Fibonacci sequence), and the even/odd pattern (Sierpenski's triangle). Descriptions are needed for all of the patterns. Animation is not started for the hockey stick pattern. With no snags, I should be able to finish this animation by next Friday.<br />
<br />
==[[User:Slombardi1|Steve]]==<br />
:Stereographic Projection applet: [http://www.tcnj.edu/~lombar26/StereoProj/StereoProj.html Stereographic Projection]<br />
:Hypotrochoid applet: [http://www.tcnj.edu/~lombar26/Hypotrochoid/Hypotrochoid.html Hypotrochoid]<br />
:Metaballs applet: [http://www.tcnj.edu/~lombar26/ImplicitSurf/ImplicitSurf.html Metaballs]<br />
:Mandelbrot applet: [http://www.tcnj.edu/~lombar26/Mandelbrot/Mandelbrot.html Mandelbrot]<br />
:Koch Snowflake applet: [http://www.tcnj.edu/~lombar26/KochSnowflake/KochSnowflake.html Koch Snowflake]<br />
<br />
Test:<br />
<java_applet code="Mandelbrot.class" width="200" height="200" archive="Mandelbrot.jar" /><br />
<br />
==[[User:Asobti1|Ayush]]==<br />
<br />
I'm a Computer Science sophomore at Drexel University. This Summer term (Summer 09) is my first term working on the Math Images project.<br />
<br />
===The Plan:===<br />
:Working with Josh and Alan to add interactivity in the pages previously created by Alan.<br />
:I plan to concentrate on Flash animation while Josh explores the Java.<br />
<br />
<br />
===Work Progress:===<br />
:'''Week 1:'''<br />
::Surfed around the MathImages website. Familiarized myself with the many different pages and projects.<br />
::Spoke with Alan and Josh and made a tentative plan of what is to be achieved in the duration of the research project.<br />
::Installed and set up Adobe Flash CS4. Started reading tutorials and watching videos to learn using Flash.<br />
::Learned basic wiki tags and wiki usage and embedding flash .swf files into wiki<br />
:::<flash>file=Test_anim.swf|width=280|height=200|</flash><br />
::Created a simple flash animation to show matrix multiplication of two 2x2 matrices. May be incorporated in the Matrix helper page.<br />
::<flash>file=Matrix_multiplication_new.swf|width=500|height=300|</flash><br />
<br />
==[[User:Jdicristo1|Josh]]==<br />
<br />
I just completed my freshman year at Drexel, going for a BS in Computer Science<br />
<br />
===Projects:===<br />
:Working with Ayush and Alan to add interactivity in the pages previously created by Alan.<br />
:Working mainly with Java<br />
<br />
===Progress After Week 1===<br />
Because I am really working on this project part-time I did not make any major strides this week but I did get a few things accomplished<br />
: I learned the basics of writing Java Applets<br />
: I'm about 1/3 of the way done a program that segments a rectangle into thirds and then illustrates the Golden Spiral<br />
<br />
==[[User:Mhershey1|Mhershey1]]==<br />
What I have so far: http://www.pages.drexel.edu/~smh86/index.html<br />
:*[[Blue Wash]], applet changing ''k'' (in '''Inclined Recursive Method''') & animation drawing the basic no ''k'' method (in '''Basic Recursive Method''') <br />
:*[[Blue Fern]], [[Henon Attractor]], redo the animations with small points<br />
:*[[Hyperbolic Tilings]], applet where users input Schläfli symbol to create a tiling<br />
:**This is far too hard for me to do. I took the applet someone made from http://aleph0.clarku.edu/~djoyce/poincare/PoincareApplet.html and decompiled it, but I still didn't understand the math they were using. Maybe someone else can do this one, or we could just use the already made applet?<br />
:*[[Newton's Basin]], redo the animation (maybe users input the equations)<br />
:*[[Logarithms]], interactive quiz with exponential and logarithmic equations<br />
:*[[Harter-Heighway Dragon]], animating the curve at each iteration stage<br />
<br />
==[[User:Mhinkle1|Matt]]==<br />
===Projects:===<br />
:*[[Change of Coordinate Systems]]::An applet which allows for a visual representation of user defined points in 2-space and 3-space<br />
:*[[Gradients and Directional Derivatives]]::An applet or animation that displays the gradient at different points on a surface<br />
<br />
===Week 1 Progress===<br />
:After getting comfortable with writing Java applets, I began to read the Java 3D tutorial provided by Sun. After getting down some of the basics, I began to work on the Change of Coordinates applet. So far I have created a 3D graph that has the ability to graphically display a point in 3-space as specified by the user. This point may then be displayed with a rectangular/cartesian, cylindrical, or spherical representation. As of now, the points are input via the console, yet in the finished version, the user will be able to click any location in 3-space to select a point. The user will also be able to navigate the space with a mouse or keyboard.</div>Tcheeseman1https://mathimages.swarthmore.edu/index.php?title=File:ShapeInversion2D.swf&diff=6946File:ShapeInversion2D.swf2009-07-02T18:47:14Z<p>Tcheeseman1: </p>
<hr />
<div></div>Tcheeseman1https://mathimages.swarthmore.edu/index.php?title=D09&diff=6725D092009-07-01T16:57:47Z<p>Tcheeseman1: </p>
<hr />
<div><center>'' '''Welcome to the Drexel Summer 09 Entry to [[Image:TmipClear.png|275px]]''' ''!</center><br />
<br />
'''IMPORTANT NOTE: Please put up contact information on Drexel-Swat Partnering page: [[Drexel-Swat_Partnering]]'''<br />
<br />
[[Getting Started]] --- [[A Brief Tour of What's Been Done So Far]]<br />
<br />
----<br />
<br />
'''Things to do:''' <br />
* browse around, leaving comments on the Math Images discussion page and the Swarthmore student's discussion page, looking around for interesting possibilities for interaction on the latter<br />
* look through the Helper Pages in the left navbar and the [http://wikis.swarthmore.edu/miwiki/index.php/Hard_Math Hard Math] page to see if you can find anything you'd like to work on--if there's anything you've struggled with that isn't there, add it!<br />
<br />
----<br />
<br />
<br />
'''[[Math for Computer Graphics and Computer Vision]]'''<br />
<br />
'''Resources:'''<br />
:* [http://www.kirupa.com/developer/flash/index.htm Flash/ActionScript Tutorials]<br />
:* [http://hgbook.red-bean.com/read/ Mercurial Book] (Online)<br />
:* [http://java.sun.com/developer/onlineTraining/java3d/ Java 3D Tutorials]<br />
<br />
<br />
__TOC__<br />
<br />
''' ''Check out the [[Drexel-Swat Partnering]] page to see who's paired up with whom and keep track of what they're working on...'' '''<br />
<br />
==[[User:Tcheeseman1|Tim]]==<br />
===Week 1===<br />
:* Set up the [http://saturn.cs.drexel.edu/mathimages/ Code Repository]. See README's and examples for standard practice. Requires installing [http://mercurial.selenic.com/wiki/ Mercurial] ([http://sourceforge.net/project/showfiles.php?group_id=199155 Windows Installer]) ([http://www.vectrace.com/mercurialeclipse/ Eclipse Plugin])<br />
:* Re-familiarize myself with ActionScript 3 and created an interactive 2D [[Inversion|Point Inversion]] Flash animation:<br />
<flash>file=PointInversion2D.swf|width=500|height=500|</flash><br />
<br />
===To Do List===<br />
:* Applet for [[Inversion|Point Inversion]] in 3D<br />
:* Applet for Shape Inversion (2D shapes about a circle and 3D polyhedra about a sphere to demonstrate creating [[Dual Polyhedron|Dual Polyhedrons]])<br />
<br />
==[[User:Egoldberg1|Emily G.]]==<br />
===Projects:===<br />
:*[[Pascal's Triangle]]-, with input from Lizah using Flash to visualize patterns.<br />
::*Status- Finished & Open for Revision (6/30) [http://www.pages.drexel.edu/~ecg32/mi/work.html See it here]<br />
:*Rhodonea ([[Cardioid]], Rose Petals, Limacons, etc.)- interactive graphing<br />
::*Status- Not Started<br />
:*[[Tessellations]] Image Gallery<br />
::*Status- Not Started<br />
<br />
====Week One====<br />
:This week after setting up Flash CS4 on my laptop and while familiarizing myself with actionscript3, I began a flash tutorial which explains and visualizes the patterns within Pascal's Triangle. The final result will be longer than I initially realized. At this point, it almost feels like I'm creating a movie, but that's alright because I want the tutorial to be thorough and to have clear visualizations of the patterns. Without thorough animation, some of the patterns would be particularly hard to see for yourself. Animation is started but not complete for the original triangle, diagonal rows, shallow diagonal rows (Fibonacci sequence), and the even/odd pattern (Sierpenski's triangle). Descriptions are needed for all of the patterns. Animation is not started for the hockey stick pattern. With no snags, I should be able to finish this animation by next Friday.<br />
<br />
==[[User:Slombardi1|Steve]]==<br />
:Stereographic Projection applet: [http://www.tcnj.edu/~lombar26/StereoProj/StereoProj.html Stereographic Projection]<br />
:Hypotrochoid applet: [http://www.tcnj.edu/~lombar26/Hypotrochoid/Hypotrochoid.html Hypotrochoid]<br />
:Metaballs applet: [http://www.tcnj.edu/~lombar26/ImplicitSurf/ImplicitSurf.html Metaballs]<br />
:Mandelbrot applet: [http://www.tcnj.edu/~lombar26/Mandelbrot/Mandelbrot.html Mandelbrot]<br />
<br />
==[[User:Asobti1|Ayush]]==<br />
<br />
I'm a Computer Science sophomore at Drexel University. This Summer term (Summer 09) is my first term working on the Math Images project.<br />
<br />
===The Plan:===<br />
:Working with Josh and Alan to add interactivity in the pages previously created by Alan.<br />
:I plan to concentrate on Flash animation while Josh explores the Java.<br />
<br />
<br />
===Work Progress:===<br />
:'''Week 1:'''<br />
::Surfed around the MathImages website. Familiarized myself with the many different pages and projects.<br />
::Spoke with Alan and Josh and made a tentative plan of what is to be achieved in the duration of the research project.<br />
::Installed and set up Adobe Flash CS4. Started reading tutorials and watching videos to learn using Flash.<br />
::Learned basic wiki tags and wiki usage and embedding flash .swf files into wiki<br />
:::<flash>file=Test_anim.swf|width=280|height=200|</flash><br />
::Created a simple flash animation to show matrix multiplication of two 2x2 matrices. May be incorporated in the Matrix helper page.<br />
::<flash>file=Matrix_multiplication_new.swf|width=500|height=300|</flash><br />
<br />
==[[User:Jdicristo1|Josh]]==<br />
<br />
I just completed my freshman year at Drexel, going for a BS in Computer Science<br />
<br />
===Projects:===<br />
:Working with Ayush and Alan to add interactivity in the pages previously created by Alan.<br />
:Working mainly with Java<br />
<br />
===Progress After Week 1===<br />
Because I am really working on this project part-time I did not make any major strides this week but I did get a few things accomplished<br />
: I learned the basics of writing Java Applets<br />
: I'm about 1/3 of the way done a program that segments a rectangle into thirds and then illustrates the Golden Spiral<br />
<br />
==[[User:Mhershey1|Mhershey1]]==<br />
What I have so far: http://www.pages.drexel.edu/~smh86/index.html<br />
:*[[Blue Wash]] with Emily, applet changing ''k'' (in '''Inclined Recursive Method''') & animation drawing the basic no ''k'' method (in '''Basic Recursive Method''') <br />
:*[[Blue Fern]], [[Henon Attractor]], redo the animations with small points<br />
:*[[Hyperbolic Tilings]], applet where users input Schläfli symbol to create a tiling<br />
:*[[Newton's Basin]], redo the animation (maybe users input the equations)<br />
:*[[Logarithms]], interactive quiz with exponential and logarithmic equations<br />
:*[[Harter-Heighway Dragon]], animating the curve at each iteration stage<br />
<br />
==[[User:Mhinkle1|Matt]]==<br />
===Projects:===<br />
:*[[Change of Coordinate Systems]]::An applet which allows for a visual representation of user defined points in 2-space and 3-space<br />
:*[[Gradients and Directional Derivatives]]::An applet or animation that displays the gradient at different points on a surface<br />
<br />
===Week 1 Progress===<br />
:After getting comfortable with writing Java applets, I began to read the Java 3D tutorial provided by Sun. After getting down some of the basics, I began to work on the Change of Coordinates applet. So far I have created a 3D graph that has the ability to graphically display a point in 3-space as specified by the user. This point may then be displayed with a rectangular/cartesian, cylindrical, or spherical representation. As of now, the points are input via the console, yet in the finished version, the user will be able to click any location in 3-space to select a point. The user will also be able to navigate the space with a mouse or keyboard.</div>Tcheeseman1https://mathimages.swarthmore.edu/index.php?title=Math_for_Computer_Graphics_and_Computer_Vision&diff=6724Math for Computer Graphics and Computer Vision2009-07-01T16:57:14Z<p>Tcheeseman1: </p>
<hr />
<div>The Drexel group may also want to focus on the math used in computer graphics<br />
and computer vision. Here are some examples.<br />
<br />
:* Vectors and matrices<br />
:* Transformations<br />
:* Quaternions<br />
:* Hierarchical coordinate systems<br />
:* Geometry<br />
::* Curves (Catmull-Rom, Bezier, B-spline)<br />
::* Bezier patches<br />
::* Subdivision surfaces<br />
::* Implicit geometry - lines, circles, ellipses<br />
::* Implicit surfaces - quadrics, superquadrics<br />
:* Surface normals<br />
:* Silhouette edges<br />
:* Procedural texture maps<br />
:* Ray-object intersection<br />
:* Perspective and parallel projection<br />
:* Edge detection<br />
:* Fourier analysis and convolution<br />
<br />
More examples may be found in the lecture slides of [http://www.cs.drexel.edu/~david/Classes/CS430 CS 430].</div>Tcheeseman1https://mathimages.swarthmore.edu/index.php?title=D09&diff=6568D092009-06-30T16:06:39Z<p>Tcheeseman1: /* Week 1 */</p>
<hr />
<div><center>'' '''Welcome to the Drexel Summer 09 Entry to [[Image:TmipClear.png|275px]]''' ''!</center><br />
<br />
<br />
[[Getting Started]] --- [[A Brief Tour of What's Been Done So Far]]<br />
<br />
----<br />
<br />
'''Things to do:''' <br />
* browse around, leaving comments on the Math Images discussion page and the Swarthmore student's discussion page, looking around for interesting possibilities for interaction on the latter<br />
* look through the Helper Pages in the left navbar and the [http://wikis.swarthmore.edu/miwiki/index.php/Hard_Math Hard Math] page to see if you can find anything you'd like to work on--if there's anything you've struggled with that isn't there, add it!<br />
<br />
----<br />
<br />
<br />
'''[[Math for Computer Graphics and Computer Vision]]'''<br />
<br />
<br />
__TOC__<br />
<br />
''' ''Check out the [[Drexel-Swat Partnering]] page to see who's paired up with whom and keep track of what they're working on...'' '''<br />
<br />
==[[User:Tcheeseman1|Tim]]==<br />
===Week 1===<br />
:* Set up the [http://saturn.cs.drexel.edu/mathimages/ Code Repository]. See README's and examples for standard practice. Requires installing [http://mercurial.selenic.com/wiki/ Mercurial] ([http://sourceforge.net/project/showfiles.php?group_id=199155 Windows Installer]) ([http://www.vectrace.com/mercurialeclipse/ Eclipse Plugin])<br />
:* Re-familiarize myself with ActionScript 3 and created an interactive 2D [[Inversion|Point Inversion]] Flash animation:<br />
<flash>file=PointInversion2D.swf|width=500|height=500|</flash><br />
<br />
===To Do List===<br />
:* Applet for [[Inversion|Point Inversion]] in 3D<br />
:* Applet for Shape Inversion (2D shapes about a circle and 3D polyhedra about a sphere to demonstrate creating [[Dual Polyhedron|Dual Polyhedrons]])<br />
<br />
==[[User:Egoldberg1|Emily G.]]==<br />
===Projects:===<br />
:*[[Pascal's Triangle]]-, with input from Lizah using Flash to visualize patterns<br />
::*Status- In Progress, creating a Flash tutorial of sorts to demonstrate/explain the patterns that are found in the triangle.<br />
:*Rhodonea ([[Cardioid]], Rose Petals, Limacons, etc.)- interactive graphing<br />
::*Status- Not Started<br />
:*[[Tessellations]] Image Gallery<br />
::*Status- Not Started<br />
<br />
====Week One====<br />
:This week after setting up Flash CS4 on my laptop and while familiarizing myself with actionscript3, I began a flash tutorial which explains and visualizes the patterns within Pascal's Triangle. The final result will be longer than I initially realized. At this point, it almost feels like I'm creating a movie, but that's alright because I want the tutorial to be thorough and to have clear visualizations of the patterns. Without thorough animation, some of the patterns would be particularly hard to see for yourself. Animation is started but not complete for the original triangle, diagonal rows, shallow diagonal rows (Fibonacci sequence), and the even/odd pattern (Sierpenski's triangle). Descriptions are needed for all of the patterns. Animation is not started for the hockey stick pattern. With no snags, I should be able to finish this animation by next Friday.<br />
<br />
==[[User:Slombardi1|Steve]]==<br />
:Stereographic Projection applet: [http://www.tcnj.edu/~lombar26/StereoProj/StereoProj.html Stereographic Projection]<br />
:Hypotrochoid applet: [http://www.tcnj.edu/~lombar26/Hypotrochoid/Hypotrochoid.html Hypotrochoid]<br />
:Metaballs applet: [http://www.tcnj.edu/~lombar26/ImplicitSurf/ImplicitSurf.html Metaballs]<br />
:Mandelbrot applet: [http://www.tcnj.edu/~lombar26/Mandelbrot/Mandelbrot.html Mandelbrot]<br />
<br />
==[[User:Asobti1|Ayush]]==<br />
<br />
I'm a Computer Science sophomore at Drexel University. This Summer term (Summer 09) is my first term working on the Math Images project.<br />
<br />
===The Plan:===<br />
:Working with Josh and Alan to add interactivity in the pages previously created by Alan.<br />
:I plan to concentrate on Flash animation while Josh explores the Java.<br />
<br />
<br />
===Work Progress:===<br />
:'''Week 1:'''<br />
::Surfed around the MathImages website. Familiarized myself with the many different pages and projects.<br />
::Spoke with Alan and Josh and made a tentative plan of what is to be achieved in the duration of the research project.<br />
::Installed and set up Adobe Flash CS4. Started reading tutorials and watching videos to learn using Flash.<br />
::Learned basic wiki tags and wiki usage and embedding flash .swf files into wiki<br />
:::<flash>file=Test_anim.swf|width=280|height=200|</flash><br />
::Created a simple flash animation to show matrix multiplication of two 2x2 matrices. May be incorporated in the Matrix helper page.<br />
::<flash>file=Matrix_multiplication_new.swf|width=500|height=300|</flash><br />
<br />
==[[User:Jdicristo1|Josh]]==<br />
<br />
I just completed my freshman year at Drexel, going for a BS in Computer Science<br />
<br />
===Projects:===<br />
:Working with Ayush and Alan to add interactivity in the pages previously created by Alan.<br />
:Working mainly with Java<br />
<br />
===Progress After Week 1===<br />
Because I am really working on this project part-time I did not make any major strides this week but I did get a few things accomplished<br />
: I learned the basics of writing Java Applets<br />
: I'm about 1/3 of the way done a program that segments a rectangle into thirds and then illustrates the Golden Spiral<br />
<br />
==[[User:Mhershey1|Mhershey1]]==<br />
What I have so far: http://www.pages.drexel.edu/~smh86/index.html<br />
:*[[Blue Wash]] with Emily, applet changing ''k'' (in '''Inclined Recursive Method''') & animation drawing the basic no ''k'' method (in '''Basic Recursive Method''') <br />
:*[[Blue Fern]], [[Henon Attractor]], redo the animations with small points<br />
:*[[Hyperbolic Tilings]], applet where users input Schläfli symbol to create a tiling<br />
:*[[Newton's Basin]], redo the animation (maybe users input the equations)<br />
:*[[Logarithms]], interactive quiz with exponential and logarithmic equations<br />
:*[[Harter-Heighway Dragon]], animating the curve at each iteration stage<br />
<br />
==[[User:Mhinkle1|Matt]]==<br />
===Projects:===<br />
:*[[Change of Coordinate Systems]]::An applet which allows for a visual representation of user defined points in 2-space and 3-space<br />
:*[[Gradients and Directional Derivatives]]::An applet or animation that displays the gradient at different points on a surface<br />
<br />
===Week 1 Progress===<br />
:After getting comfortable with writing Java applets, I began to read the Java 3D tutorial provided by Sun. After getting down some of the basics, I began to work on the Change of Coordinates applet. So far I have created a 3D graph that has the ability to graphically display a point in 3-space as specified by the user. This point may then be displayed with a rectangular/cartesian, cylindrical, or spherical representation. As of now, the points are input via the console, yet in the finished version, the user will be able to click any location in 3-space to select a point. The user will also be able to navigate the space with a mouse or keyboard.</div>Tcheeseman1https://mathimages.swarthmore.edu/index.php?title=File:PointInversion2D.swf&diff=6567File:PointInversion2D.swf2009-06-30T16:06:27Z<p>Tcheeseman1: </p>
<hr />
<div></div>Tcheeseman1https://mathimages.swarthmore.edu/index.php?title=D09&diff=6566D092009-06-30T16:05:43Z<p>Tcheeseman1: /* Week 1 */</p>
<hr />
<div><center>'' '''Welcome to the Drexel Summer 09 Entry to [[Image:TmipClear.png|275px]]''' ''!</center><br />
<br />
<br />
[[Getting Started]] --- [[A Brief Tour of What's Been Done So Far]]<br />
<br />
----<br />
<br />
'''Things to do:''' <br />
* browse around, leaving comments on the Math Images discussion page and the Swarthmore student's discussion page, looking around for interesting possibilities for interaction on the latter<br />
* look through the Helper Pages in the left navbar and the [http://wikis.swarthmore.edu/miwiki/index.php/Hard_Math Hard Math] page to see if you can find anything you'd like to work on--if there's anything you've struggled with that isn't there, add it!<br />
<br />
----<br />
<br />
<br />
'''[[Math for Computer Graphics and Computer Vision]]'''<br />
<br />
<br />
__TOC__<br />
<br />
''' ''Check out the [[Drexel-Swat Partnering]] page to see who's paired up with whom and keep track of what they're working on...'' '''<br />
<br />
==[[User:Tcheeseman1|Tim]]==<br />
===Week 1===<br />
:* Set up the [http://saturn.cs.drexel.edu/mathimages/ Code Repository]. See README's and examples for standard practice. Requires installing [http://mercurial.selenic.com/wiki/ Mercurial] ([http://sourceforge.net/project/showfiles.php?group_id=199155 Windows Installer]) ([http://www.vectrace.com/mercurialeclipse/ Eclipse Plugin])<br />
:* Re-familiarize myself with ActionScript 3 and created an interactive 2D [[Inversion|Point Inversion]] Flash animation:<br />
<flash>file=PointInversion2D.swf|width=500|height=300|</flash><br />
<br />
===To Do List===<br />
:* Applet for [[Inversion|Point Inversion]] in 3D<br />
:* Applet for Shape Inversion (2D shapes about a circle and 3D polyhedra about a sphere to demonstrate creating [[Dual Polyhedron|Dual Polyhedrons]])<br />
<br />
==[[User:Egoldberg1|Emily G.]]==<br />
===Projects:===<br />
:*[[Pascal's Triangle]]-, with input from Lizah using Flash to visualize patterns<br />
::*Status- In Progress, creating a Flash tutorial of sorts to demonstrate/explain the patterns that are found in the triangle.<br />
:*Rhodonea ([[Cardioid]], Rose Petals, Limacons, etc.)- interactive graphing<br />
::*Status- Not Started<br />
:*[[Tessellations]] Image Gallery<br />
::*Status- Not Started<br />
<br />
====Week One====<br />
:This week after setting up Flash CS4 on my laptop and while familiarizing myself with actionscript3, I began a flash tutorial which explains and visualizes the patterns within Pascal's Triangle. The final result will be longer than I initially realized. At this point, it almost feels like I'm creating a movie, but that's alright because I want the tutorial to be thorough and to have clear visualizations of the patterns. Without thorough animation, some of the patterns would be particularly hard to see for yourself. Animation is started but not complete for the original triangle, diagonal rows, shallow diagonal rows (Fibonacci sequence), and the even/odd pattern (Sierpenski's triangle). Descriptions are needed for all of the patterns. Animation is not started for the hockey stick pattern. With no snags, I should be able to finish this animation by next Friday.<br />
<br />
==[[User:Slombardi1|Steve]]==<br />
:Stereographic Projection applet: [http://www.tcnj.edu/~lombar26/StereoProj/StereoProj.html Stereographic Projection]<br />
:Hypotrochoid applet: [http://www.tcnj.edu/~lombar26/Hypotrochoid/Hypotrochoid.html Hypotrochoid]<br />
:Metaballs applet: [http://www.tcnj.edu/~lombar26/ImplicitSurf/ImplicitSurf.html Metaballs]<br />
:Mandelbrot applet: [http://www.tcnj.edu/~lombar26/Mandelbrot/Mandelbrot.html Mandelbrot]<br />
<br />
==[[User:Asobti1|Ayush]]==<br />
<br />
I'm a Computer Science sophomore at Drexel University. This Summer term (Summer 09) is my first term working on the Math Images project.<br />
<br />
===The Plan:===<br />
:Working with Josh and Alan to add interactivity in the pages previously created by Alan.<br />
:I plan to concentrate on Flash animation while Josh explores the Java.<br />
<br />
<br />
===Work Progress:===<br />
:'''Week 1:'''<br />
::Surfed around the MathImages website. Familiarized myself with the many different pages and projects.<br />
::Spoke with Alan and Josh and made a tentative plan of what is to be achieved in the duration of the research project.<br />
::Installed and set up Adobe Flash CS4. Started reading tutorials and watching videos to learn using Flash.<br />
::Learned basic wiki tags and wiki usage and embedding flash .swf files into wiki<br />
:::<flash>file=Test_anim.swf|width=280|height=200|</flash><br />
::Created a simple flash animation to show matrix multiplication of two 2x2 matrices. May be incorporated in the Matrix helper page.<br />
::<flash>file=Matrix_multiplication_new.swf|width=500|height=300|</flash><br />
<br />
==[[User:Jdicristo1|Josh]]==<br />
<br />
I just completed my freshman year at Drexel, going for a BS in Computer Science<br />
<br />
===Projects:===<br />
:Working with Ayush and Alan to add interactivity in the pages previously created by Alan.<br />
:Working mainly with Java<br />
<br />
===Progress After Week 1===<br />
Because I am really working on this project part-time I did not make any major strides this week but I did get a few things accomplished<br />
: I learned the basics of writing Java Applets<br />
: I'm about 1/3 of the way done a program that segments a rectangle into thirds and then illustrates the Golden Spiral<br />
<br />
==[[User:Mhershey1|Mhershey1]]==<br />
What I have so far: http://www.pages.drexel.edu/~smh86/index.html<br />
:*[[Blue Wash]] with Emily, applet changing ''k'' (in '''Inclined Recursive Method''') & animation drawing the basic no ''k'' method (in '''Basic Recursive Method''') <br />
:*[[Blue Fern]], [[Henon Attractor]], redo the animations with small points<br />
:*[[Hyperbolic Tilings]], applet where users input Schläfli symbol to create a tiling<br />
:*[[Newton's Basin]], redo the animation (maybe users input the equations)<br />
:*[[Logarithms]], interactive quiz with exponential and logarithmic equations<br />
:*[[Harter-Heighway Dragon]], animating the curve at each iteration stage<br />
<br />
==[[User:Mhinkle1|Matt]]==<br />
===Projects:===<br />
:*[[Change of Coordinate Systems]]::An applet which allows for a visual representation of user defined points in 2-space and 3-space<br />
:*[[Gradients and Directional Derivatives]]::An applet or animation that displays the gradient at different points on a surface<br />
<br />
===Week 1 Progress===<br />
:After getting comfortable with writing Java applets, I began to read the Java 3D tutorial provided by Sun. After getting down some of the basics, I began to work on the Change of Coordinates applet. So far I have created a 3D graph that has the ability to graphically display a point in 3-space as specified by the user. This point may then be displayed with a rectangular/cartesian, cylindrical, or spherical representation. As of now, the points are input via the console, yet in the finished version, the user will be able to click any location in 3-space to select a point. The user will also be able to navigate the space with a mouse or keyboard.</div>Tcheeseman1https://mathimages.swarthmore.edu/index.php?title=D09&diff=6489D092009-06-29T22:07:12Z<p>Tcheeseman1: /* Week 1 */</p>
<hr />
<div><center>'' '''Welcome to the Drexel Summer 09 Entry to [[Image:TmipClear.png|275px]]''' ''!</center><br />
<br />
<br />
[[Getting Started]] --- [[A Brief Tour of What's Been Done So Far]]<br />
<br />
----<br />
<br />
'''Things to do:''' <br />
* browse around, leaving comments on the Math Images discussion page and the Swarthmore student's discussion page, looking around for interesting possibilities for interaction on the latter<br />
* look through the Helper Pages in the left navbar and the [http://wikis.swarthmore.edu/miwiki/index.php/Hard_Math Hard Math] page to see if you can find anything you'd like to work on--if there's anything you've struggled with that isn't there, add it!<br />
<br />
----<br />
<br />
<br />
'''Math for Computer Graphics and Computer Vision:'''<br />
<br />
<br />
The Drexel group may also want to focus on the math used in computer graphics<br />
and computer vision. Here are some examples.<br />
<br />
:* Vectors and matrices<br />
:* Transformations<br />
:* Quaternions<br />
:* Hierarchical coordinate systems<br />
:* Geometry<br />
::* Curves (Catmull-Rom, Bezier, B-spline)<br />
::* Bezier patches<br />
::* Subdivision surfaces<br />
::* Implicit geometry - lines, circles, ellipses<br />
::* Implicit surfaces - quadrics, superquadrics<br />
:* Surface normals<br />
:* Silhouette edges<br />
:* Procedural texture maps<br />
:* Ray-object intersection<br />
:* Perspective and parallel projection<br />
:* Edge detection<br />
:* Fourier analysis and convolution<br />
<br />
More examples may be found in the lecture slides of [http://www.cs.drexel.edu/~david/Classes/CS430 CS 430].<br />
<br />
'''Resources:'''<br />
:* [http://www.kirupa.com/developer/flash/index.htm Flash/ActionScript Tutorials]<br />
:* [http://hgbook.red-bean.com/read/ Mercurial Book] (Online)<br />
:* [http://java.sun.com/developer/onlineTraining/java3d/ Java 3D Tutorials]<br />
<br />
<br />
----<br />
<br />
<br />
__TOC__<br />
<br />
''' ''Check out the [[Drexel-Swat Partnering]] page to see who's paired up with whom and keep track of what they're working on...'' '''<br />
<br />
==[[User:Tcheeseman1|Tim]]==<br />
===Week 1===<br />
:* Set up the [http://saturn.cs.drexel.edu/mathimages/ Code Repository]. See README's and examples for standard practice. Requires installing [http://mercurial.selenic.com/wiki/ Mercurial] ([http://sourceforge.net/project/showfiles.php?group_id=199155 Windows Installer]) ([http://www.vectrace.com/mercurialeclipse/ Eclipse Plugin])<br />
:* Re-familiarize myself with ActionScript 3 and created an interactive 2D [[Inversion|Point Inversion]] Flash animation<br />
<br />
===To Do List===<br />
:* Applet for [[Inversion|Point Inversion]] in 3D<br />
:* Applet for Shape Inversion (2D shapes about a circle and 3D polyhedra about a sphere to demonstrate creating [[Dual Polyhedron|Dual Polyhedrons]])<br />
<br />
==[[User:Egoldberg1|Emily G.]]==<br />
===Projects:===<br />
:*[[Pascal's Triangle]]-, with input from Lizah using Flash to visualize patterns<br />
::*Status- In Progress, creating a Flash tutorial of sorts to demonstrate/explain the patterns that are found in the triangle.<br />
:*Rhodonea ([[Cardioid]], Rose Petals, Limacons, etc.)- interactive graphing<br />
::*Status- Not Started<br />
:*[[Tessellations]] Image Gallery<br />
::*Status- Not Started<br />
<br />
====Week One====<br />
:This week after setting up Flash CS4 on my laptop and while familiarizing myself with actionscript3, I began a flash tutorial which explains and visualizes the patterns within Pascal's Triangle. The final result will be longer than I initially realized. At this point, it almost feels like I'm creating a movie, but that's alright because I want the tutorial to be thorough and to have clear visualizations of the patterns. Without thorough animation, some of the patterns would be particularly hard to see for yourself. Animation is started but not complete for the original triangle, diagonal rows, shallow diagonal rows (Fibonacci sequence), and the even/odd pattern (Sierpenski's triangle). Descriptions are needed for all of the patterns. Animation is not started for the hockey stick pattern. With no snags, I should be able to finish this animation by next Friday.<br />
<br />
==[[User:Slombardi1|Steve]]==<br />
:Stereographic Projection applet: [http://www.tcnj.edu/~lombar26/StereoProj/StereoProj.html Stereographic Projection]<br />
:Hypotrochoid applet: [http://www.tcnj.edu/~lombar26/Hypotrochoid/Hypotrochoid.html Hypotrochoid]<br />
:Metaballs applet: [http://www.tcnj.edu/~lombar26/ImplicitSurf/ImplicitSurf.html Metaballs]<br />
:Mandelbrot applet: [http://www.tcnj.edu/~lombar26/Mandelbrot/Mandelbrot.html Mandelbrot]<br />
<br />
==[[User:Asobti1|Ayush]]==<br />
<br />
I'm a Computer Science sophomore at Drexel University. This Summer term (Summer 09) is my first term working on the Math Images project.<br />
<br />
===The Plan:===<br />
:Working with Josh and Alan to add interactivity in the pages previously created by Alan.<br />
:I plan to concentrate on Flash animation while Josh explores the Java.<br />
<br />
<br />
===Work Progress:===<br />
:'''Week 1:'''<br />
::Surfed around the MathImages website. Familiarized myself with the many different pages and projects.<br />
::Spoke with Alan and Josh and made a tentative plan of what is to be achieved in the duration of the research project.<br />
::Installed and set up Adobe Flash CS4. Started reading tutorials and watching videos to learn using Flash.<br />
::Learned basic wiki tags and wiki usage and embedding flash .swf files into wiki<br />
:::<flash>file=Test_anim.swf|width=280|height=200|</flash><br />
::Created a simple flash animation to show matrix multiplication of two 2x2 matrices. May be incorporated in the Matrix helper page.<br />
::<flash>file=Matrix_multiplication_new.swf|width=500|height=300|</flash><br />
<br />
==[[User:Jdicristo1|Josh]]==<br />
<br />
I just completed my freshman year at Drexel, going for a BS in Computer Science<br />
<br />
===Projects:===<br />
:Working with Ayush and Alan to add interactivity in the pages previously created by Alan.<br />
:Working mainly with Java<br />
<br />
===Progress After Week 1===<br />
Because I am really working on this project part-time I did not make any major strides this week but I did get a few things accomplished<br />
: I learned the basics of writing Java Applets<br />
: I'm about 1/3 of the way done a program that segments a rectangle into thirds and then illustrates the Golden Spiral<br />
<br />
==[[User:Mhershey1|Mhershey1]]==<br />
What I have so far: http://www.pages.drexel.edu/~smh86/index.html<br />
:*[[Blue Wash]] with Emily, applet changing ''k'' (in '''Inclined Recursive Method''') & animation drawing the basic no ''k'' method (in '''Basic Recursive Method''') <br />
:*[[Blue Fern]], [[Henon Attractor]], redo the animations with small points<br />
:*[[Hyperbolic Tilings]], applet where users input Schläfli symbol to create a tiling<br />
:*[[Newton's Basin]], redo the animation (maybe users input the equations)<br />
:*[[Logarithms]], interactive quiz with exponential and logarithmic equations<br />
:*[[Harter-Heighway Dragon]], animating the curve at each iteration stage<br />
<br />
==[[User:Mhinkle1|Matt]]==<br />
===Projects:===<br />
:*[[Change of Coordinate Systems]]::An applet which allows for a visual representation of user defined points in 2-space and 3-space<br />
:*[[Gradients and Directional Derivatives]]::An applet or animation that displays the gradient at different points on a surface<br />
<br />
===Week 1 Progress===<br />
:After getting comfortable with writing Java applets, I began to read the Java 3D tutorial provided by Sun. After getting down some of the basics, I began to work on the Change of Coordinates applet. So far I have created a 3D graph that has the ability to graphically display a point in 3-space as specified by the user. This point may then be displayed with a rectangular/cartesian, cylindrical, or spherical representation. As of now, the points are input via the console, yet in the finished version, the user will be able to click any location in 3-space to select a point. The user will also be able to navigate the space with a mouse or keyboard.</div>Tcheeseman1https://mathimages.swarthmore.edu/index.php?title=D09&diff=6488D092009-06-29T22:06:05Z<p>Tcheeseman1: /* Week 1 */</p>
<hr />
<div><center>'' '''Welcome to the Drexel Summer 09 Entry to [[Image:TmipClear.png|275px]]''' ''!</center><br />
<br />
<br />
[[Getting Started]] --- [[A Brief Tour of What's Been Done So Far]]<br />
<br />
----<br />
<br />
'''Things to do:''' <br />
* browse around, leaving comments on the Math Images discussion page and the Swarthmore student's discussion page, looking around for interesting possibilities for interaction on the latter<br />
* look through the Helper Pages in the left navbar and the [http://wikis.swarthmore.edu/miwiki/index.php/Hard_Math Hard Math] page to see if you can find anything you'd like to work on--if there's anything you've struggled with that isn't there, add it!<br />
<br />
----<br />
<br />
<br />
'''Math for Computer Graphics and Computer Vision:'''<br />
<br />
<br />
The Drexel group may also want to focus on the math used in computer graphics<br />
and computer vision. Here are some examples.<br />
<br />
:* Vectors and matrices<br />
:* Transformations<br />
:* Quaternions<br />
:* Hierarchical coordinate systems<br />
:* Geometry<br />
::* Curves (Catmull-Rom, Bezier, B-spline)<br />
::* Bezier patches<br />
::* Subdivision surfaces<br />
::* Implicit geometry - lines, circles, ellipses<br />
::* Implicit surfaces - quadrics, superquadrics<br />
:* Surface normals<br />
:* Silhouette edges<br />
:* Procedural texture maps<br />
:* Ray-object intersection<br />
:* Perspective and parallel projection<br />
:* Edge detection<br />
:* Fourier analysis and convolution<br />
<br />
More examples may be found in the lecture slides of [http://www.cs.drexel.edu/~david/Classes/CS430 CS 430].<br />
<br />
'''Resources:'''<br />
:* [http://www.kirupa.com/developer/flash/index.htm Flash/ActionScript Tutorials]<br />
:* [http://hgbook.red-bean.com/read/ Mercurial Book] (Online)<br />
:* [http://java.sun.com/developer/onlineTraining/java3d/ Java 3D Tutorials]<br />
<br />
<br />
----<br />
<br />
<br />
__TOC__<br />
<br />
''' ''Check out the [[Drexel-Swat Partnering]] page to see who's paired up with whom and keep track of what they're working on...'' '''<br />
<br />
==[[User:Tcheeseman1|Tim]]==<br />
===Week 1===<br />
:* Set up the [http://saturn.cs.drexel.edu/mathimages/ Code Repository]. See README's and examples for standard practice. Requires installing [http://mercurial.selenic.com/wiki/ Mercurial] ([http://sourceforge.net/project/showfiles.php?group_id=199155 Windows Installer]) ([http://www.vectrace.com/mercurialeclipse/ Eclipse Plugin])<br />
:* Re-familiarize myself with ActionScript 3 and created an interactive 2D [[Inversion|Point Inversion]] Flash animation:<br />
<br />
===To Do List===<br />
:* Applet for [[Inversion|Point Inversion]] in 3D<br />
:* Applet for Shape Inversion (2D shapes about a circle and 3D polyhedra about a sphere to demonstrate creating [[Dual Polyhedron|Dual Polyhedrons]])<br />
<br />
==[[User:Egoldberg1|Emily G.]]==<br />
===Projects:===<br />
:*[[Pascal's Triangle]]-, with input from Lizah using Flash to visualize patterns<br />
::*Status- In Progress, creating a Flash tutorial of sorts to demonstrate/explain the patterns that are found in the triangle.<br />
:*Rhodonea ([[Cardioid]], Rose Petals, Limacons, etc.)- interactive graphing<br />
::*Status- Not Started<br />
:*[[Tessellations]] Image Gallery<br />
::*Status- Not Started<br />
<br />
====Week One====<br />
:This week after setting up Flash CS4 on my laptop and while familiarizing myself with actionscript3, I began a flash tutorial which explains and visualizes the patterns within Pascal's Triangle. The final result will be longer than I initially realized. At this point, it almost feels like I'm creating a movie, but that's alright because I want the tutorial to be thorough and to have clear visualizations of the patterns. Without thorough animation, some of the patterns would be particularly hard to see for yourself. Animation is started but not complete for the original triangle, diagonal rows, shallow diagonal rows (Fibonacci sequence), and the even/odd pattern (Sierpenski's triangle). Descriptions are needed for all of the patterns. Animation is not started for the hockey stick pattern. With no snags, I should be able to finish this animation by next Friday.<br />
<br />
==[[User:Slombardi1|Steve]]==<br />
:Stereographic Projection applet: [http://www.tcnj.edu/~lombar26/StereoProj/StereoProj.html Stereographic Projection]<br />
:Hypotrochoid applet: [http://www.tcnj.edu/~lombar26/Hypotrochoid/Hypotrochoid.html Hypotrochoid]<br />
:Metaballs applet: [http://www.tcnj.edu/~lombar26/ImplicitSurf/ImplicitSurf.html Metaballs]<br />
:Mandelbrot applet: [http://www.tcnj.edu/~lombar26/Mandelbrot/Mandelbrot.html Mandelbrot]<br />
<br />
==[[User:Asobti1|Ayush]]==<br />
<br />
I'm a Computer Science sophomore at Drexel University. This Summer term (Summer 09) is my first term working on the Math Images project.<br />
<br />
===The Plan:===<br />
:Working with Josh and Alan to add interactivity in the pages previously created by Alan.<br />
:I plan to concentrate on Flash animation while Josh explores the Java.<br />
<br />
<br />
===Work Progress:===<br />
:'''Week 1:'''<br />
::Surfed around the MathImages website. Familiarized myself with the many different pages and projects.<br />
::Spoke with Alan and Josh and made a tentative plan of what is to be achieved in the duration of the research project.<br />
::Installed and set up Adobe Flash CS4. Started reading tutorials and watching videos to learn using Flash.<br />
::Learned basic wiki tags and wiki usage and embedding flash .swf files into wiki<br />
:::<flash>file=Test_anim.swf|width=280|height=200|</flash><br />
::Created a simple flash animation to show matrix multiplication of two 2x2 matrices. May be incorporated in the Matrix helper page.<br />
::<flash>file=Matrix_multiplication_new.swf|width=500|height=300|</flash><br />
<br />
==[[User:Jdicristo1|Josh]]==<br />
<br />
I just completed my freshman year at Drexel, going for a BS in Computer Science<br />
<br />
===Projects:===<br />
:Working with Ayush and Alan to add interactivity in the pages previously created by Alan.<br />
:Working mainly with Java<br />
<br />
===Progress After Week 1===<br />
Because I am really working on this project part-time I did not make any major strides this week but I did get a few things accomplished<br />
: I learned the basics of writing Java Applets<br />
: I'm about 1/3 of the way done a program that segments a rectangle into thirds and then illustrates the Golden Spiral<br />
<br />
==[[User:Mhershey1|Mhershey1]]==<br />
What I have so far: http://www.pages.drexel.edu/~smh86/index.html<br />
:*[[Blue Wash]] with Emily, applet changing ''k'' (in '''Inclined Recursive Method''') & animation drawing the basic no ''k'' method (in '''Basic Recursive Method''') <br />
:*[[Blue Fern]], [[Henon Attractor]], redo the animations with small points<br />
:*[[Hyperbolic Tilings]], applet where users input Schläfli symbol to create a tiling<br />
:*[[Newton's Basin]], redo the animation (maybe users input the equations)<br />
:*[[Logarithms]], interactive quiz with exponential and logarithmic equations<br />
:*[[Harter-Heighway Dragon]], animating the curve at each iteration stage<br />
<br />
==[[User:Mhinkle1|Matt]]==<br />
===Projects:===<br />
:*[[Change of Coordinate Systems]]::An applet which allows for a visual representation of user defined points in 2-space and 3-space<br />
:*[[Gradients and Directional Derivatives]]::An applet or animation that displays the gradient at different points on a surface<br />
<br />
===Week 1 Progress===<br />
:After getting comfortable with writing Java applets, I began to read the Java 3D tutorial provided by Sun. After getting down some of the basics, I began to work on the Change of Coordinates applet. So far I have created a 3D graph that has the ability to graphically display a point in 3-space as specified by the user. This point may then be displayed with a rectangular/cartesian, cylindrical, or spherical representation. As of now, the points are input via the console, yet in the finished version, the user will be able to click any location in 3-space to select a point. The user will also be able to navigate the space with a mouse or keyboard.</div>Tcheeseman1https://mathimages.swarthmore.edu/index.php?title=D09&diff=6487D092009-06-29T22:04:59Z<p>Tcheeseman1: /* Tim */</p>
<hr />
<div><center>'' '''Welcome to the Drexel Summer 09 Entry to [[Image:TmipClear.png|275px]]''' ''!</center><br />
<br />
<br />
[[Getting Started]] --- [[A Brief Tour of What's Been Done So Far]]<br />
<br />
----<br />
<br />
'''Things to do:''' <br />
* browse around, leaving comments on the Math Images discussion page and the Swarthmore student's discussion page, looking around for interesting possibilities for interaction on the latter<br />
* look through the Helper Pages in the left navbar and the [http://wikis.swarthmore.edu/miwiki/index.php/Hard_Math Hard Math] page to see if you can find anything you'd like to work on--if there's anything you've struggled with that isn't there, add it!<br />
<br />
----<br />
<br />
<br />
'''Math for Computer Graphics and Computer Vision:'''<br />
<br />
<br />
The Drexel group may also want to focus on the math used in computer graphics<br />
and computer vision. Here are some examples.<br />
<br />
:* Vectors and matrices<br />
:* Transformations<br />
:* Quaternions<br />
:* Hierarchical coordinate systems<br />
:* Geometry<br />
::* Curves (Catmull-Rom, Bezier, B-spline)<br />
::* Bezier patches<br />
::* Subdivision surfaces<br />
::* Implicit geometry - lines, circles, ellipses<br />
::* Implicit surfaces - quadrics, superquadrics<br />
:* Surface normals<br />
:* Silhouette edges<br />
:* Procedural texture maps<br />
:* Ray-object intersection<br />
:* Perspective and parallel projection<br />
:* Edge detection<br />
:* Fourier analysis and convolution<br />
<br />
More examples may be found in the lecture slides of [http://www.cs.drexel.edu/~david/Classes/CS430 CS 430].<br />
<br />
'''Resources:'''<br />
:* [http://www.kirupa.com/developer/flash/index.htm Flash/ActionScript Tutorials]<br />
:* [http://hgbook.red-bean.com/read/ Mercurial Book] (Online)<br />
:* [http://java.sun.com/developer/onlineTraining/java3d/ Java 3D Tutorials]<br />
<br />
<br />
----<br />
<br />
<br />
__TOC__<br />
<br />
''' ''Check out the [[Drexel-Swat Partnering]] page to see who's paired up with whom and keep track of what they're working on...'' '''<br />
<br />
==[[User:Tcheeseman1|Tim]]==<br />
===Week 1===<br />
:* Set up the [http://saturn.cs.drexel.edu/mathimages/ Code Repository]. See README's and examples for standard practice. Requires installing [http://mercurial.selenic.com/wiki/ Mercurial] ([http://sourceforge.net/project/showfiles.php?group_id=199155 Windows Installer]) ([http://www.vectrace.com/mercurialeclipse/ Eclipse Plugin])<br />
:* Created Interactive 2D [[Inversion|Point Inversion]] Flash Animation:<br />
<br />
===To Do List===<br />
:* Applet for [[Inversion|Point Inversion]] in 3D<br />
:* Applet for Shape Inversion (2D shapes about a circle and 3D polyhedra about a sphere to demonstrate creating [[Dual Polyhedron|Dual Polyhedrons]])<br />
<br />
==[[User:Egoldberg1|Emily G.]]==<br />
===Projects:===<br />
:*[[Pascal's Triangle]]-, with input from Lizah using Flash to visualize patterns<br />
::*Status- In Progress, creating a Flash tutorial of sorts to demonstrate/explain the patterns that are found in the triangle.<br />
:*Rhodonea ([[Cardioid]], Rose Petals, Limacons, etc.)- interactive graphing<br />
::*Status- Not Started<br />
:*[[Tessellations]] Image Gallery<br />
::*Status- Not Started<br />
<br />
====Week One====<br />
:This week after setting up Flash CS4 on my laptop and while familiarizing myself with actionscript3, I began a flash tutorial which explains and visualizes the patterns within Pascal's Triangle. The final result will be longer than I initially realized. At this point, it almost feels like I'm creating a movie, but that's alright because I want the tutorial to be thorough and to have clear visualizations of the patterns. Without thorough animation, some of the patterns would be particularly hard to see for yourself. Animation is started but not complete for the original triangle, diagonal rows, shallow diagonal rows (Fibonacci sequence), and the even/odd pattern (Sierpenski's triangle). Descriptions are needed for all of the patterns. Animation is not started for the hockey stick pattern. With no snags, I should be able to finish this animation by next Friday.<br />
<br />
==[[User:Slombardi1|Steve]]==<br />
:Stereographic Projection applet: [http://www.tcnj.edu/~lombar26/StereoProj/StereoProj.html Stereographic Projection]<br />
:Hypotrochoid applet: [http://www.tcnj.edu/~lombar26/Hypotrochoid/Hypotrochoid.html Hypotrochoid]<br />
:Metaballs applet: [http://www.tcnj.edu/~lombar26/ImplicitSurf/ImplicitSurf.html Metaballs]<br />
:Mandelbrot applet: [http://www.tcnj.edu/~lombar26/Mandelbrot/Mandelbrot.html Mandelbrot]<br />
<br />
==[[User:Asobti1|Ayush]]==<br />
<br />
I'm a Computer Science sophomore at Drexel University. This Summer term (Summer 09) is my first term working on the Math Images project.<br />
<br />
===The Plan:===<br />
:Working with Josh and Alan to add interactivity in the pages previously created by Alan.<br />
:I plan to concentrate on Flash animation while Josh explores the Java.<br />
<br />
<br />
===Work Progress:===<br />
:'''Week 1:'''<br />
::Surfed around the MathImages website. Familiarized myself with the many different pages and projects.<br />
::Spoke with Alan and Josh and made a tentative plan of what is to be achieved in the duration of the research project.<br />
::Installed and set up Adobe Flash CS4. Started reading tutorials and watching videos to learn using Flash.<br />
::Learned basic wiki tags and wiki usage and embedding flash .swf files into wiki<br />
:::<flash>file=Test_anim.swf|width=280|height=200|</flash><br />
::Created a simple flash animation to show matrix multiplication of two 2x2 matrices. May be incorporated in the Matrix helper page.<br />
::<flash>file=Matrix_multiplication_new.swf|width=500|height=300|</flash><br />
<br />
==[[User:Jdicristo1|Josh]]==<br />
<br />
I just completed my freshman year at Drexel, going for a BS in Computer Science<br />
<br />
===Projects:===<br />
:Working with Ayush and Alan to add interactivity in the pages previously created by Alan.<br />
:Working mainly with Java<br />
<br />
===Progress After Week 1===<br />
Because I am really working on this project part-time I did not make any major strides this week but I did get a few things accomplished<br />
: I learned the basics of writing Java Applets<br />
: I'm about 1/3 of the way done a program that segments a rectangle into thirds and then illustrates the Golden Spiral<br />
<br />
==[[User:Mhershey1|Mhershey1]]==<br />
What I have so far: http://www.pages.drexel.edu/~smh86/index.html<br />
:*[[Blue Wash]] with Emily, applet changing ''k'' (in '''Inclined Recursive Method''') & animation drawing the basic no ''k'' method (in '''Basic Recursive Method''') <br />
:*[[Blue Fern]], [[Henon Attractor]], redo the animations with small points<br />
:*[[Hyperbolic Tilings]], applet where users input Schläfli symbol to create a tiling<br />
:*[[Newton's Basin]], redo the animation (maybe users input the equations)<br />
:*[[Logarithms]], interactive quiz with exponential and logarithmic equations<br />
:*[[Harter-Heighway Dragon]], animating the curve at each iteration stage<br />
<br />
==[[User:Mhinkle1|Matt]]==<br />
===Projects:===<br />
:*[[Change of Coordinate Systems]]::An applet which allows for a visual representation of user defined points in 2-space and 3-space<br />
:*[[Gradients and Directional Derivatives]]::An applet or animation that displays the gradient at different points on a surface<br />
<br />
===Week 1 Progress===<br />
:After getting comfortable with writing Java applets, I began to read the Java 3D tutorial provided by Sun. After getting down some of the basics, I began to work on the Change of Coordinates applet. So far I have created a 3D graph that has the ability to graphically display a point in 3-space as specified by the user. This point may then be displayed with a rectangular/cartesian, cylindrical, or spherical representation. As of now, the points are input via the console, yet in the finished version, the user will be able to click any location in 3-space to select a point. The user will also be able to navigate the space with a mouse or keyboard.</div>Tcheeseman1https://mathimages.swarthmore.edu/index.php?title=D09&diff=5690D092009-06-24T18:30:47Z<p>Tcheeseman1: </p>
<hr />
<div><center>'' '''Welcome to the Drexel Summer 09 Entry to [[Image:TmipClear.png|275px]]''' ''!</center><br />
<br />
'''To get started''' go to the upper right of the page and click on ''' "Log in/create account" ''' with the username you've been sent. (If you have questions or complications, email '''Keith''', [mailto:kblaha1@swarthmore.edu kblaha1@swarthmore.edu]).<br />
<br />
As a first step, '''click on "edit"''' and at the top of this page [or wherever], put three tildas ("~") which will produce your username when you click the Save page button at the bottom. Do that so that you see your username in red--an unused page. Click on it and fill it in with a brief description about yourself--your interests and background, in particular. <br />
<br />
----<br />
<br />
<br />
'''A Brief Tour of What's Been Done So Far:'''<br />
<br />
[http://wikis.swarthmore.edu/miwiki/ MIwiki] is the original work wiki for the Math Image Project. At the top you'll find the username pages of the current students and faculty working on it. Other things that might be of interest:<br />
<br />
:* [http://wikis.swarthmore.edu/miwiki/index.php/History_and_Goals History and Goals], very brief<br />
:* [http://wikis.swarthmore.edu/miwiki/index.php/Image_Candidates Image Candidates], and [http://wikis.swarthmore.edu/miwiki/index.php/Useful_Image_Sites Useful Image Sites], selected from an old database, in case you wish ideas for making an image page (they don't have to be restricted to these!)<br />
<br />
<br />
[http://mathforum.org/mathimages/index.php/HomeDraft Math Images] is the draft homepage of the site--if you browse around it please click on the Discussion page and leave comments--we'll have to revise it soon (in fact, [[User:Mkelly1| Maria's]] in the process of making some revisions).<br />
<br />
<br />
[http://mathforum.org/mathimages/index.php/S09 swat09] is the Swarthmore student main entry site equivalent to this Drexel09. The Exhortations at the top may not be of great interest to you, but check out the student names in the Table of Contents. Keith, Maria, and Anna are a bit different but you'll see draft Math Image page names below the others. Some even have "Drexel" following them. You can look at any of the image pages, but are especially invited to check out those with the Drexel. Take a look to see what the Swarthmore students have been doing, and click on the discussion page and leave a comment! You should be looking for possible partners and also brainstorming ideas about possible applets, graphics, and animations to go with some of the pages folks have made.<br />
<br />
----<br />
<br />
'''Getting Started:''' <br />
* make up your userpage, as described above, to get started using the wiki<br />
* browse around, leaving comments on the Math Images discussion page and the Swarthmore student's discussion page, looking around for interesting possibilities for interaction on the latter<br />
* look through the Helper Pages in the left navbar and the [http://wikis.swarthmore.edu/miwiki/index.php/Hard_Math Hard Math] page to see if you can find anything you'd like to work on--if there's anything you've struggled with that isn't there, add it!<br />
<br />
----<br />
<br />
<br />
'''Math for Computer Graphics and Computer Vision:'''<br />
<br />
<br />
The Drexel group may also want to focus on the math used in computer graphics<br />
and computer vision. Here are some examples.<br />
<br />
:* Vectors and matrices<br />
:* Transformations<br />
:* Quaternions<br />
:* Hierarchical coordinate systems<br />
:* Geometry<br />
::* Curves (Catmull-Rom, Bezier, B-spline)<br />
::* Bezier patches<br />
::* Subdivision surfaces<br />
::* Implicit geometry - lines, circles, ellipses<br />
::* Implicit surfaces - quadrics, superquadrics<br />
:* Surface normals<br />
:* Silhouette edges<br />
:* Procedural texture maps<br />
:* Ray-object intersection<br />
:* Perspective and parallel projection<br />
:* Edge detection<br />
:* Fourier analysis and convolution<br />
<br />
More examples may be found in the lecture slides of [http://www.cs.drexel.edu/~david/Classes/CS430 CS 430].<br />
<br />
'''Resources:'''<br />
:* [http://www.kirupa.com/developer/flash/index.htm Flash/ActionScript Tutorials]<br />
:* [http://hgbook.red-bean.com/read/ Mercurial Book] (Online)<br />
<br />
<br />
----<br />
<br />
<br />
__TOC__<br />
<br />
''' ''Check out the [[Drexel-Swat Partnering]] page to see who's paired up with whom and keep track of what they're working on...'' '''<br />
<br />
==[[User:Tcheeseman1|Tim]]==<br />
===Projects:===<br />
:* [http://saturn.cs.drexel.edu/mathimages/ Code Repository] - Up and Running. See README's and examples for standard practice. Requires installing [http://mercurial.selenic.com/wiki/ Mercurial] ([http://sourceforge.net/project/showfiles.php?group_id=199155 Windows Installer]) ([http://www.vectrace.com/mercurialeclipse/ Eclipse Plugin])<br />
:* Applet for [[Inversion|Point Inversion]] 2D and 3D<br />
:* Applet for Shape Inversion (2D shapes about a circle and 3D polyhedra about a sphere to demonstrate creating [[Dual Polyhedron|Dual Polyhedrons]])<br />
<br />
==[[User:Egoldberg1|Emily G.]]==<br />
===Projects:===<br />
:*[[Pascal's Triangle]]-, with input from Lizah using Flash to visualize patterns<br />
:*[[Blue Wash]]- maybe work with Mike H. on this?<br />
:*Rhodonea ([[Cardioid]], Rose Petals, Limacons, etc.)- interactive graphing<br />
<br />
==[[User:Slombardi1|Steve]]==<br />
<br />
==[[User:Asobti1|Ayush]]==<br />
<br />
I'm a Computer Science Freshman at Drexel University. This Summer term (Summer 09) is my first term working on the Math Images project.<br />
<br />
===Work:===<br />
:Working with Josh and Alan to add interactivity in the pages previously created by Alan.<br />
<br />
==[[User:Jdicristo1|Josh]]==<br />
<br />
I just completed my freshman year of Drexel, going for a BS in Computer Science<br />
<br />
===Projects:===<br />
:Working with Ayush and Alan to add interactivity in the pages previously created by Alan.<br />
:Working mainly with Java<br />
<br />
==[[User:Mhershey1|Mhershey1]]==<br />
:*[[Blue Wash]] with Emily, applet changing ''k'' (in '''Inclined Recursive Method''') & animation drawing the basic no ''k'' method (in '''Basic Recursive Method''')<br />
:*[[Blue Fern]], [[Henon Attractor]], redo the animations with small points<br />
:*[[Hyperbolic Tilings]], applet where users input Schläfli symbol to create a tiling<br />
:*[[Newton's Basin]], redo the animation (maybe users input the equations)<br />
:*[[Logarithms]], interactive quiz with exponential and logarithmic equations<br />
:*[[Harter-Heighway Dragon]], animating the curve at each iteration stage<br />
<br />
==[[User:Mhinkle1|Matt]]==<br />
===Projects:===<br />
:*[[Change of Coordinate Systems]]::An applet which allows for a visual representation of user defined points in 2-space and 3-space<br />
:*[[Gradients and Directional Derivatives]]::An applet or animation that displays the gradient at different points on a surface</div>Tcheeseman1https://mathimages.swarthmore.edu/index.php?title=D09&diff=5675D092009-06-24T17:40:49Z<p>Tcheeseman1: /* Projects: */</p>
<hr />
<div><center>'' '''Welcome to the Drexel Summer 09 Entry to [[Image:TmipClear.png|275px]]''' ''!</center><br />
<br />
'''To get started''' go to the upper right of the page and click on ''' "Log in/create account" ''' with the username you've been sent. (If you have questions or complications, email '''Keith''', [mailto:kblaha1@swarthmore.edu kblaha1@swarthmore.edu]).<br />
<br />
As a first step, '''click on "edit"''' and at the top of this page [or wherever], put three tildas ("~") which will produce your username when you click the Save page button at the bottom. Do that so that you see your username in red--an unused page. Click on it and fill it in with a brief description about yourself--your interests and background, in particular. <br />
<br />
----<br />
<br />
<br />
'''A Brief Tour of What's Been Done So Far:'''<br />
<br />
[http://wikis.swarthmore.edu/miwiki/ MIwiki] is the original work wiki for the Math Image Project. At the top you'll find the username pages of the current students and faculty working on it. Other things that might be of interest:<br />
<br />
:* [http://wikis.swarthmore.edu/miwiki/index.php/History_and_Goals History and Goals], very brief<br />
:* [http://wikis.swarthmore.edu/miwiki/index.php/Image_Candidates Image Candidates], and [http://wikis.swarthmore.edu/miwiki/index.php/Useful_Image_Sites Useful Image Sites], selected from an old database, in case you wish ideas for making an image page (they don't have to be restricted to these!)<br />
<br />
<br />
[http://mathforum.org/mathimages/index.php/HomeDraft Math Images] is the draft homepage of the site--if you browse around it please click on the Discussion page and leave comments--we'll have to revise it soon (in fact, [[User:Mkelly1| Maria's]] in the process of making some revisions).<br />
<br />
<br />
[http://mathforum.org/mathimages/index.php/S09 swat09] is the Swarthmore student main entry site equivalent to this Drexel09. The Exhortations at the top may not be of great interest to you, but check out the student names in the Table of Contents. Keith, Maria, and Anna are a bit different but you'll see draft Math Image page names below the others. Some even have "Drexel" following them. You can look at any of the image pages, but are especially invited to check out those with the Drexel. Take a look to see what the Swarthmore students have been doing, and click on the discussion page and leave a comment! You should be looking for possible partners and also brainstorming ideas about possible applets, graphics, and animations to go with some of the pages folks have made.<br />
<br />
----<br />
<br />
'''Getting Started:''' <br />
* make up your userpage, as described above, to get started using the wiki<br />
* browse around, leaving comments on the Math Images discussion page and the Swarthmore student's discussion page, looking around for interesting possibilities for interaction on the latter<br />
* look through the Helper Pages in the left navbar and the [http://wikis.swarthmore.edu/miwiki/index.php/Hard_Math Hard Math] page to see if you can find anything you'd like to work on--if there's anything you've struggled with that isn't there, add it!<br />
<br />
----<br />
<br />
<br />
'''Math for Computer Graphics and Computer Vision:'''<br />
<br />
<br />
The Drexel group may also want to focus on the math used in computer graphics<br />
and computer vision. Here are some examples.<br />
<br />
:* Vectors and matrices<br />
:* Transformations<br />
:* Quaternions<br />
:* Hierarchical coordinate systems<br />
:* Geometry<br />
::* Curves (Catmull-Rom, Bezier, B-spline)<br />
::* Bezier patches<br />
::* Subdivision surfaces<br />
::* Implicit geometry - lines, circles, ellipses<br />
::* Implicit surfaces - quadrics, superquadrics<br />
:* Surface normals<br />
:* Silhouette edges<br />
:* Procedural texture maps<br />
:* Ray-object intersection<br />
:* Perspective and parallel projection<br />
:* Edge detection<br />
:* Fourier analysis and convolution<br />
<br />
More examples may be found in the lecture slides of [http://www.cs.drexel.edu/~david/Classes/CS430 CS 430].<br />
<br />
'''Resources:'''<br />
[http://www.kirupa.com/developer/flash/index.htm Flash/ActionScript Tutorials]<br />
<br />
<br />
----<br />
<br />
<br />
__TOC__<br />
<br />
''' ''Check out the [[Drexel-Swat Partnering]] page to see who's paired up with whom and keep track of what they're working on...'' '''<br />
<br />
==[[User:Tcheeseman1|Tim]]==<br />
===Projects:===<br />
:* [http://saturn.cs.drexel.edu/mathimages/ Code Repository] - Up and Running. See README's and examples for standard practice. Requires installing [http://mercurial.selenic.com/wiki/ Mercurial] ([http://sourceforge.net/project/showfiles.php?group_id=199155 Windows Installer])<br />
:* Applet for [[Inversion|Point Inversion]] 2D and 3D<br />
:* Applet for Shape Inversion (2D shapes about a circle and 3D polyhedra about a sphere to demonstrate creating [[Dual Polyhedron|Dual Polyhedrons]])<br />
<br />
==[[User:Egoldberg1|Emily G.]]==<br />
===Projects:===<br />
:*[[Pascal's Triangle]]-, with input from Lizah using Flash to visualize patterns<br />
:*[[Blue Wash]]- maybe work with Mike H. on this?<br />
:*Rhodonea ([[Cardioid]], Rose Petals, Limacons, etc.)- interactive graphing<br />
<br />
==[[User:Slombardi1|Steve]]==<br />
<br />
==[[User:Asobti1|Ayush]]==<br />
<br />
I'm a Computer Science Freshman at Drexel University. This Summer term (Summer 09) is my first term working on the Math Images project.<br />
<br />
===Work:===<br />
:Working with Josh and Alan to add interactivity in the pages previously created by Alan.<br />
<br />
==[[User:Jdicristo1|Josh]]==<br />
<br />
I just completed my freshman year of Drexel, going for a BS in Computer Science<br />
<br />
===Projects:===<br />
:Working with Ayush and Alan to add interactivity in the pages previously created by Alan.<br />
:Working mainly with Java<br />
<br />
==[[User:Mhershey1|Mhershey1]]==<br />
:*[[Blue Wash]] with Emily, applet changing ''k'' (in '''Inclined Recursive Method''') & animation drawing the basic no ''k'' method (in '''Basic Recursive Method''')<br />
:*[[Blue Fern]], [[Henon Attractor]], redo the animations with small points<br />
:*[[Hyperbolic Tilings]], applet where users input Schläfli symbol to create a tiling<br />
:*[[Newton's Basin]], redo the animation (maybe users input the equations)<br />
:*[[Logarithms]], interactive quiz with exponential and logarithmic equations<br />
:*[[Harter-Heighway Dragon]], animating the curve at each iteration stage<br />
<br />
==[[User:Mhinkle1|Matt]]==<br />
===Projects:===<br />
:*[[Change of Coordinate Systems]]::An applet which allows for a visual representation of user defined points in 2-space and 3-space<br />
:*[[Gradients and Directional Derivatives]]::An applet or animation that displays the gradient at different points on a surface</div>Tcheeseman1https://mathimages.swarthmore.edu/index.php?title=D09&diff=5674D092009-06-24T17:38:16Z<p>Tcheeseman1: </p>
<hr />
<div><center>'' '''Welcome to the Drexel Summer 09 Entry to [[Image:TmipClear.png|275px]]''' ''!</center><br />
<br />
'''To get started''' go to the upper right of the page and click on ''' "Log in/create account" ''' with the username you've been sent. (If you have questions or complications, email '''Keith''', [mailto:kblaha1@swarthmore.edu kblaha1@swarthmore.edu]).<br />
<br />
As a first step, '''click on "edit"''' and at the top of this page [or wherever], put three tildas ("~") which will produce your username when you click the Save page button at the bottom. Do that so that you see your username in red--an unused page. Click on it and fill it in with a brief description about yourself--your interests and background, in particular. <br />
<br />
----<br />
<br />
<br />
'''A Brief Tour of What's Been Done So Far:'''<br />
<br />
[http://wikis.swarthmore.edu/miwiki/ MIwiki] is the original work wiki for the Math Image Project. At the top you'll find the username pages of the current students and faculty working on it. Other things that might be of interest:<br />
<br />
:* [http://wikis.swarthmore.edu/miwiki/index.php/History_and_Goals History and Goals], very brief<br />
:* [http://wikis.swarthmore.edu/miwiki/index.php/Image_Candidates Image Candidates], and [http://wikis.swarthmore.edu/miwiki/index.php/Useful_Image_Sites Useful Image Sites], selected from an old database, in case you wish ideas for making an image page (they don't have to be restricted to these!)<br />
<br />
<br />
[http://mathforum.org/mathimages/index.php/HomeDraft Math Images] is the draft homepage of the site--if you browse around it please click on the Discussion page and leave comments--we'll have to revise it soon (in fact, [[User:Mkelly1| Maria's]] in the process of making some revisions).<br />
<br />
<br />
[http://mathforum.org/mathimages/index.php/S09 swat09] is the Swarthmore student main entry site equivalent to this Drexel09. The Exhortations at the top may not be of great interest to you, but check out the student names in the Table of Contents. Keith, Maria, and Anna are a bit different but you'll see draft Math Image page names below the others. Some even have "Drexel" following them. You can look at any of the image pages, but are especially invited to check out those with the Drexel. Take a look to see what the Swarthmore students have been doing, and click on the discussion page and leave a comment! You should be looking for possible partners and also brainstorming ideas about possible applets, graphics, and animations to go with some of the pages folks have made.<br />
<br />
----<br />
<br />
'''Getting Started:''' <br />
* make up your userpage, as described above, to get started using the wiki<br />
* browse around, leaving comments on the Math Images discussion page and the Swarthmore student's discussion page, looking around for interesting possibilities for interaction on the latter<br />
* look through the Helper Pages in the left navbar and the [http://wikis.swarthmore.edu/miwiki/index.php/Hard_Math Hard Math] page to see if you can find anything you'd like to work on--if there's anything you've struggled with that isn't there, add it!<br />
<br />
----<br />
<br />
<br />
'''Math for Computer Graphics and Computer Vision:'''<br />
<br />
<br />
The Drexel group may also want to focus on the math used in computer graphics<br />
and computer vision. Here are some examples.<br />
<br />
:* Vectors and matrices<br />
:* Transformations<br />
:* Quaternions<br />
:* Hierarchical coordinate systems<br />
:* Geometry<br />
::* Curves (Catmull-Rom, Bezier, B-spline)<br />
::* Bezier patches<br />
::* Subdivision surfaces<br />
::* Implicit geometry - lines, circles, ellipses<br />
::* Implicit surfaces - quadrics, superquadrics<br />
:* Surface normals<br />
:* Silhouette edges<br />
:* Procedural texture maps<br />
:* Ray-object intersection<br />
:* Perspective and parallel projection<br />
:* Edge detection<br />
:* Fourier analysis and convolution<br />
<br />
More examples may be found in the lecture slides of [http://www.cs.drexel.edu/~david/Classes/CS430 CS 430].<br />
<br />
'''Resources:'''<br />
[http://www.kirupa.com/developer/flash/index.htm Flash/ActionScript Tutorials]<br />
<br />
<br />
----<br />
<br />
<br />
__TOC__<br />
<br />
''' ''Check out the [[Drexel-Swat Partnering]] page to see who's paired up with whom and keep track of what they're working on...'' '''<br />
<br />
==[[User:Tcheeseman1|Tim]]==<br />
===Projects:===<br />
:* [[Code Repository]] - Up and Running<br />
:* Applet for [[Inversion|Point Inversion]] 2D and 3D<br />
:* Applet for Shape Inversion (2D shapes about a circle and 3D polyhedra about a sphere to demonstrate creating [[Dual Polyhedron|Dual Polyhedrons]])<br />
<br />
==[[User:Egoldberg1|Emily G.]]==<br />
===Projects:===<br />
:*[[Pascal's Triangle]]-, with input from Lizah using Flash to visualize patterns<br />
:*[[Blue Wash]]- maybe work with Mike H. on this?<br />
:*Rhodonea ([[Cardioid]], Rose Petals, Limacons, etc.)- interactive graphing<br />
<br />
==[[User:Slombardi1|Steve]]==<br />
<br />
==[[User:Asobti1|Ayush]]==<br />
<br />
I'm a Computer Science Freshman at Drexel University. This Summer term (Summer 09) is my first term working on the Math Images project.<br />
<br />
===Work:===<br />
:Working with Josh and Alan to add interactivity in the pages previously created by Alan.<br />
<br />
==[[User:Jdicristo1|Josh]]==<br />
<br />
I just completed my freshman year of Drexel, going for a BS in Computer Science<br />
<br />
===Projects:===<br />
:Working with Ayush and Alan to add interactivity in the pages previously created by Alan.<br />
:Working mainly with Java<br />
<br />
==[[User:Mhershey1|Mhershey1]]==<br />
:*[[Blue Wash]] with Emily, applet changing ''k'' (in '''Inclined Recursive Method''') & animation drawing the basic no ''k'' method (in '''Basic Recursive Method''')<br />
:*[[Blue Fern]], [[Henon Attractor]], redo the animations with small points<br />
:*[[Hyperbolic Tilings]], applet where users input Schläfli symbol to create a tiling<br />
:*[[Newton's Basin]], redo the animation (maybe users input the equations)<br />
:*[[Logarithms]], interactive quiz with exponential and logarithmic equations<br />
:*[[Harter-Heighway Dragon]], animating the curve at each iteration stage<br />
<br />
==[[User:Mhinkle1|Matt]]==<br />
===Projects:===<br />
:*[[Change of Coordinate Systems]]::An applet which allows for a visual representation of user defined points in 2-space and 3-space<br />
:*[[Gradients and Directional Derivatives]]::An applet or animation that displays the gradient at different points on a surface</div>Tcheeseman1https://mathimages.swarthmore.edu/index.php?title=D09&diff=5507D092009-06-23T19:52:30Z<p>Tcheeseman1: </p>
<hr />
<div><center>'' '''Welcome to the Drexel Summer 09 Entry to [[Image:TmipClear.png|275px]]''' ''!</center><br />
<br />
'''To get started''' go to the upper right of the page and click on ''' "Log in/create account" ''' with the username you've been sent. (If you have questions or complications, email '''Keith''', [mailto:kblaha1@swarthmore.edu kblaha1@swarthmore.edu]).<br />
<br />
As a first step, '''click on "edit"''' and at the top of this page [or wherever], put three tildas ("~") which will produce your username when you click the Save page button at the bottom. Do that so that you see your username in red--an unused page. Click on it and fill it in with a brief description about yourself--your interests and background, in particular. <br />
<br />
----<br />
<br />
<br />
'''A Brief Tour of What's Been Done So Far:'''<br />
<br />
[http://wikis.swarthmore.edu/miwiki/ MIwiki] is the original work wiki for the Math Image Project. At the top you'll find the username pages of the current students and faculty working on it. Other things that might be of interest:<br />
<br />
:* [http://wikis.swarthmore.edu/miwiki/index.php/History_and_Goals History and Goals], very brief<br />
:* [http://wikis.swarthmore.edu/miwiki/index.php/Image_Candidates Image Candidates], and [http://wikis.swarthmore.edu/miwiki/index.php/Useful_Image_Sites Useful Image Sites], selected from an old database, in case you wish ideas for making an image page (they don't have to be restricted to these!)<br />
<br />
<br />
[http://mathforum.org/mathimages/index.php/HomeDraft Math Images] is the draft homepage of the site--if you browse around it please click on the Discussion page and leave comments--we'll have to revise it soon (in fact, [[User:Mkelly1| Maria's]] in the process of making some revisions).<br />
<br />
<br />
[http://mathforum.org/mathimages/index.php/S09 swat09] is the Swarthmore student main entry site equivalent to this Drexel09. The Exhortations at the top may not be of great interest to you, but check out the student names in the Table of Contents. Keith, Maria, and Anna are a bit different but you'll see draft Math Image page names below the others. Some even have "Drexel" following them. You can look at any of the image pages, but are especially invited to check out those with the Drexel. Take a look to see what the Swarthmore students have been doing, and click on the discussion page and leave a comment! You should be looking for possible partners and also brainstorming ideas about possible applets, graphics, and animations to go with some of the pages folks have made.<br />
<br />
----<br />
<br />
'''Getting Started:''' <br />
* make up your userpage, as described above, to get started using the wiki<br />
* browse around, leaving comments on the Math Images discussion page and the Swarthmore student's discussion page, looking around for interesting possibilities for interaction on the latter<br />
* look through the Helper Pages in the left navbar and the [http://wikis.swarthmore.edu/miwiki/index.php/Hard_Math Hard Math] page to see if you can find anything you'd like to work on--if there's anything you've struggled with that isn't there, add it!<br />
<br />
----<br />
<br />
<br />
'''Math for Computer Graphics and Computer Vision:'''<br />
<br />
<br />
The Drexel group may also want to focus on the math used in computer graphics<br />
and computer vision. Here are some examples.<br />
<br />
:* Vectors and matrices<br />
:* Transformations<br />
:* Hierarchical coordinate systems<br />
:* Geometry<br />
::* Curves (Catmull-Rom, Bezier, B-spline)<br />
::* Bezier patches<br />
::* Subdivision surfaces<br />
::* Implicit geometry - lines, circles, ellipses<br />
::* Implicit surfaces - quadrics, superquadrics<br />
:* Surface normals<br />
:* Silhouette edges<br />
:* Procedural texture maps<br />
:* Ray-object intersection<br />
:* Perspective and parallel projection<br />
:* Edge detection<br />
:* Fourier analysis and convolution<br />
<br />
More examples may be found in the lecture slides of [http://www.cs.drexel.edu/~david/Classes/CS430 CS 430].<br />
<br />
'''Resources:'''<br />
[http://www.kirupa.com/developer/flash/index.htm Flash/ActionScript Tutorials]<br />
<br />
<br />
----<br />
<br />
<br />
__TOC__<br />
<br />
''' ''Check out the [[Drexel-Swat Partnering]] page to see who's paired up with whom and keep track of what they're working on...'' '''<br />
<br />
==[[User:Tcheeseman1|Tim]]==<br />
<br />
==[[User:Egoldberg1|Egoldberg1]]==<br />
<br />
==[[User:Slombardi1|Steve]]==<br />
<br />
==[[User:Asobti1|Asobti1]]==<br />
<br />
I'm a Computer Science Freshman at Drexel University. <br />
<br />
This Summer term (Summer 09) is my first term working on the Math Images project.<br />
<br />
==[[User:Mhershey1|Mhershey1]]==<br />
:*[[Blue Wash]] with Emily, applet changing ''k'' (in '''Inclined Recursive Method''') & animation drawing the basic no ''k'' method (in '''Basic Recursive Method''')<br />
:*[[Blue Fern]], [[Henon Attractor]], redo the animations with small points<br />
:*[[Hyperbolic Tilings]], applet where users input Schläfli symbol to create a tiling<br />
:*[[Newton's Basin]], redo the animation (maybe users input the equations)<br />
:*[[Logarithms]], interactive quiz with exponential and logarithmic equations<br />
:*[[Harter-Heighway Dragon]], animating the curve at each iteration stage</div>Tcheeseman1https://mathimages.swarthmore.edu/index.php?title=User:Tcheeseman1&diff=5266User:Tcheeseman12009-06-20T01:11:05Z<p>Tcheeseman1: create user page</p>
<hr />
<div></div>Tcheeseman1https://mathimages.swarthmore.edu/index.php?title=D09&diff=5265D092009-06-20T01:10:20Z<p>Tcheeseman1: </p>
<hr />
<div><center><font size="4">'' '''Welcome to the Drexel Summer 09 Entry to [[Image:TmipClear.png|275px]]''' ''!</font></center><br />
<br />
[Welcome message from Dave?]<br />
<br />
'''To get started''' go to the upper right of the page and click on ''' "Log in/create account" ''' with the username you've been sent. (If you have questions or complications, email '''Keith''', [mailto:kblaha1@swarthmore.edu kblaha1@swarthmore.edu]).<br />
<br />
As a first step, '''click on "edit"''' and at the top of this page [or wherever], put three tildas ("~") which will produce your username when you click the Save page button at the bottom. Do that so that you see your username in red--an unused page. Click on it and fill it in with a brief description about yourself--your interests and background, in particular. <br />
<br />
<br />
----<br />
<br />
<br />
'''A Brief Tour of What's Been Done So Far:'''<br />
<br />
[http://wikis.swarthmore.edu/miwiki/ MIwiki] is the original work wiki for the Math Image Project. At the top you'll find the username pages of the current students and faculty working on it. Other things that might be of interest:<br />
<br />
:* [http://wikis.swarthmore.edu/miwiki/index.php/History_and_Goals History and Goals], very brief<br />
:* [http://wikis.swarthmore.edu/miwiki/index.php/Image_Candidates Image Candidates], and [http://wikis.swarthmore.edu/miwiki/index.php/Useful_Image_Sites Useful Image Sites], selected from an old database, in case you wish ideas for making an image page (they don't have to be restricted to these!)<br />
<br />
<br />
[http://mathforum.org/mathimages/index.php/HomeDraft Math Images] is the draft homepage of the site--if you browse around it please click on the Discussion page and leave comments--we'll have to revise it soon (in fact, [[User:Mkelly1| Maria's]] in the process of making some revisions).<br />
<br />
<br />
[http://mathforum.org/mathimages/index.php/S09 swat09] is the Swarthmore student main entry site equivalent to this Drexel09. The Exhortations at the top may not be of great interest to you, but check out the student names in the Table of Contents. Keith, Maria, and Anna are a bit different but you'll see draft Math Image page names below the others. Some even have "Drexel" following them. You can look at any of the image pages, but are especially invited to check out those with the Drexel. Take a look to see what the Swarthmore students have been doing, and click on the discussion page and leave a comment! You should be looking for possible partners and also brainstorming ideas about possible applets, graphics, and animations to go with some of the pages folks have made.<br />
<br />
----<br />
<br />
'''Getting Started:''' <br />
* make up your userpage, as described above, to get started using the wiki<br />
* browse around, leaving comments on the Math Images discussion page and the Swarthmore student's discussion page, looking around for interesting possibilities for interaction on the latter<br />
* look through the Helper Pages in the left navbar and the [http://wikis.swarthmore.edu/miwiki/index.php/Hard_Math Hard Math] page to see if you can find anything you'd like to work on--if there's anything you've struggled with that isn't there, add it!<br />
<br />
__TOC__<br />
<br />
==[[User:Tcheeseman1|Tim]]==</div>Tcheeseman1