Things to do:
- 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
- look through the Helper Pages in the left navbar and the 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!
Math for Computer Graphics and Computer Vision:
The Drexel group may also want to focus on the math used in computer graphics and computer vision. Here are some examples.
- Vectors and matrices
- Hierarchical coordinate systems
- Curves (Catmull-Rom, Bezier, B-spline)
- Bezier patches
- Subdivision surfaces
- Implicit geometry - lines, circles, ellipses
- Implicit surfaces - quadrics, superquadrics
- Surface normals
- Silhouette edges
- Procedural texture maps
- Ray-object intersection
- Perspective and parallel projection
- Edge detection
- Fourier analysis and convolution
More examples may be found in the lecture slides of CS 430.
Check out the Drexel-Swat Partnering page to see who's paired up with whom and keep track of what they're working on...
To Do List
- Pascal's Triangle-, with input from Lizah using Flash to visualize patterns
- Status- In Progress, creating a Flash tutorial of sorts to demonstrate/explain the patterns that are found in the triangle.
- Rhodonea (Cardioid, Rose Petals, Limacons, etc.)- interactive graphing
- Status- Not Started
- Tessellations Image Gallery
- Status- Not Started
- 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.
- Stereographic Projection applet: Stereographic Projection
- Hypotrochoid applet: Hypotrochoid
- Metaballs applet: Metaballs
- Mandelbrot applet: Mandelbrot
I'm a Computer Science sophomore at Drexel University. This Summer term (Summer 09) is my first term working on the Math Images project.
- Working with Josh and Alan to add interactivity in the pages previously created by Alan.
- I plan to concentrate on Flash animation while Josh explores the Java.
- Week 1:
- Surfed around the MathImages website. Familiarized myself with the many different pages and projects.
- Spoke with Alan and Josh and made a tentative plan of what is to be achieved in the duration of the research project.
- Installed and set up Adobe Flash CS4. Started reading tutorials and watching videos to learn using Flash.
- Learned basic wiki tags and wiki usage and embedding flash .swf files into wiki
- Created a simple flash animation to show matrix multiplication of two 2x2 matrices. May be incorporated in the Matrix helper page.
I just completed my freshman year at Drexel, going for a BS in Computer Science
- Working with Ayush and Alan to add interactivity in the pages previously created by Alan.
- Working mainly with Java
Progress After Week 1
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
- I learned the basics of writing Java Applets
- I'm about 1/3 of the way done a program that segments a rectangle into thirds and then illustrates the Golden Spiral
What I have so far: http://www.pages.drexel.edu/~smh86/index.html
- Blue Wash with Emily, applet changing k (in Inclined Recursive Method) & animation drawing the basic no k method (in Basic Recursive Method)
- Blue Fern, Henon Attractor, redo the animations with small points
- Hyperbolic Tilings, applet where users input Schläfli symbol to create a tiling
- Newton's Basin, redo the animation (maybe users input the equations)
- Logarithms, interactive quiz with exponential and logarithmic equations
- Harter-Heighway Dragon, animating the curve at each iteration stage
Week 1 Progress
- 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.