# Planar Projection

Summary

## Contents

### Projection Parameters

Each of the parameters uses either the *world-coordinate* (WC) or *viewing reference-coordinate* (VRC) system.

- The
**View Reference Point**(VRP) is the point (WC) from which the camera is viewing the 3D geometry. - The
**View Plane Normal**(VPN) is the normal (WC) ... - The
**View Up Vector**(VUP) is the vector (WC) that defines the orientation of the camera (i.e. which way is up) - The
**Projection Reference Point**(PRP) is the point (VRC) ... - The
**Viewing Window**is the rectangle (VRC) that defines the size of the 2D window upon which the 3D geometry will be projected. - The
**projection type**can be either parallel or perspective

- The

## Parallel Projection

Summary

### Orthographic Projection

The first step is to translate the VRP to the origin, which can be achieved by multiplying its complement with the following matrix **T**:

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:

The components of these vectors (e.g. ) then form the rotation matrix R:

The final transformation matrix for orthographic projection is then the result of the following multiplication:

### Oblique Projection

## Perspective Projection

Summary