Planar Projection

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Math for Computer Graphics and Computer Vision

Summary

Contents

Projection Parameters

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.

• 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) which, once projected, defines the n axis.
• 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.
• 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. It is defined by umin, umax, vmin, and vmax.
• The projection type can be either parallel or perspective.

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: multiplication:

$N_{par} = (S_{par} \cdot (T_{par} \cdot (SH_{par} \cdot (R \cdot T \cdot (-VRP)))))$

Summary