Orthographic projection (geometry)
|This article does not cite any references or sources. (December 2009)|
For each point v = (vx, vy, vz), the transformed point would be
Often, it is more useful to use homogeneous coordinates. The transformation above can be represented for homogeneous coordinates as
For each homogeneous vector v = (vx, vy, vz, 1), the transformed vector would be
In computer graphics, one of the most common matrices used for orthographic projection can be defined by a 6-tuple, (left, right, bottom, top, near, far), which defines the clipping planes. These planes form a box with the minimum corner at (left, bottom, near) and the maximum corner at (right, top, far).
The box is translated so that its center is at the origin, then it is scaled to the unit cube which is defined by having a minimum corner at (-1,-1,-1) and a maximum corner at (1,1,1).
The orthographic transform can be given by the following matrix:
The inversion of the Projection Matrix, which can be used as the Unprojection Matrix is defined: