So far we have been using a type of projection where any points not on the plane, which we wish to project onto the plane, are moved along a line perpendicular to the plane until they intersect with the plane.
This type of projection is very useful, in engineering drawings for example, because it preserves the size of the object being projected.
However, when we look at a scene or take a picture of it, this is not what we see. Things nearer to us appear to be bigger and things further away appear to be smaller. Also parallel lines appear to converge at the horizon so, to model this type of projection, we need to use a different type of projection: frustum projection.
This type of projection can be modeled by projective geometry.
Frustum Projection Matrix
This projection is represented by the following matrix.
|FD/aspect||Up CN32 Leatherette Over Heel Fashion 5 Women'S The Winter EU33 US3 Round Boots Pu Novelty Stiletto 5 Boots Shoes Comfort For RTRY Lace Knee Boots Toe Fall UK1 Lace Round Comfort Leatherette Up EU33 Novelty Boots Winter Pu Boots RTRY Toe Heel 5 Fashion CN32 Shoes The 5 Women'S Over US3 For Stiletto Knee Fall Boots UK1 0||0||EU33 Lace Heel Boots Comfort Knee Over Novelty 5 Toe Round Stiletto Leatherette Shoes The 5 UK1 Fall For Fashion Up US3 Boots Winter CN32 Pu Boots Women'S RTRY 0|
|0||FD||025 Black Shoe Women's Kayano Black Running Asics Gel wZStOU||0|
|0||0||(zFar + zNear)/(zFar - zNear)||-1|
|0||0US 12 Jordan Size Retro 2012 'Playoff Release' 153265 Air GS 001 zS5dq5||(2 * zFar * zNear)/(zFar - zNear)||0|
This assumes that we are projecting along z-axis, that is we are looking along the z axis, so the x and y axes are not altered by the transform apart from a fixed scaling factor. The z axis is modified by both the z and w components. The w component can be though of, in this case, as a scaling factor which depends on how far we are away from the object.