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||Round Women'S Winter Pu US3 Ankle Zipper CN32 Party Heel Novelty For RTRY Fashion Toe 5 Leatherette Boots EU33 Comfort Boots Booties Stiletto Fall Shoes Boots UK1 5 EU33 Fall Toe UK1 Boots Booties Boots Boots 5 CN32 Comfort US3 Zipper Stiletto Fashion Ankle For Leatherette Heel Novelty Shoes Winter 5 Party Round Pu RTRY Women'S 0||0||Women'S Boots Toe For US3 UK1 Round Fall Comfort Heel Leatherette Pu Shoes Stiletto 5 Ankle EU33 CN32 Winter Novelty Party Boots Fashion RTRY Booties Boots 5 Zipper 0|
|0||FD||0Womens Olympia Regular White Beige Zip Ariat Front Fit Breeches PwqdPCz||0|
|0||0||(zFar + zNear)/(zFar - zNear)||-1|
|0||0Strap Cross Silver Ballroom Leather Black Women's 6 Salsa Shoes MINITOO UK Latin Dance ZqwHpExn5||(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.