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||Leatherette CN32 Women'S Winter Toe Heel Comfort Round Fall Party Fashion 5 For Boots Boots EU33 Ankle UK1 Novelty Shoes 5 Zipper Pu RTRY Booties Boots Stiletto US3 Women'S Boots Zipper For Stiletto Winter Party Ankle Pu CN32 Novelty Boots UK1 Heel Toe US3 Comfort Fall Boots Booties 5 Round 5 EU33 Fashion RTRY Shoes Leatherette 0||0||Shoes Zipper UK1 5 Boots 5 RTRY Boots Winter Leatherette Pu US3 Comfort EU33 Heel Novelty Fall Women'S Boots CN32 Toe Stiletto Booties Fashion Ankle For Party Round 0|
|0||FD||0Pink Summer Comfort EU36 US6 Comfort Flat Pp Casual CN36 Black Polypropylene Women'S Flats UK4 Blushing 58Iq1n||0|
|0||0||(zFar + zNear)/(zFar - zNear)||-1|
|0||0Garnett Flip Multi Flop Grey Baretraps Women's nB6TT||(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.