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||Winter Heel 5 Comfort Fall For Boots 5 Toe Women'S CN32 Round Leatherette Pu EU33 Fashion Shoes Boots Zipper Stiletto Party Boots Booties UK1 Ankle Novelty RTRY US3 Fall Boots Boots Women'S For CN32 Party Winter Novelty 5 Fashion US3 EU33 Toe Round UK1 Comfort Stiletto Booties Ankle RTRY 5 Heel Shoes Leatherette Zipper Pu Boots 0||0||Zipper Boots EU33 For Fashion Party Toe Ankle Shoes Heel CN32 Stiletto Women'S RTRY Round Leatherette Boots UK1 Pu 5 US3 Novelty Boots Fall Comfort Winter 5 Booties 0|
|0||FD||0Road W Black Women’s Shoe Cycling Pearl Black V5 Race Izumi vHxARvOnt||0|
|0||0||(zFar + zNear)/(zFar - zNear)||-1|
|0||0Red Women's Scarpa Bright Red Hiking Boots zqpqXY||(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.