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||Women Suede Out Boots Toe Clearance Solid Khaki Boots Flat OverDose Vintage Cut Hasp Suede Round Ankle Shoes Booties Shoes Martin Color Martin Flat Boots Clearance Color Shoes Booties Boots Cut Women Hasp Ankle Toe Khaki Out OverDose Solid Shoes Suede Suede Round Vintage 0||0||Ankle Shoes Flat Cut Hasp Shoes Boots Solid Clearance Women Booties Color Boots Out OverDose Toe Khaki Vintage Round Suede Suede Martin 0|
|0||FD||0Gray Shoes Heels Heel Purple Chunky Green ShangYi Women's Dress Heels Green Wedding Silk Burgundy Black a1Fw7||0|
|0||0||(zFar + zNear)/(zFar - zNear)||-1|
|0||0Shoes Fizik BOA M6 Mountain Donna Cycling Women's qYax6w0||(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.