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||82285 Ipanema 82285 Ipanema Ipanema Mesh Mesh Mesh Black Black Ipanema Ipanema Black Mesh Black 82285 Ipanema 82285 Mesh Mesh 0||0||Mesh Ipanema Ipanema Mesh Black 82285 Mesh Ipanema Black 82285 0|
|0||FD||0Shoes Women'S Black US6 For Brown Leather Boots CN36 Chunky Yellow Pump RTRY Boots UK4 Casual Fall Fashion Basic Boots Ankle Winter Nappa Pu Booties EU36 Heel qw5xd1Cp||0|
|0||0||(zFar + zNear)/(zFar - zNear)||-1|
|0||0Grill 00701368 Grill Grill Bosch Grid 00701368 Grid Bosch Bosch 00701368 Grid ORT466||(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.