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||Fall RTRY Heel Evening Dress 5 EU36 US5 Silver Gladiator Gladiator Leather Patent Summer CN35 Stiletto amp;Amp; 5 UK3 3In Gold Women'S Casual 4In Sandals 3 Party 3 Stiletto EU36 Heel 3 Summer RTRY CN35 5 Sandals 4In 5 UK3 Gladiator Leather Party US5 Silver Dress 3 Gladiator Gold Women'S 3In Fall Casual Patent amp;Amp; Evening 0||0||Casual Party Gladiator 3 RTRY 5 Evening 3In Women'S Dress Summer CN35 Patent UK3 EU36 Sandals 5 US5 Gold Gladiator 3 Heel Leather amp;Amp; Silver Stiletto Fall 4In 0|
|0||FD||0Nubuck Pu Women'S Boots CN39 Fashion US8 Fall Winter Brown Leather Toe RTRY Shoes Comfort Black UK6 Round For Casual Block Heel Boots EU39 qECdzIww||0|
|0||0||(zFar + zNear)/(zFar - zNear)||-1|
|0||0Mizuno Mizuno D1GB1845 D1GB1845 Sneakers Women Blue ROqYvx||(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.