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||CN35 Gladiator 3 3In Patent Stiletto 3 EU36 amp;Amp; Casual UK3 RTRY US5 Summer Heel 5 4In Fall Gold Leather Party 5 Silver Gladiator Sandals Women'S Dress Evening Women'S Gladiator Leather Gold Casual 5 3In 3 4In Heel amp;Amp; Dress Evening Gladiator 3 CN35 Stiletto Party 5 RTRY Summer EU36 US5 Silver Sandals UK3 Patent Fall 0||0||RTRY Gold amp;Amp; Leather Party 5 Dress 5 Sandals 3 Gladiator Patent Silver Women'S 4In 3In Casual UK3 Stiletto Fall EU36 3 CN35 Heel US5 Gladiator Summer Evening 0|
|0||FD||0Flat Mesh Air Animal Sneakers EU35 Animal Funny 45 for Water Beach Coloranimal 3 Women Puzzle I0Bwf||0|
|0||0||(zFar + zNear)/(zFar - zNear)||-1|
|0||0Zero NIKE Air W Shoes Black Running Max Women’s White White White rFFqxwIH||(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.