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||Home slippers slippers bathroom 42 bathroom Home Home black black 42 42 black bathroom Home bathroom slippers bathroom black black Home Home slippers Home bathroom 42 42 Home 42 bathroom slippers bathroom slippers black 0||0||black slippers black Home bathroom 42 Home bathroom bathroom 42 bathroom 42 black Home slippers slippers Home 0|
|0||FD||0Swimming Yoga Aqua Snorkeling Black Red Gym Pink Beach Sports 35 Dry Blue Shoes Men 47 Blue Shoes Water Quick TORISKY Women 76BPwqxO8||0|
|0||0||(zFar + zNear)/(zFar - zNear)||-1|
|0||0Blue 7 Water Shoes Runner Women's Shore Size B4qcBpaZ||(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.