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||Teaching Freed Teaching Pink Teaching Freed Shoe Pink Teaching Freed Shoe Freed Shoe Freed Shoe Pink Pink Teaching Pink Teaching Teaching Teaching Freed Teaching Pink Shoe Shoe Freed Teaching Pink Freed Shoe Freed Shoe Pink Freed 0||0||Teaching Shoe Shoe Teaching Pink Freed Pink Teaching Teaching Pink Freed Shoe Freed Shoe Teaching Freed Pink Freed 0|
|0||FD||0Black White T669N 8 White Shoes Asics Patriot Women's Black Running zUY1w||0|
|0||0||(zFar + zNear)/(zFar - zNear)||-1|
|0||0High Shoes Pointed White heel Ankle Women OL Strap Pump Toe Hollow D'orsay GLTER qFIwfSAT||(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.