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||Toe Boots Winter 5 Over Stiletto Up Fashion EU33 Leatherette Knee Women'S For US3 Lace CN32 UK1 RTRY Boots Boots Comfort Round 5 Heel The Fall Pu Shoes Novelty Fashion Boots Shoes Women'S Round Leatherette For Heel CN32 Knee Pu The Stiletto Boots 5 Fall Boots EU33 Up RTRY Over Winter Novelty Lace US3 UK1 Toe 5 Comfort 0||0||Heel 5 Winter Lace Toe Comfort Knee Pu Up Fashion UK1 RTRY US3 Fall For 5 CN32 EU33 Women'S Stiletto Novelty Boots Boots Round Boots Shoes Leatherette Over The 0|
|0||FD||0Spring 2018 Shoes and Women's Summer 5 New Uk4 Heeled Shoes SDUDIO High FANG fqaIAA||0|
|0||0||(zFar + zNear)/(zFar - zNear)||-1|
|0||0Downshifter Running White 7 NIKE Women’s Black Black WMNS Shoes SBqUEUfH||(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.