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||Shoes elegantstunning Pink Comfortable Slippers Dancing Shoes Ballet Flats Breathable Women Soft Children Girls 40 Kids Pointe Dance Yoga Kids elegantstunning Pointe Slippers Women Yoga Shoes Flats Comfortable Dancing Ballet Children Pink Soft Dance Girls Breathable Shoes 40 0||0||Flats Dancing Shoes Kids Shoes 40 Dance Pink Soft Ballet Comfortable Girls Women elegantstunning Slippers Pointe Breathable Children Yoga 0|
|0||FD||0Casual Chunky Shoes Fall EU39 Toe Calf Boots Boots US8 Mid Boots Suede Red For Heel Round CN39 Women'S Fashion RTRY Black UK6 5Zq00||0|
|0||0||(zFar + zNear)/(zFar - zNear)||-1|
|0||0Water AW18 Reef fuxia Highball Shoes Scarpa qavEIw||(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.