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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.

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FD/aspect Star Zoom White Anthracite Metallic Gold Black WMNS Shoes 34 Pegasus Air NIKE Women’s Running Black WMNS NIKE Zoom Star Running Shoes Anthracite Pegasus Women’s Metallic Gold White 34 Air Black Black 0 0 34 Metallic Gold White Air Black NIKE Star Running Zoom Shoes Black WMNS Women’s Pegasus Anthracite 0
0 FD 0 0
0 0 (zFar + zNear)/(zFar - zNear) -1
0 0 (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.

WMNS Pegasus Shoes Black Running Zoom Anthracite White Air Black NIKE Metallic 34 Women’s Gold Star 85xq0wIT WMNS Pegasus Shoes Black Running Zoom Anthracite White Air Black NIKE Metallic 34 Women’s Gold Star 85xq0wIT WMNS Pegasus Shoes Black Running Zoom Anthracite White Air Black NIKE Metallic 34 Women’s Gold Star 85xq0wIT WMNS Pegasus Shoes Black Running Zoom Anthracite White Air Black NIKE Metallic 34 Women’s Gold Star 85xq0wIT WMNS Pegasus Shoes Black Running Zoom Anthracite White Air Black NIKE Metallic 34 Women’s Gold Star 85xq0wIT WMNS Pegasus Shoes Black Running Zoom Anthracite White Air Black NIKE Metallic 34 Women’s Gold Star 85xq0wIT

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