The thing to understand is that the perspective transform in homogeneous coordinates doesn't just shrink the X and Y coordinates based on Z distance, but it als

The thing to understand is that the perspective transform in homogeneous coordinates doesn't just shrink the X and Y coordinates based on Z distance, but it also shrinks the Z coordinate too! The farther some objects are from the viewer, the closer together they are bunched in Z space. Basically, the points out at infinity where parallel lines appear to converge under perspective are translated to a finite Z distance. So all of infinity is squeezed into that range. Why is Z also transformed? In order to keep the transformation affine: to keep the correctness of straight lines under the perspective transformation. If you have an arbitrarily rotated straight line in a perspective view, and you just divide the X and Y coordinates along that line by Z, the line will look just fine in the perspective view, because the viewer does not see the Z coordinate. But in fact in the perspective-transformed space (which is 3 dimensional), it will not be a straight line. Now that is fine for wireframe or even certain polygon graphics, in which we can regard the perspective as a projection from 3D to 2D and basically drop the Z coordinate entirely after dividing X and Y by it. An example of where it breaks down is when you're using a Z-buffer for the visibility calculations. If you have two polygons that intersect, and you don't handle the Z coordinate in the perspective transform, they will not correctly intersect: the line at which they intersect, calculated by your Z buffer, will not be the right one, and that will be particularly obvious under movement, appearing as a weird artifact where that intersecting line shifts around. You won't see this when you have polygons that only join at their vertices to form surfaces. The 2D transform is good enough: the endpoints of a shared edge are correctly transformed from 3D into 2D taking into account perspective, and we just render a straight line between them in 2D and all is good. In the intersecting case, there are interpolated points involved which are not represented as vertices and have not been individually transformed. That interpolation then goes wrong. Another area where this is important, I think, is correctness of texture maps. If it is wrong, then a rotating polygon with a texture map will have creeping artifacts, where the pixels of the texture don't stick to the same spot on the polygon, except near the vertices.