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In a perspective projection matrix, the bottom-right element must be 0 to ensure correct perspective division.
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In a perspective projection matrix, the homogeneous coordinate w must depend on z (depth) to enable correct perspective division.
This ensures objects farther from the camera appear smaller and depth is properly mapped.
I found a useful resource explaining this in detail, which you can check here:
https://www.scratchapixel.com/lessons/3d-basic-rendering/perspective-and-orthographic-projection-matrix/opengl-perspective-projection-matrix.html
The issue with
wis explained in the beggining of the article.In the attached GIF, I demonstrate the issue with a 3D scene - although it looks like the camera is rotating around the origin, the real problem lies in the incorrect perspective projection formula.