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Chapter 25: Homogeneous Divide

Outline

• Why it’s necessary to have the w at all for perspective (can’t we just divide by z?)
  • i.e. the difference between w and z in clip space
• Mathematics behind it (projected coordinate systems)
• History behind left hand and right handed use in graphics (explanation of why OpenGL uses left-handed in clip space?)
• Possibility of using a projection matrix with inifinite far
• Precision issues in the depth buffer and ways to fix it
  • Using the reversed “DirectX” mapping (0 to 1)
  • Real logarithmic depth buffer using gl_FragDepth writes

References

• http://deltaorange.com/2012/03/08/the-truth-behind-homogenous-coordinates/
• https://stackoverflow.com/questions/4124041/is-opengl-coordinate-system-left-handed-or-right-handed
• https://softwareengineering.stackexchange.com/questions/17519/why-does-directx-use-a-left-handed-coordinate-system/88776#88776
• http://www.songho.ca/math/homogeneous/homogeneous.html
• http://www.terathon.com/gdc07_lengyel.pdf
• http://www.songho.ca/opengl/gl_transform.html#projection
• http://www.songho.ca/opengl/gl_projectionmatrix.html
• https://www.scratchapixel.com/lessons/3d-basic-rendering/perspective-and-orthographic-projection-matrix/opengl-perspective-projection-matrix
• https://stackoverflow.com/questions/31686664/perspective-divide-why-use-the-w-component
• https://en.wikipedia.org/wiki/Z-buffering#W-buffer

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