3D Fundamentals Tutorial 10

In this tutorial we get the butt wiggling texture to respect our authoritae! In other words, we upgrade our affine texture mapping to perspective-correct texture mapping, putting the kibosh on the fucked-up texture distortion.

Video

The tutorial video is on YouTube here.

You can see a video that really exaggerates what affine (warpy) textures look like here.

[Expand]

• The need for perspective correction: texture warping 0:47
• Explanation & visualization of the problem 1:57

• Linear mapping of screen coordinates to texture coordinates is not correct
• Reason: interpolation in screenspace is different from interpolation in object space (and all attributes of the object)
• We need "foreshortening": far things get compressed, close things get expanded

• The math: the z divide makes mapping nonlinear 4:28
• Solution: interpolate between the z-divided texture coordinates 5:00
• Implementing this into code 8:40

• In PubeScreenTransformer.h (where the projection / z-divide is applied)
• In Pipeline.h (where the interpolation is done) 10:57

• Demo 11:57
• How perspective correction was (not) handled in early 3d games 12:16

• To fully correct, you need an expensive reciprocal operation 1/z for every pixel drawn
• PS1 just didn't give a shit 13:45

• Solution used in hardware pipelines / GPUs 14:11

• Control how each vertex attribute is interpolated independently (interpolation modifiers)

• References to full math derivations 14:50
• Side effect of our solution: we now have the correct z-values for each pixel 16:20

Downloads

The GitHub repository for the tutorial code is here.

Mathematical Derivations

• Scratchapixel

• Paper

See also

• Planet Chili Patreon
• Next in series (Tutorial 11)
• 3D Fundamentals Series