Perspective-Correct Interpolation

Why Linear Screen-Space Interpolation Fails

After projection and perspective division, triangle vertices live in normalized device coordinates. Attributes like color, texture coordinates, and normals are not linear in screen space under perspective projection. Linear interpolation stretches values near the camera and compresses them far away.

For example, a textured wall viewed at a steep angle shows visible warping if you interpolate UVs linearly across the triangle. PlayStation 1 titles skipped perspective correction to save cycles, and the swimming textures were a signature artifact.

The 1/w Trick

The fix: interpolate A/w and 1/w in screen space, then divide:

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Here u, v, w are screen-space barycentric coordinates and w0, w1, w2 are homogeneous w values from the projection matrix. Any attribute divided by w becomes linear in screen space; the final division corrects perspective distortion.

• Linear interpolation: fast but wrong under perspective
• Perspective-correct: standard in GPU hardware since 3dfx Voodoo
• Software rasterizers: must implement this by hand

For This Exercise

You will compare linear and perspective-correct color interpolation at a test point with known barycentric coordinates and w values. This task asks you to print both results side by side so the difference is visible. Anyone writing a WebGL fallback or software renderer must implement this 1/w division themselves.