Z-Buffer Depth Testing

The Visibility Problem

When multiple triangles overlap on screen, which one is visible? The z-buffer (depth buffer), invented independently by Wolfgang Straßer and Edwin Catmull in 1974, solves this with a second buffer parallel to the color framebuffer.

Algorithm:

1. Initialize z-buffer to far depth (e.g., 1.0)
2. For each triangle, rasterize covered pixels
3. Interpolate depth at each pixel
4. If depth < z-buffer[x][y], update z-buffer and write color

Screen-Space Depth and Z-Fighting

The z-buffer operates in screen space after vertex transformation. Each vertex carries (x, y, z) in normalized device coordinates where z typically runs 0 (near) to 1 (far).

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For example, a red triangle at z=0.3 and a blue triangle at z=0.7 both covering pixel (5,5): the red triangle wins because 0.3 < 0.7. Z-fighting occurs when two surfaces are nearly equal in depth; limited float precision makes them flicker. Perspective-correct interpolation uses 1/z, not linear z, for accurate results under projection.

• Advantage: no triangle sorting needed, trivially parallel per pixel
• Cost: extra memory buffer (width * height floats)
• Alternatives: painter's algorithm (sort back-to-front), ray tracing

For This Exercise

You will implement a 10x10 z-buffer with two overlapping triangles and print the final framebuffer colors. This task requires depth testing on every covered pixel. Z-buffering is the visibility algorithm behind Quake through Unreal Engine 5, and z-fighting bugs appear in every graphics programmer's career eventually.