Rasterization Basics

Rasterization: take 3D triangles, output 2D pixels.

Pipeline:

3D vertices
  ↓ transform (model + view + projection)
clip-space coords
  ↓ perspective divide (w)
NDC (normalized device coords, -1..1)
  ↓ viewport mapping
screen pixels
  ↓ for each triangle: rasterize to pixels
fragment shaders compute color
  ↓ depth test, blend
frame buffer

For each triangle:

1. Compute screen-space bounding box.
2. For each pixel in box: check if inside triangle.
3. If inside: interpolate vertex attributes (color, UV, normal).
4. Run fragment shader → pixel color.
5. Depth test: only write if closer.

Inside-triangle test (edge function):

The edge function gives signed area; positive on one side, negative on other.

Barycentric coordinates (u, v, w):

• Each pixel inside triangle has barycentric weights for the 3 vertices.
• u + v + w = 1.
• Compute via edge functions / triangle area.

Interpolate:

Use for: color, depth, normal, UV.

Z-buffer (depth test):

• Buffer same size as frame buffer.
• Per pixel: store depth of nearest surface so far.
• New pixel passes if its depth < stored.
• Update buffer + frame buffer.

Performance:

• GPU: parallel across all pixels.
• CPU: per-triangle inner loops.
• Modern GPUs: hundreds of millions of triangles per second.

Software rasterizers exist (tinyrenderer is famous educational one). Slower, but understanding rasterization → understanding GPUs.