Tile-Based Rasterization

Why Process the Whole Screen Per Triangle?

A modern GPU rasterizes millions of triangles per frame. Most triangles are small and touch only a tiny screen fraction. Testing every pixel on the full framebuffer for every triangle wastes work and destroys cache locality.

Tile-based rasterization divides the screen into rectangles (typically 8x8, 16x16, or 32x32 pixels). The rasterizer first finds which tiles a triangle overlaps, then runs fine per-pixel tests only inside those tiles.

The Assignment Algorithm

1. Compute the triangle's axis-aligned bounding box
2. Find tiles intersecting the bounding box
3. Coarse test: does the triangle actually overlap each candidate tile?
4. Fine rasterize: per-pixel barycentric tests inside passing tiles

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For example, on a 32x32 screen with 8x8 tiles, a small triangle in the top-left corner might touch only tile (0,0) instead of all 16 tiles. Mobile GPUs (ARM Mali, PowerVR, Apple) extend this with tile-based deferred rendering, keeping intermediate results in on-chip memory to cut VRAM bandwidth.

• Desktop GPUs: hybrid tiled binning (NVIDIA, AMD)
• Mobile GPUs: full TBDR with on-chip G-buffer
• Tradeoff: setup overhead vs massive bandwidth savings

For This Exercise

You will implement tile assignment for three triangles on a 32x32 screen divided into 4x4 tiles of 8x8 pixels. This task asks you to print which tiles each triangle touches. The cache-friendly chunking you model here is why phones render complex 3D scenes without draining the battery on constant memory traffic.