Texture Mapping with Bilinear Filtering

UV Coordinates on Triangle Surfaces

Texture mapping applies a 2D image to a 3D surface. Edwin Catmull introduced the idea in 1974; today every real-time renderer depends on it. Each vertex carries texture coordinates (u, v) in the range 0 to 1. During rasterization, UVs interpolate across the triangle (with perspective correction) and each fragment looks up a texel color.

Texture mapping decouples surface detail from geometry. A flat triangle can look like brick, wood, or skin without extra vertices.

Nearest vs Bilinear Sampling

Nearest-neighbor rounds (u, v) to the closest texel. Fast but blocky when magnified.

Bilinear filtering blends four neighboring texels:

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For example, sampling (u=0.375, v=0.625) on a 4x4 texture blends texels at (1,2), (2,2), (1,3), and (2,3). Mipmaps (Lance Williams, 1983) add precomputed smaller versions to fix minification aliasing when distant textures shrink to a few pixels.

• Nearest: one texel lookup, sharp but pixelated
• Bilinear: four lookups + three lerps, smoother
• Trilinear: bilinear across two mipmap levels

For This Exercise

You will sample a 4x4 gradient texture using nearest-neighbor and bilinear filtering at test UV coordinates. This task requires you to print both results so the quality difference is visible. Understanding these two modes is essential for software renderers, image resizers, and any GLSL texture() call where you choose sampler settings.