Textures and Mipmaps

Texture Types

Type	Dimensions	Use Case
1D	Linear array	Gradients, lookup tables
2D	Width × height	Most common, images
3D	Volume texture	Medical imaging, volumetric effects
Cube map	6 faces	Environment mapping, skyboxes

Texture Mapping Pipeline

1. Define texture: Load image (TGA, PNG) as pixel data
2. Specify UV mapping: Each vertex has texture coordinates $(u, v)$
3. Sampling: Look up texture colour using interpolated UV

Power-of-Two Textures

GPUs prefer dimensions that are powers of two ($2^n$, e.g., 256, 512, 1024):

• Better caching and filtering performance
• Required for mipmaps
• Non-POT textures may have limited features

Texture Tiling

Repeating textures (brick, tile patterns) use wrapped coordinates:

$T(u, v) = T(u - \lfloor u \rfloor, v - \lfloor v \rfloor)$

Example: $T(1.1, 0) = T(0.1, 0)$—the texture wraps.

Texture Filtering

Magnification

Pixel larger than texel (zooming in):

Filter	Result
Nearest neighbour	Pick closest texel (blocky)
Bilinear	Weighted average of 4 texels (smooth)

Minification

Pixel smaller than texel (zooming out):

• Many texels may map to one pixel
• Causes aliasing and flickering
• Solution: Use mipmaps

Mipmaps

A mipmap is a pre-filtered pyramid of textures at decreasing resolutions:

• Each level is half the size of the previous
• Only 1/3 additional storage required: $1 + \frac{1}{4} + \frac{1}{16} + ... = \frac{4}{3}$
• Used when textures are minified

Generating Mipmaps

glGenerateMipmap(GL_TEXTURE_2D);

Mipmap Filtering

glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_LINEAR_MIPMAP_LINEAR);

Mode	Description
GL_LINEAR_MIPMAP_NEAREST	Use nearest mipmap level, bilinear filtering
GL_LINEAR_MIPMAP_LINEAR	Trilinear (interpolate between mipmap levels)

Texture Parameters

glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_LINEAR);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_LINEAR_MIPMAP_NEAREST);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, GL_CLAMP_TO_EDGE);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_T, GL_CLAMP_TO_EDGE);

Wrap Modes

Mode	Behaviour
GL_CLAMP_TO_EDGE	Clamp to edge texels
GL_REPEAT	Tile texture
GL_MIRRORED_REPEAT	Tile with mirroring

Advanced Texture Techniques

Technique	Description
Normal mapping	Perturb normals for fake surface detail
Displacement mapping	Modify geometry (requires tessellation)
Environment mapping	Cube map stores reflections

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Summary

• Textures store image data sampled using UV coordinates
• Filtering determines quality: nearest (fast), bilinear (smooth), trilinear (best)
• Mipmaps pre-filter textures to prevent aliasing when minified
• POT dimensions preferred for GPU efficiency

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Past Paper Questions

2024 Paper 3 Question 4: Explain texture filtering. When would you use mipmaps?

2023 Paper 3 Question 4: What is the difference between GL_NEAREST and GL_LINEAR filtering?

2022 Paper 3 Question 4: Calculate the additional storage required for mipmaps on a 1024×1024 texture.