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Mipmapping

Samples prefiltered texture levels so distant surfaces avoid aliasing and cache waste.

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Quick Facts

Compact metadata for implementation and discovery.

Category: Rendering
Difficulty: Intermediate
Family: Texture Filtering
Tier: Core
Status: Verified
Review: Source Checked
Sources: 1
Formulas: 1
Relationships: 2
Code example: Ready
Visualization: Ready

Overview

Mipmapping stores a pyramid of downsampled texture images and selects or blends levels based on the screen-space footprint of each texture lookup.

Core Concepts

texture pyramidpixel footprintprefilteringlevel selection

Quick facts

Complexity

Runtime and memory behavior at a glance.

Best

O(1)

Average

O(pixels)

Worst

O(pixels)

Space

O(texture size)

When to Use

Use when textured surfaces can appear smaller than the original texture resolution.
Use when reducing shimmer, minification aliasing, and texture-cache pressure matters.

When Not to Use

Avoid when the texture is never minified or memory for extra levels is unavailable.
Avoid relying on mipmaps alone for highly anisotropic viewing angles.

What It Does

Samples prefiltered texture levels to reduce aliasing and improve cache behavior
Uses texture pyramid and pixel footprint to guide the work.
Produces rendered image.

Use Cases

Real-time graphics
Offline rendering
Lighting and visibility effects

Inputs

Scene geometry
Materials
Camera and lighting state

Outputs

Rendered image
Visibility or shading buffers

Key Formulas (1)

Mip level

level = log2(texture_footprint)

level = log2(texture_footprint)

Chooses a texture level based on projected pixel footprint.

Pseudocode

1.Generate downsampled texture levels
2.For each texture lookup, estimate the pixel footprint in texture space
3.Choose or blend nearby mip levels from that footprint
4.Sample the selected level with normal texture filtering
5.Return the filtered texel value

Canonical Example

Input: a brick wall texture viewed far away
Output: sample a smaller prefiltered mip level instead of the full-resolution image
Explanation: The smaller level averages many texels before sampling, reducing shimmer.

Implementation Notes

Build each level with proper filtering and color-space handling.
Use texture-coordinate derivatives to estimate level of detail.
Clamp or bias LOD deliberately for sharpness and stability.

Common Pitfalls

Generating levels in the wrong color space can blur or darken textures.
Missing edge handling can create seams in atlases.
Choosing a level only by distance ignores texture-coordinate derivatives.

Interactive Mechanism Walkthrough

Spatial Primitive & Sweep-Line Canvas

Show rays, samples, buffers, or shading terms that contribute to the final pixel.

Step 1 of 5: Generate downsampled texture levels

rendering-mechanism

Notes

Mipmaps improve minification; anisotropic filtering is often needed for steep viewing angles.

Sources (1)

What each reference supports for this entry.

Williams 1983

Paper

Original mipmapping paper introducing pyramidal texture filtering.

Open source

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Used byRasterization

Rendering · Foundation

Raster pipelines use mipmaps to reduce texture aliasing.

Compare with this

Conceptual neighborImage Pyramid

Image Processing · Core

Both store progressively lower-resolution image levels.