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Mesh reduction

As explained in Geometry for Programmers

The technique of decreasing a mesh's element count while preserving its important shape characteristics within acceptable error.

Mesh reduction decreases a mesh’s triangle count while keeping its important shape characteristics within acceptable accuracy. It trades detail for efficiency in applications such as 3D printing, game programming, and design automation. section 11.2.1 section 1.0

A typical reduction operation follows this geometric idea:

  • Find edges on flat surfaces, together with their neighboring triangles. section 11.2.1
  • Collapse a selected edge to a point when the resulting shape remains sufficiently accurate. section 11.2.1
  • Remove the associated pair of triangles and let neighboring triangles fill the gap. section 11.2.1

A cube does not need thousands of triangles

A perfect cube can be represented with 12 triangles rather than 65,536. The reduction preserves the cube’s essential geometry while removing unnecessary representation detail. section 11.2.1

v  0.0  0.0  0.0
v  0.0  0.0  1.0
v  0.0  1.0  0.0
v  0.0  1.0  1.0
v  1.0  0.0  0.0
v  1.0  0.0  1.0
v  1.0  1.0  0.0
v  1.0  1.0  1.0
f  1 7 5
f  1 3 7
f  1 4 3
f  1 2 4
f  3 8 7
f  3 4 8
f  5 7 8
f  5 8 6
f  1 5 6
f  1 6 2
f  2 6 8
f  2 8 4

Use the indexed vertices and triangular faces as a concrete mesh representation before considering which edges and neighboring triangles can be collapsed. section 11.2.1

How Geometry for Programmers covers it

How deep it goes
Explains edge-collapse mechanics and topology requirements, but stops short of specifying a complete reduction algorithm or quality metric.
Examples
Uses a cube reduced from 65,536 triangles to 12 and an indexed vertex-and-face mesh representation.
What it assumes
Assumes triangle-based surface representations and teaches why neighboring-triangle topology matters during reduction.
What you can do after
Evaluate mesh reduction by identifying collapsible edges, their neighboring triangles, and the resulting accuracy trade-off.
How it connects
Connects mesh reduction to triangle meshes, topology, edge collapse, half-edge data structures, and surface smoothing.
Cover of Geometry for Programmers
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This explainer was generated by Manning's knowledge graph from the text of Geometry for Programmers. The section links point to the parts of the book it draws on.