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lecture13

# lecture13 - CS 551/651 Advanced Computer Graphics LOD A...

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David Luebke 1 12/09/11 CS 551/651: Advanced Computer Graphics LOD: A Sampling of Influential Algorithms

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David Luebke 2 12/09/11 Recap: Quadric Error Metrics What is a quadric in this algorithm? How is it calculated? How is it used?
David Luebke 3 12/09/11 Recap: Quadric Error Metric Minimize distance to all planes at a vertex Plane equation for each face: 0 : p = + + + D Cz By Ax v [ ] = 1 z y x D C B A T v p Distance to vertex v :

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David Luebke 4 12/09/11 Recap: Quadric Derivation = ) ( ) )( ( v planes p T T v p p v = ) ( ) ( v planes p T T v pp v v pp v v planes p T T = ) ( = ) ( 2 ) ( ) ( v planes p T v p v
David Luebke 5 12/09/11 Recap: Quadric Derivation (cont’d) pp T is simply the plane equation squared: The pp T sum at a vertex v is a matrix, Q : ( 29 v Q v v T = ) ( = 2 2 2 2 D CD BD AD CD C BC AC BD BC B AB AD AC AB A pp T

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David Luebke 6 12/09/11 Construct a quadric Q for every vertex Q 1 Q 2 v 2 v 1 Q 1 T 1 Qv v cost edge = Sort edges based on edge cost Suppose we contract to v 1 : v 1 ’s new quadric is simply: Q 2 1 Q Q Q + = The edge quadric : Recap: Using Quadrics
David Luebke 7 12/09/11 Recap: Minimize Q to calculate optimal coordinates for placing new vertex Details in paper; involves inverting Q Authors claim 40-50% less error Boundary preservation: add planes perpendicular to

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