CS 175 – Week 5 Mesh Decimation Fairness Criteria

CS 175 – Week 5Mesh DecimationFairness Criteria

Overview • coarse mesh hierarchies • fairness criteria • error quadrics

Remark on Edge Collapse • let i be valency of vi • edge collapse c(i,j,r,l) modifies • i!i + j – 4 • j!0 • r!r – 1 • l!l – 1 • don’t collapse if r=3 or l=3

Coarse Mesh Hierachy • repeat • unlock all vertices • while unlocked vertices remain • remove cheapest unlocked vertex • lock all neighbours • removes ¼ 25% in each outer loop • defines a “coarse” hierarchy

Fairness Criteria • distance (order 0) • triangle roundness (order 1) • dihedral angles (order 2)

Order 0 • distance vertex $ plane • maximal parametric distance • uses parametric correspondencies • maximal geometric distance • one-sided Hausdorff distance

Order 1 • approximates local distortion • triangle roundness • longest edge / inradius • analytical approach • distortion of linear map • singular values of Jacobian • condition number

Order 2 • approximates local curvature • discrete Laplacian • discrete Gauss and mean curvature • sum of dihedral angles • measure normal deviation

Error Quadrics • planes defined by triangles • sum of squared distances to planes • quadratic form • ellipsoidal level sets • accumulateerror quadrics

Next Week • subdivision • polygons • triangle meshes

CS 175 – Week 5 Mesh Decimation Fairness Criteria