CS CS 175 – Week 5 Mesh Decimation Fairness Criteria

CS Overview coarse mesh hierarchies fairness criteria error quadrics

CS Remark on Edge Collapse let  i be valency of v i 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

CS 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

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

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

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

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

CS Error Quadrics planes defined by triangles sum of squared distances to planes quadratic form ellipsoidal level sets accumulate error quadrics

CS Next Week subdivision polygons triangle meshes