1. CS175 2003 1 CS 175 – Week 5 Mesh Decimation Fairness Criteria

2. CS175 2003 2 Overview coarse mesh hierarchies fairness criteria error quadrics

3. CS175 2003 3 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

4. CS175 2003 4 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

5. CS175 2003 5 Fairness Criteria distance (order 0) triangle roundness (order 1) dihedral angles (order 2)

6. CS175 2003 6 Order 0 distance vertex $ plane maximal parametric distance uses parametric correspondencies maximal geometric distance one-sided Hausdorff distance

7. CS175 2003 7 Order 1 approximates local distortion triangle roundness longest edge / inradius analytical approach distortion of linear map singular values of Jacobian condition number

8. CS175 2003 8 Order 2 approximates local curvature discrete Laplacian discrete Gauss and mean curvature sum of dihedral angles measure normal deviation

9. CS175 2003 9 Error Quadrics planes defined by triangles sum of squared distances to planes quadratic form ellipsoidal level sets accumulate error quadrics

10. CS175 2003 10 Next Week subdivision polygons triangle meshes