1. CS175 2003 1 CS 175 – Week 4 Mesh Decimation General Framework, Progressive Meshes

2. CS175 2003 2 Overview motivation general framework topological operators progressive meshes geomorphs parameterization

3. CS175 2003 3 Motivation problems with huge meshes storage transmission editing rendering

4. CS175 2003 4 Motivation redundant information many triangles in planar region triangle smaller than a pixel reduce size remove vertices, edges, triangles preserve shape (geometry)

5. CS175 2003 5 Motivation non-manifold simplification vertex clustering topology may change manifold simplification mesh decimation incremental operation

6. CS175 2003 6 Motivation objectives intuitive control few parameters flexibility

7. CS175 2003 7 Mesh Decimation general framework topological operator local simplification fairness criterion cost of local simplification iteratively apply cheapest simplification

8. CS175 2003 8 Mesh Decimation basic algorithm compute cost of all simplifications sort into priority queue while queue not empty perform cheapest simplification update queue

9. CS175 2003 9 Topological Operators vertex removal re-triangulate hole edge collapse choose new point position half-edge collapse purely topological operator

10. CS175 2003 10 Progressive Meshes edge collapse c(i,j,r,l) remove v j and  (I,j,l),  (j,I,r) reconnect neighbours of v j with v i inverse vertex split s(i,j,r,l) insert v j and  (i,j,l),  (j,I,r) reconnect neighbours of v i with v j

11. CS175 2003 11 Progressive Meshes store base mesh M 0 sequence of vertex splits properties full sequence of hierarchies more compact than shared vertex

12. CS175 2003 12 Geomorphs interpolate between M k 0 and M k 1 build correspondence between removed and remaining vertices vertices in M k 1 have corresponding vertex in M k 0 linearly interpolate vertex positions avoids “snapping”

13. CS175 2003 13 Parameterization correspondence between removed vertices and remaining triangles index plus barycentric coordinates build progressively exponential map around v j gives parametric distances

14. CS175 2003 14 Related Issues feature lines collapse vertices to neighbouring feature vertices only selective refinement apply vertex splits only in areas that are visible from the viewpoint e.g. flight simulator

15. CS175 2003 15 Related Issues mesh compression connectivity 2 bits per vertex geometry linear predictors difference vectors regular remeshing

16. CS175 2003 16 Next Session fairness criteria Hausdorff distance first and second order fairness error quadrics