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Nonobtuse Remeshing and Mesh Decimation

Nonobtuse Remeshing and Mesh Decimation. John Y.S. Li and Richard (Hao) Zhang GrUVi lab, Simon Fraser University, Canada. Nonobtuse Remeshing and Mesh Decimation. SGP 2006 Cagliari, Italy. Introduction. I changed spacing. Goal Nonobtuse = at most 90 o Motivation Delaunay Triangulation

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Nonobtuse Remeshing and Mesh Decimation

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  1. Nonobtuse Remeshing and Mesh Decimation John Y.S. Li and Richard (Hao) Zhang GrUVi lab, Simon Fraser University, Canada

  2. Nonobtuse Remeshing and Mesh Decimation SGP 2006 Cagliari, Italy Introduction I changed spacing • Goal • Nonobtuse = at most 90o • Motivation • Delaunay Triangulation • Finite Element Method • Geodesic Computation • Planar Mesh Embedding

  3. Nonobtuse Remeshing and Mesh Decimation SGP 2006 Cagliari, Italy Related work • Open problem. [GY03]– a bit misleading • Nonobtuse triangulation of polygons. [BMR94] • 30o - 120o angle bound. [Che93] • Minimum 30o angle bound. [CS05] • 3D domain tiling with acute tetrahedra. [ESU04]

  4. Nonobtuse Remeshing and Mesh Decimation SGP 2006 Cagliari, Italy Overview of our Approach 1 2 3 Generate initial nonobtuse mesh Deform-to-fit optimization Nonobtuse decimation Generality and flexibility of our framework to allow … ??? I think this is quite important.

  5. Nonobtuse Remeshing and Mesh Decimation SGP 2006 Cagliari, Italy Modified Marching Cubes 1 Input is mesh and convert to SDF? • Input: Signed distance field • Based on midpoint-based Marching Cubes (MC) • Some new vertices are inserted inside the cubes • Guaranteed nonobtusity • No angles less than 30o • Handling open mesh is a bit tricky, but possible

  6. Nonobtuse Remeshing and Mesh Decimation SGP 2006 Cagliari, Italy Optimization 2 Clearly separate error reduction and smoothing • Objective • Quadric term • Associate closest triangle T to v • Average squared distances • Smoothing: • Better angle quality Mark T, v, etc. below

  7. Nonobtuse Remeshing and Mesh Decimation SGP 2006 Cagliari, Italy Optimization 2 • Constraints • feasible region of an edge • feasible region of a vertex

  8. Nonobtuse Remeshing and Mesh Decimation SGP 2006 Cagliari, Italy Optimization 2 • Quadratic Programming • Iterative optimization • Priority Queue • Updating quadrics • Local search of closest triangle T to v ― a heuristic • Stopping condition • Smoothing You need to elaborate a bit on this slide. Indicate alternating between …

  9. Nonobtuse Remeshing and Mesh Decimation SGP 2006 Cagliari, Italy Nonobtuse Decimation 3 • Similar framework for nonobtuse edge collapse • Optimal location for the unified vertex • Cost of edge collapse • Updating quadrics If you are short on time, this slide can be simplified. The framework is quite standard.

  10. Nonobtuse Remeshing and Mesh Decimation SGP 2006 Cagliari, Italy Results • Different sampling grids in Modified MC

  11. Nonobtuse Remeshing and Mesh Decimation SGP 2006 Cagliari, Italy Results • Effects of smoothness term and smoothing

  12. Nonobtuse Remeshing and Mesh Decimation SGP 2006 Cagliari, Italy Results No slide on speed? • Angle distribution

  13. Nonobtuse Remeshing and Mesh Decimation SGP 2006 Cagliari, Italy Future work Improving speed? • Better angle bound • Recently achieved 30o – 90o bound • Nonobtuse meshing from point cloud • Handling meshes with boundaries • Feature preservation • Guaranteed acute remeshing

  14. Thank you! Any questions?

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