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Mesh Simplification

Mesh Simplification

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Mesh Simplification

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Presentation Transcript

  1. Mesh Simplification

  2. Plan • Introduction • Mesh Simplifications • Current Techniques • The Projet • Results

  3. Introduction • What’s a mesh? • Vertices, edges, polygones • Manifold (machine are able to make it) • Non-manifold • Meshes usage • Scientific imaging, movies, games… • Common problems • Stocking, rendering, data transferts…

  4. Plan • Introduction • Mesh Simplification • Current Techniques • The Project • Results

  5. Mesh Simplification • Idea • Remove « negligeable » elements • Caracteristics • Fidelity to original morphology • Topology • Re-exploitation

  6. Plan • Introduction • Mesh Simplification • Current Techniques • The Project • Results

  7. Current Techniques • Decimation • Contraction • Clustering • Progressive Mesh • Statistics • Wavelets, fractals,…

  8. Decimation

  9. Contraction

  10. Clustering

  11. Plan • Introduction • Mesh Simplification • Current Techniques • The Project • Results

  12. The Project (1) • Studies on current techniques • Schroeder, Lorensen, Zarge • Garland, Heckbert • Implementation • C/C++ • OpenGL • GLUT, GLUI

  13. The Project (2) • Bounds • Triangulated meshes • Implemented triangulations methods • Triangle Fan • Triangle Strip • Optimal solution • Delaunay’s Triangulation

  14. Triangulation : Triangle Fan

  15. Triangulation : Triangle Strip

  16. The Project (3) • Method 1: Edge Contraction • Edge Length • Distance criteria • Percentage • How many vertices to remove? • Cardinality ordering • Stronger • Weaker • Goal : avoid « dumb » mesh browsing

  17. Cardinalities, examples

  18. The Project (4) • Method 2: QEM • Quadric Error Metric • One error value per vertex • Create valid vertices pairs • Compute the contraction cost • Percentage • How many vertices to remove?

  19. The Project (5) • Method 2: QEM • p = [a b c d] T , ax + by +cz +d = 0 • Δ(v) = Σ p Є plans (v) (pT v) ² • Δ(v) = Σ p Є plans (v) (vT p) (pT v) = Σ p Є plans (v) vT (ppT) v = vT [ Σ p Є plans (v) Kp] v

  20. The Project (6) • Méthode 2: QEM (suite) a² ab ac ad • Kp = ppT = ab b² bc bd ac bc c² cd ad bd cd d² • Q = Σ p Є plans (v) Kp

  21. Plan • Introduction • Mesh Simplification • Current Techniques • The Project • Results

  22. Results

  23. Results

  24. Results

  25. Results

  26. Results

  27. Results

  28. Results

  29. Results

  30. Results

  31. Results

  32. Results

  33. Results

  34. Results

  35. Results

  36. Results

  37. Results « cow.obj » model (5804 faces) QEM « cow.obj » model (5804 faces) Method 1

  38. Plan • Introduction • Mesh Simplification • Current Techniques • The Project • Results The

  39. EOF ;)