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) (p T v) ² Δ(v) = Σ p Є plans (v) (v T p) (p T v) = Σ p Є plans (v) v T (pp T ) v = v T [ Σ p Є plans (v) Kp] v

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

22. Plan Introduction Mesh Simplification Current Techniques The Project Results

38. ReductionTime(s) 10%0.390 50%0.810 80%1.051 « cow.obj » model (5804 faces) Method 1 ReductionTime(s) 10%1.081 50%3.044 80%3.825 « cow.obj » model (5804 faces) QEM

39. Plan Introduction Mesh Simplification Current Techniques The Project Results The

40. EOF ;)