1. Triangulation of uniform particle systems: its application to the implicit surface texturing F. Levet, X. Granier, C. Schlick IPARLA Project (INRIA futurs, LaBRI) University of Bordeaux 1 - FRANCE

2. Outline of the presentation  Presentation of particle systems  Mesh creation from uniform particles Triangulation Tesselation  Texturation  Results

3. A particle-based system  Witkin and Heckbert [94]  Sampling Split/death criterion Particles migration Adaptive repulsion Uniform distribution

4. Some improvements  Isotropic sampling With an energy function  Crossno and Angel [97]  Rosh et al. [97]  Meyer et al. [05] With repulsion forces  Turk [91]  Pauly et al. [02]  Levet et al. [05]  Galin et al [06] Uniform case Non-uniform case Each one but slower Anisotropic sampling BlobTree

5. Triangulation of the particles  Crossno et Angel, SpiralingEdge [99] Uniform and non-uniform Result  very complex algorithm Lots of special cases  Adapted triangulation to the uniform case

6. An adapted triangulation  Distance between neighboring particles Near 2r (r the repulsion radius)

7. An adapted triangulation  Approach Gather the particles (with a 3r distance) Polygonize them as a ring p p 1 p 2 p 3 p 4 p 5 p 0

8. An adapted triangulation  Approach Gather the particles (with a 3r distance) Polygonize them as a ring

9. An adapted triangulation  Results Intersections between triangles

10. An adapted triangulation  Results Intersections between triangles Three bad configurations

14. Results  Quasi-equilateral triangles  Very fast # particlesTriangulation time# triangles 6820.0101 360 2 8130.0455 622 17 1780.26334 292 36 4640.68572 915 73 3791.175146 671

15. Triangle tesselation  Triangulation of the particules Minimization of the deformations  Few particules Subdivision of the obtained triangles  Projection

16. Texturation with particle systems  Turk [92] Expensive for high frequency details  Pedersen [95] Defines a set of patches Complex to avoid deformation  Zonenschein [97, 98] Particles follow the gradient field Not robust with high-order genus surfaces

17. Texturation  Neyret et Cani [99] 1. Original mesh

18.  Neyret et Cani [99] 1. Original mesh 2. Simplified mesh Texturation

19.  Neyret et Cani [99] 1. Original mesh 2. Simplified mesh 3. Texturation support Texturation

20.  Neyret et Cani [99] 1. Original mesh 2. Simplified mesh 3. Texturation support 4. Local parametrization Texturation

21.  Neyret et Cani [99] 1. Original mesh 2. Simplified mesh 3. Texturation support 4. Local parametrization Texturation

22.  Neyret et Cani [99] 1. Original mesh 2. Simplified mesh 3. Texturation support 4. Local parametrization Texturation

23.  Triangles : Texture mesh  Subdivision : parametrization Texturation

24. Results

25. Conclusion  Fast triangulation of uniform particles  On-the-fly mesh refinement  2D pattern-based texturing of immplicit surfaces

26. Future works  Texturing of huge scanned objects  Curvature informations  Local edition of the particle system