1. Remeshing for FEM Analysis of Viscous Objects CPSC 524 Final Project Tricia Pang, Kyle Porter, Josna Rao January 8, 2008

2. 2 Outline Introduction Dataset Method Results Discussion

3. 3 Introduction FEM analysis of viscous objects  Useful for modeling food bolus on tongue in human oral cavity Mark A. Nicosia. “Planar Finite Element Modeling of Bolus Containment in the Oral Cavity.” Computers in Biology & Medicine, 2007. Screenshot from Artisynth Toolkit Food bolus Tongue surface

4. 4 Introduction Problems result from large physical deformations  Triangle mesh uniformity disrupted  Poor distribution of physical properties (node mass/velocity) Further deformation requires well-conditioned meshes Mark A. Nicosia. “Planar Finite Element Modeling of Bolus Containment in the Oral Cavity.” Computers in Biology & Medicine, 2007.

5. 5 Project Goal Remesh viscous model after high deformation  User-defined level of detail (number of vertices)  Good triangle uniformity  Preserve geometry Extension: execute topological changes when required  Eg. Mesh splitting

6. 6 Dataset Generate in Artisynth  Java-based 3D biomechanical modelling toolkit  Physical simulation using FEM mechanics  Node connectivity described by tetrahedrons Replicate high-viscosity by setting material property Simulate physical deformations until failure

7. 7 Method Explicit surface remeshing ( Surazhsky and Gotsman, 2003 )  2D remeshing using local parameterizations  Adjust vertices to maximize angles of triangles in mesh  Use error metrics to ensure mesh fidelity  Reference current mesh to original mesh

8. 8 Method Adjust number of vertices  Alternate between edge splits/collapses and area-based remeshing Area-based remeshing  Local 2D parameterizations  Relocate vertices in current mesh  Improve angles of incident triangles for each neighbourhood  Measure error between new mesh and original mesh Delaunay edge flips Regularize connectivity  Obtain ideal valence for each vertex Angle-based smoothing

9. 9 Method Overlapping Parameterization  Patch parameterization scheme for performing local operations  Patches stored and reused

10. 10 Method Extension: Mesh Splitting  Execute when “bottleneck” occurs  Method #1: Principal curvature  Method #2: Medial axis  No working implementation for project Kmin < 0 Kmax > 0 x

11. 11 Results

12. 12 Results

13. 13 Discussion High triangle uniformity in final meshes Limitation of method:  Sharp features sometimes not preserved  More fine-tuning of error metrics Limited dataset  Could not reproduce highly-deformed meshes in Artisynth because poor mesh quality results in deformation failure

14. 14 References V. Surazhsky and C. Gotsman. Explicit Surface Remeshing. Eurographics Symposium on Geometry Processing, pages 17–28, 2003. V. Surazhsky and C. Gotsman. High quality compatible triangulations. Proceedings of 11th International Meshing Roundtable, pages 183-192, Sept. 2002. S. Fels, F. Vogt, K. van den Doel, J. Lloyd, I. Stavness and E. Vatikiotis-Bateson. Developing Physically-Based, Dynamic Vocal Tract Models using ArtiSynth. Proc. Int. Seminar Speech Production, pages 419-426, 2006.

15. 15 Questions?