1. Recent Progress in Mesh Generation Joshua A. Levine, Jonathan R. Bronson, Ross T. Whitaker

2. Meshing Techniques Delaunay Refinement Advancing Front Variational Grid-based

3. Variational Techniques: Psystem for CAD Meshing

4. Psystem Contributions Variational Method (2D) Particles move in parametric space. Sizing field inferred Adaptively. 2D Triangulation, Edge flips, TetGen for volume Next Steps: integrate ideas to BioMesh3D Best Paper at 19 th International Meshing Roundtable (IMR) 2010!

5. Grid-Based Techniques: Isosurface Stuffing *François Labelle, Jonathan Richard Shewchuk. Isosurface stuffing: fast tetrahedral meshes with good dihedral angles. ACM Trans. Graph. 26(3): 57 (2007).

6. Isosurface Stuffing BCC Lattice-based. Vertices are warped to surface for geometric fit. Stencils based on inside/outside surface. Adaptively-sized tets. Spectacular dihedral angle bounds (w/ proof)

7. Multi-Material Stuffing A stencil-based approach for multiple materials. Conform to complex topologies, material boundaries Implemented and tested for two-dimensions.

8. 3D Multi-Material Stuffing Four topological cases – 3 edge cuts (2 mats) – 4 edge cuts (2 mats) – 5 edge cuts (3 mats) – 6 edge cuts (4 mats) *Gregory M. Nielson, Richard Franke. Computing the separating surface for segmented data. IEEE Visualization 1997: 229-233

9. Four Cases Illustrated

10. An Empirical Proof for Angles 3 and 4 cut cases extend from Shewchuk’s proof 6 cut case behaves like 3 material in 2D 5 cut case is the focus of our efforts

11. Summary and Future Goals Developing a suite of meshing techniques. Comprehensive approach, favoring technologies for their particular strengths. Community outreach: MeshMed workshop

12. Thank you Questions?