VoroCrust: Simultaneous Surface Reconstruction and Volume Meshing - - PowerPoint PPT Presentation
VoroCrust: Simultaneous Surface Reconstruction and Volume Meshing with Voronoi cells Scott A. Mitchell (speaker), joint work with Ahmed H. Mahmoud, Ahmad A. Rushdi, Scott A. Mitchell, Ahmad Abdelkader Abdelrazek, Chandrajit L. Bajaj, John D.
Scott A. Mitchell (speaker), joint work with Ahmed H. Mahmoud, Ahmad A. Rushdi, Scott A. Mitchell, Ahmad Abdelkader Abdelrazek, Chandrajit L. Bajaj, John D. Owens, Mohamed S. Ebeida
Polytopal Element Methods in Mathematics and Engineering Atlanta, Georgia 28 Oct 2015, 10:55-11:20am (25 minutes)
– talk has no finite element content, just geometry
– Produces 3D Voronoi cells
– Surface (boundary) mesh is reconstructed (naturally, without clipping, snapping or cleanup) by the boundary between inside and outside 3D cells
– Open quality goals
no small area faces ...
Sandia National Laboratories
Input: domain with boundary (3D algorithm, illustrated in 2D) Theory for smooth manifolds Practical rules for sharp features
– Weighted Voronoi balls cover bdy – Spheres have uncovered interior and exterior point: “north” and “south” poles
– local feature size lfs spacing and – no ball center inside another ball
Spheres Intersect at two points = unweighted seeds pairs
red = exterior blue = interior
Ideal: both intersection points lie outside all other balls Want seeds sufficient to reconstruct surface surface mesh nodes are Voronoi vertices surface mesh edges are Voronoi edges surface mesh triangles are Voronoi facets
Properties surface mesh nodes are Voronoi vertices surface mesh edges are Voronoi edges surface mesh triangles are Voronoi facets Build unweighted Voronoi diagram of seeds. Boundary between interior and exterior cells = surface mesh, it reconstructs surface
Freedom: Additional seeds outside balls. Achieve aspect ratio bound. Additional goals: lattice points for a hex-dominant mesh
Freedom: Additional seeds outside balls. Achieve aspect ratio bound. Additional goals: lattice points for a hex-dominant mesh
– 2D: 2 circles ∧ two points – 3D: 3 spheres ∧ two points
dual to triangle
wDel triangle, negative circumradius
none inside a sphere
and none are closer = definition of a Voronoi vertex
light = triangle seen from below dark = triangle seen from above
G 2 ↑ g 1 ↑ G 1 ↓ g 2 ↓
G 234 ↑ G 124 ↑ G 123 ↓ G 134 ↓
Densely sample boundary. (Same lfs density.
balls covering boundary.) Use as weighted seeds. (vs. unweighted seeds) Select weighted Delaunay triangles for mesh and surface reconstruction. (vs. Voronoi cells) Far unweighted Voronoi vertices lie near medial axis. (vs. close points from weighted Voronoi edges near surface.)
images courtesy Nina Amenta, power crust author https://www.cs.utah.edu/~jeffp/8F-CG/namenta.ppt
Both have sliver issues, but they’re different issues. VoroCrust allows additional seeds and a well-shaped mesh.
ignoring sharp features results in bad sphere overlaps small spheres can avoid overlaps ideal is to share overlaps
– Robust polyhedral meshing with true Voronoi cells has arrived – “ideal” polytopal mesh with
– provable surface convergence
– paper nearly complete – reimplementing production software
– mesh quality
– mesh quality needed for polytopal elements?
– (bad surface normals in pathological cases?)