Past Event: Oden Institute Seminar

VoroCrust: Conforming Polyhedral meshing of non-convex domains with sharp features and narrow regions

Mohamed S. Ebeida, Sandia National Laboratories

Abstract

We present VoroCrust: a novel approach to polyhedral meshing that simultaneously generates a quality mesh of the surface of a Piecewise Linear Complex (PLC) model and decomposes the enclosed volume by unweighted Voronoi cells with good aspect ratios conforming to the surface mesh, without clipping or bad normals. VoroCrust has an embedded sizing function that capture the curvature of the model, and robustly represents sharp features and narrow regions that may be associated with the input model. Up to our knowledge, VoroCrust is the first to solve this open problem. VoroCrust also outputs an approximation of the medial axis of the input model and provides a fast technique for in/out point classification. A variation of VoroCrust can also handle non-manifold and non-watertight inputs. We illustrate the robustness and output quality of VoroCrust through a collection of models of varying complexity. In this talk we also present the recently released VoroCrust software and discuss its performance in practice. Bio Mohamed Ebeida is an expert in computational geometry related to Voronoi diagrams, hyperplane sampling and sphere packing. He is the creator of several novel Voronoi-based algorithms with application to meshing, high-dimensional sampling, uncertainty quantification, and optimization. He graduated from University of California Davis in 2008 with a PhD in Mechanical and Aeronautical Engineering and a Masters in Applied Mathematics. He worked for two years as a Postdoc at Carnegie Mellon University. In 2010, he joined Sandia National Laboratories where he actively works in exploring the potential of Voronoi decompositions for a wide range on non-traditional applications. Mohamed is the inventor on three patents for novel applications of the emerging VoroCrust technology in low and high-dimensions.