Bubble mesh: automated triangular meshing of non-manifold geometry by sphere packing

This paper presents a new computational method for fully automated triangular mesh generation, consistently applicable to wire-frame, surface, solid, and nonmanifold geometries. The method, called bubble rrzeshing, is based on the observation that a pattern of tightly packed spheres mimics a Voronoi diagram, from which a set of well-shaped Delaunay triangles and tetrahedral can be created by connecting the centers of the spheres. Given a domain geometry and a node-spacing function, spheres are packed on geometric entities, namely, vertices, edges, faces, and volumes, in ascending order of dimension. Once the domain is filled with spheres, mesh nodes are placed at the centers of these spheres and are then connected by constrained Delaunay triangulation and tet rahedrizat ion. To obtain a closely packed configuration of spheres, the authors devised a technique for physically based mesh relaxation with adaptive population control, The process of mesh relaxation significantly reduces the number of ill-shaped triangles and tetrahedral.

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