A fast and practical method to pack spheres for mesh generation

Abstract

Sphere packing is an attractive way to generate high quality mesh. Several algorithms have been proposed in this topic, however these algorithms are not sufficiently fast for large scale problems. The paper presents an efficient sphere packing algorithm which is much faster and appears to be the most practical among all sphere packing methods presented so far for mesh generation. The algorithm packs spheres inside a domain using advancing front method. High efficiency has resulted from a concept of 4R measure, which localizes all the computations involved in the whole sphere packing process.

An automatic method for generating carbon nanostructure atomistic models using hexagonal meshes with properly distributed defects

“…The sphere‐packing method was previously proposed by our research group to generate meshes for finite element analysis (FEA), and in this work, it is adapted for the purpose of atomistic modeling. We use imaginary spheres with diameters equal to 2.46 Å to fill the surface of the 3D model.…”

A novel three-dimensional mesh deformation method based on sphere relaxation

“…The basic idea of the modified sphere relaxation algorithm is to redistribute the nodes by reducing or eliminating overlaps and spaces between spheres, for the exactly compacted configuration of spheres will preserve high mesh quality directly [20]. In this work, considering the complex connectivity of tetrahedral elements, the attractive and repulsive interactions are derived from some opposite facets of the node instead of all contacting spheres.…”

“…Sphere packing has been used in the mesh generation [20], for the compacted distribution of spheres preserves tetrahedral elements in high quality. Lo and Wang [21] packed the spheres tightly together by means of the advancing front approach to generate a set of ideal locations for the Delaunay point insertion.…”

An Algorithm to Generate Random Sphere Packs in Arbitrary Domains

“…The level of a front is defined as the sum of the level of its particles. Liu et al (27) proposed a sphere packing algorithm with the objective of generate high quality meshes with the Delaunay triangulation. The method packs meshes starting with an initial front constructed by placing particles in the vertices, edges and faces of the mesh.…”

“…Benabbou (2, 3) places three spheres for each triangle (one in each vertex) to create the first particles. Similarly in (27) the quality of the initial front is restricted to the container triangulation and the level of detail of the mesh. Jerier (20) limits the size of the radii, defined by the mean length of the mesh, which must be previously tetrahedralized.…”