物理モデルによる自動メッシュ分割(<小特集>自然界に学ぶアルゴリズム)

概要

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Automated mesh generation is a significant problem in many computer applications such as engineering analysis, computer graphics and layered manufacturing. Although various algorithms have been proposed thus far, their functionality and coverage are limited, in most cases being application-specific. This paper provides a summary of those algorithms by classifying them and pointing out unsolved problems. In reviewing them, it is clear that none sufficiently address the major problem of node placement, that is to say the locating of nodes such that they maintain a specified distance between nodes and create a mesh with minimal distortion. This paper introduces a new, physically-based approach to this problem. The method was inspired by the pattern of soap bubbles floating in liquid which gives topology and geometry similar to ideal meshes. Each mesh node is modeled as a bubble with a point mass and viscous damping. The force field exerts repelling/attracting forces between bubbles much like intermolecular van del Waals forces. The equilibrium bubble configuration is obtained by solving numerically the governing equation of motion to yield the static force balance. After the bubble locations are decided, their center points are connected by Delaunay triangulation to give a complete mesh topology.
1993-03-15