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An algorithm for the medial axis transform of 3D polyhedral solids

机译:3D多面体的中轴变换算法

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The medial axis transform (MAT) is a representation of an objectnwhich has been shown to be useful in design, interrogation, animation,nfinite element mesh generation, performance analysis, manufacturingnsimulation, path planning and tolerance specification. In this paper, annalgorithm for determining the MAT is developed for general 3D polyhedralnsolids of arbitrary genus without cavities, with nonconvex vertices andnedges. The algorithm is based on a classification scheme which relatesndifferent pieces of the medial axis (MA) to one another, even in thenpresence of degenerate MA points. Vertices of the MA are connected tonone another by tracing along adjacent edges, and finally the faces ofnthe axis are found by traversing closed loops of vertices and edges.nRepresentation of the MA and its associated radius function isnaddressed, and pseudocode for the algorithm is given along withnrecommended optimizations. A connectivity theorem is proven to show thencompleteness of the algorithm. Complexity estimates and stabilitynanalysis for the algorithms are presented. Finally, examples illustratenthe computational properties of the algorithm for convex and nonconvexn3D polyhedral solids with polyhedral holes
机译:中间轴变换(MAT)是对象的表示,已被证明可用于设计,询问,动画,有限元网格生成,性能分析,制造模拟,路径规划和公差说明。在本文中,针对无腔,具有非凸顶点和边缘的任意属的一般3D多面体,开发了确定MAT的算法。该算法基于一种分类方案,即使在存在退化的MA点的情况下,中间轴(MA)的不同部分也相互关联。 MA的顶点通过沿相邻边进行跟踪而彼此相连,最后通过遍历顶点和边的闭环来找到轴的面。n对MA的表示及其关联的半径函数进行寻址,并给出算法的伪代码建议不要使用优化。证明了连通性定理表明算法的完备性。给出了算法的复杂度估计和稳定性分析。最后,实例说明了具有多面孔的凸面和非凸面3D多面体的算法的计算性质

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