Splines for Meshes with Irregularities

J. Peters
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引用次数: 16

Abstract

Splines form an elegant bridge between the continuous real world and the discrete computational world. Their tensor-product form lifts many univariate properties effortlessly to the surfaces, volumes and beyond. Irregularities, where the tensor-structure breaks down, therefore deserve attention – and provide a rich source of mathematical challenges and insights. This paper reviews and categorizes techniques for splines on meshes with irregularities. Of particular interest are quad-dominant meshes that can have n 6= 4 valent interior points and T-junctions where quad-strips end. “Generalized” splines can use quad-dominant meshes as control nets both for modeling geometry and to support engineering analysis without additional meshing. 2010 Mathematics Subject Classification. 65N35, 15A15.
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不规则网格的样条
样条曲线在连续的真实世界和离散的计算世界之间架起了一座优雅的桥梁。它们的张量积形式将许多单变量性质毫不费力地提升到表面、体积和其他地方。因此,张量结构破坏的不规则性值得关注,并为数学挑战和见解提供了丰富的来源。本文对不规则网格上的样条处理技术进行了综述和分类。特别感兴趣的是可以有n 6= 4个价内点和t结点的四主导网格,其中四条带结束。“广义”样条可以使用四主导网格作为控制网,既可以进行几何建模,也可以在没有额外网格的情况下支持工程分析。2010数学学科分类。65N35, 15A15。
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