Computational topology and swept volumes

被引：0

作者：

Blackmore, D ^{[1
]}

Mileyko, Y ^{[1
]}

Leu, MC ^{[1
]}

Regli, WC ^{[1
]}

Sun, W ^{[1
]}

机构：

[1] New Jersey Inst Technol, Dept Math Sci, Newark, NJ 07102 USA

来源：

GEOMETRIC AND ALGORITHMIC ASPECTS OF COMPUTER-AIDED DESIGN AND MANUFACTURING | 2005年 / 67卷

关键词：

shape; consistency; stability; sweeps; stratification; homology; virtual sculpting; heterogeneous material;

D O I：

暂无

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

Some fundamental principles of computational topology are formulated and discussed. It is demonstrated that swept volumes comprise a class of geometric objects that is particularly well suited to the application and development of the advanced mathematics/computer science based foundations of computational topology. Two new results in this vein are presented: (1) every smooth swept volume is proved to have a Whitney regular stratification; and (2) it is shown how homology can be used to characterize surface intersections. Applications of the dynamical systems approach to swept volumes in virtual sculpting and modeling of heterogeneous material such as bones are also described.

引用

页码：53 / 78

页数：26

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