期刊
COMPUTERS & GRAPHICS-UK
卷 97, 期 -, 页码 88-98出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.cag.2021.04.026
关键词
Toric volume; Injectivity; Rational Bezier volume; Mixed product; Clean and empty tetrahedron
资金
- National Natural Science Foundation of China [12071057, 11671068]
Parameterizations are widely used in various fields like computer aided design and computer graphics, and the injective property of toric volumes is discussed in this paper. An algorithm for checking the compatibility of two sets using the mixed product of three vectors is proposed, and the effectiveness of the method is demonstrated through examples. Additionally, the algorithm is improved based on properties of clean and empty tetrahedrons in combinatorics.
Parameterizations, which map parametric domains into certain domains, are widely used in computer aided design, computer aided geometric design, computer graphics, isogeometric analysis, and related fields. The parameterizations of curves, surfaces, and volumes are injective means that they do not have self-intersections. A 3D toric volume is defined via a set of 3D control points with weights that corre-spond to a set of finite 3D lattice points. Rational tensor product or tetrahedral B & eacute;zier volumes are special cases of toric volumes. In this paper, we proved that a toric volume is injective for any positive weights if and only if the lattice points set and control points set are compatible. An algorithm is also presented for checking the compatibility of the two sets by the mixed product of three vectors. Some examples illustrate the effectiveness of the proposed method. Moreover, we improve the algorithm based on the properties and results of clean and empty tetrahedrons in combinatorics. (c) 2021 Elsevier Ltd. All rights reserved.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据