Geometric conditions for injectivity of 3D Bézier volumes
Geometric conditions for injectivity of 3D Bézier volumes
复制标题
3D Bézier 体积注入性的几何条件
DOI：
10.3934/math.2021694
复制
发表时间：
2021
期刊：
影响因子：
2.2
通讯作者：
Chungang Zhu
中科院分区：
文献类型：
--
作者：
Xuanyi Zhao;Jinggai Li;Shiqi He;Chungang Zhu
The one-to-one property of injectivity is a crucial concept in computer-aided design, geometry, and graphics. The injectivity of curves (or surfaces or volumes) means that there is no self-intersection in the curves (or surfaces or volumes) and their images or deformation models. Bézier volumes are a special class of Bézier polytope in which the lattice polytope equals $ \Box_{m, n, l}, (m, n, l\in Z) $. Piecewise 3D Bézier volumes have a wide range of applications in deformation models, such as for face mesh deformation. The injectivity of 3D Bézier volumes means that there is no self-intersection. In this paper, we consider the injectivity conditions of 3D Bézier volumes from a geometric point of view. We prove that a 3D Bézier volume is injective for any positive weight if and only if its control points set is compatible. An algorithm for checking the injectivity of 3D Bézier volumes is proposed, and several explicit examples are presented.
登录
查看更多内容
DOI：
--
发表时间：
1989
期刊：
--
影响因子：
--
作者：
C. Hoffmann
通讯作者：
C. Hoffmann
有理贝塞尔曲面的注入性条件
影响因子：
2.5
作者：
Zhao Xuan-Yi;Zhu Chun-Gang
通讯作者：
Zhu Chun-Gang
DOI：
10.1016/0167-8396(88)90029-5
发表时间：
1988-07
期刊：
Comput. Aided Geom. Des.
影响因子：
--
作者：
T. Sederberg;R. J. Meyers
通讯作者：
T. Sederberg;R. J. Meyers
影响因子：
4.1
作者：
Emanuele Trucco;Konstantinos Plakas
通讯作者：
Emanuele Trucco;Konstantinos Plakas
DOI：
10.1007/978-3-642-76598-8
发表时间：
1992-03
期刊：
--
影响因子：
--
作者：
M. Hosaka
通讯作者：
M. Hosaka