Sufficient condition for injectivity of NURBS volumes by tangent cones
Sufficient condition for injectivity of NURBS volumes by tangent cones
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DOI：
10.1016/j.cam.2023.115303
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发表时间：
2023-05
期刊：
影响因子：
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通讯作者：
Yingying Yu;Ye Ji;Chungang Zhu
中科院分区：
文献类型：
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作者：
Yingying Yu;Ye Ji;Chungang Zhu
NURBS方法是描述曲线/曲面/体积形状的标准数学方法，广泛应用于计算机辅助设计、计算机辅助制造、计算机图形学等领域。NURBS体的注入性意味着它们没有自交。由于参数化的注入性依赖于它们的雅可比函数的符号，而NURBS体积的雅可比矩阵是由其切向量在三个方向上的行列式决定的，因此本文首先提出了一种计算NURBS体积切锥边界向量的方法。然后给出了NURBS体注入性的充分条件。并给出了一种检测算法。算例验证了该算法的有效性。
NURBS method is the standard mathematical method for describing the shapes of curves/surfaces/volumes, and it is extensively used in computer-aided design, computer-aided manufacturing, and computer graphics. The injectivity of NURBS volumes means that they do not have self-intersections. Since the injectivity of parameterizations depend on the signs of their Jacobian functions, and the Jacobian of a NURBS volume is determined by the determinant of its tangent vectors in three directions, we first propose a method to compute the bounding vectors of the tangent cones of NURBS volume in this paper. Then the sufficient condition for the injectivity of NURBS volume is proposed. A checking algorithm is also presented. Some examples are given to verify the effectiveness of the algorithm.