Sufficient condition for injectivity of NURBS volumes by tangent cones

Journal article (2023)

Authors

Y. Ji Key Laboratory for Computational Mathematics and Data Intelligence of Liaoning Province, Dalian University of Technology

Chun-Gang Zhu Dalian University of Technology, Key Laboratory for Computational Mathematics and Data Intelligence of Liaoning Province

Affiliation

External organisation

To reference this document use:

http://resolver.tudelft.nl/uuid:c855ab05-3fe4-4d3c-815a-322b44832e5a

More Info

expand_more

Published Date

2023-11

Language

English

Reuse Rights

Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.

Affiliation

External organisation

Abstract

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.