A High-Performance Method for Calculating the Minimum Distance between Two 2D and 3D NURBS Curves

Ma, YingLiang ORCID: https://orcid.org/0000-0001-5770-5843, Hewitt, W. T. and Turner, Martin (2006) A High-Performance Method for Calculating the Minimum Distance between Two 2D and 3D NURBS Curves. Journal of Graphics Tools, 11 (1). pp. 37-50. ISSN 2165-3488

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Abstract

We present a fast, accurate, and robust method to compute the minimum distance between two 2D and 3D NURBS curves. This is carried out by first decomposing both of the NURBS curves into their piecewise-Bézier forms. Candidate pairs, as a subset of all possible pairs, are extracted based on a two-level selection process. The first-level selection uses upper-lower bounds of Bézier subcurves to remove pairs. The second-level selection is based on the spatial relationship test between a pair of Bézier curves. An iterative multidimensional Newton-Raphson method is applied on all candidate pairs in order to calculate the approximate local minimum distances. Finally, by comparing all local minimum distances between a pair of Bézier subcurves, we are able to find the global minimum distance. The accuracy is improved by further use of the multidimensional Newton-Raphson method to give high accuracy. Source code is available online.

Item Type: Article
Faculty \ School: Faculty of Science > School of Computing Sciences
Related URLs:
Depositing User: LivePure Connector
Date Deposited: 05 Jan 2023 11:30
Last Modified: 05 Jan 2023 11:30
URI: https://ueaeprints.uea.ac.uk/id/eprint/90417
DOI: 10.1080/2151237X.2006.10129214

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