Article
Version 1
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Quasi Cubic Trigonometric Curve and Surface
Version 1
: Received: 17 October 2019 / Approved: 18 October 2019 / Online: 18 October 2019 (11:33:13 CEST)
How to cite: Zhang, G.; Wang, K. Quasi Cubic Trigonometric Curve and Surface. Preprints 2019, 2019100213. https://doi.org/10.20944/preprints201910.0213.v1 Zhang, G.; Wang, K. Quasi Cubic Trigonometric Curve and Surface. Preprints 2019, 2019100213. https://doi.org/10.20944/preprints201910.0213.v1
Abstract
Firstly, a new set of Quasi-Cubic Trigonometric Bernstein basis with two tension shape parameters is constructed, and we prove that it is an optimal normalized totally basis in the framework of Quasi Extended Chebyshev space. And the Quasi-Cubic Trigonometric Bézier curve is generated by the basis function and the cutting algorithm of the curve are given, the shape features (cusp, inflection point, loop and convexity) of the Quasi-Cubic Trigonometric Bézier curve are analyzed by using envelope theory and topological mapping; Next we construct the non-uniform Quasi-Cubic Trigonometric B-spline basis by assuming the linear combination of the optimal normalized totally positive basis have partition of unity and continuity, and its expression is obtained. And the non-uniform B-spline basis is proved to have totally positive and high-order continuity. Finally, the non-uniform Quasi Cubic Trigonometric B-spline curve and surface are defined, the shape features of the non-uniform Quasi-Cubic Trigonometric B-spline curve are discussed, and the curve and surface are proved to be continuous.
Keywords
Quasi Extended Chebyshev space; optimal normalized totally positive basis; high-order continuity; shape preserving; shape features
Subject
Computer Science and Mathematics, Computational Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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