Unified Representation of Curves and Surfaces
Abstract
:1. Introduction
2. Knot Interval
3. I-Splines
3.1. Basic Concepts
3.2. Mathematical Description
3.2.1. Coordinates of Control Points
3.2.2. I-Spline Formula
3.2.3. I-Spline Curves
3.2.4. I-Spline Surfaces
4. Local Refinement of I-Splines
4.1. Refinement of the Blending Functions
4.2. Local Refinement Algorithm
4.2.1. The Topology Stage
4.2.2. The Geometry Stage
5. Unified Representation of Curves and Surfaces
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
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Wang, A.; Zhao, G.; He, C. Unified Representation of Curves and Surfaces. Mathematics 2021, 9, 1019. https://doi.org/10.3390/math9091019
Wang A, Zhao G, He C. Unified Representation of Curves and Surfaces. Mathematics. 2021; 9(9):1019. https://doi.org/10.3390/math9091019
Chicago/Turabian StyleWang, Aizeng, Gang Zhao, and Chuan He. 2021. "Unified Representation of Curves and Surfaces" Mathematics 9, no. 9: 1019. https://doi.org/10.3390/math9091019