Evaluation Algorithms for Parametric Curves and Surfaces
This paper extends Woźny and Chudy’s linear-complexity Bézier evaluation algorithm (2020) to all parametric curves/surfaces with normalized basis functions via a novel basis function matrix decomposition. The unified framework covers the following: (i) B-spline/NURBS models; (ii) Bézier-type surface...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-07-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/14/2248 |
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| Summary: | This paper extends Woźny and Chudy’s linear-complexity Bézier evaluation algorithm (2020) to all parametric curves/surfaces with normalized basis functions via a novel basis function matrix decomposition. The unified framework covers the following: (i) B-spline/NURBS models; (ii) Bézier-type surfaces (tensor-product, rational, and triangular); (iii) enhanced models with shape parameters or non-polynomial basis spaces. For curves, we propose sequential and reverse corner-cutting modes. Surface evaluation adapts to type: non-tensor-product surfaces are processed through index-linearization to match the curve format, while tensor-product surfaces utilize nested curve evaluation. This approach reduces computational complexity, resolves cross-model compatibility issues, and establishes an efficient evaluation framework for diverse parametric geometries. |
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| ISSN: | 2227-7390 |