Evaluation Algorithms for Parametric Curves and Surfaces

Lanlan Yan ()
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Lanlan Yan: College of Science, East China University of Technology, Nanchang 330013, China

Mathematics, 2025, vol. 13, issue 14, 1-20

Abstract: 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.

Keywords: geometric design; parametric curves and surfaces; normalized basis functions; evaluation algorithms; corner-cutting; linear complexity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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