Polynomial-Based Non-Uniform Ternary Interpolation Surface Subdivision on Quadrilateral Mesh

Kaijun Peng, Jieqing Tan () and Li Zhang ()
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Kaijun Peng: School of Computer and Information, Hefei University of Technology, Hefei 230601, China
Jieqing Tan: School of Computer and Information, Hefei University of Technology, Hefei 230601, China
Li Zhang: School of Mathematics, Hefei University of Technology, Hefei 230601, China

Mathematics, 2023, vol. 11, issue 2, 1-22

Abstract: For non-uniform control polygons, a parameterized four-point interpolation curve ternary subdivision scheme is proposed, and its convergence and continuity are demonstrated. Following curve subdivision, a non-uniform interpolation surface ternary subdivision on regular quadrilateral meshes is proposed by applying the tensor product method. Analyses were conducted on the updating rules of parameters, proving that the limit surface is continuous. In this paper, we present a novel interpolation subdivision method to generate new virtual edge points and new face points of the extraordinary points of quadrilateral mesh. We also provide numerical examples to assess the validity of various interpolation methods.

Keywords: interpolation; ternary; surface subdivision; non-uniform subdivision; extraordinary point (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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