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

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 propos...

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Bibliographic Details
Published in:Mathematics (Basel) 2023-01, Vol.11 (2), p.486
Main Authors: Peng, Kaijun, Tan, Jieqing, Zhang, Li
Format: Article
Language:English
Subjects:
Approximation
Computer graphics
Design
extraordinary point
Interpolation
non-uniform subdivision
Polynomials
Quadrilaterals
surface subdivision
Tensors
ternary
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11020486