Open Access

ARTICLE

Parameterization Transfer for a Planar Computational Domain in Isogeometric Analysis

by Jinlan Xu^*, Shuxin Xiao, Gang Xu, Renshu Gu

School of Computer Science and Technology, Hangzhou Dianzi University, Hangzhou, 310018, China

* Corresponding Author: Jinlan Xu. Email:

(This article belongs to the Special Issue: Integration of Geometric Modeling and Numerical Simulation)

Computer Modeling in Engineering & Sciences 2023, 137(2), 1957-1973. https://doi.org/10.32604/cmes.2023.028665

Received 31 December 2022; Accepted 15 February 2023; Issue published 26 June 2023

Abstract

In this paper, we propose a parameterization transfer algorithm for planar domains bounded by B-spline curves, where the shapes of the planar domains are similar. The domain geometries are considered to be similar if their simplified skeletons have the same structures. One domain we call source domain, and it is parameterized using multi-patch B-spline surfaces. The resulting parameterization is C1 continuous in the regular region and G1 continuous around singular points regardless of whether the parameterization of the source domain is C1/G1 continuous or not. In this algorithm, boundary control points of the source domain are extracted from its parameterization as sequential points, and we establish a correspondence between sequential boundary control points of the source domain and the target boundary through discrete sampling and fitting. Transfer of the parametrization satisfies C1/G1 continuity under discrete harmonic mapping with continuous constraints. The new algorithm has a lower calculation cost than a decomposition-based parameterization with a high-quality parameterization result. We demonstrate that the result of the parameterization transfer in this paper can be applied in isogeometric analysis. Moreover, because of the consistency of the parameterization for the two models, this method can be applied in many other geometry processing algorithms, such as morphing and deformation.

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Keywords

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