Constructing IGA-suitable planar parameterization from complex CAD boundary by domain partition and global/local optimization

Gang Xu 1 Ming Li 2 Bernard Mourrain 3 Timon Rabczuk 4 Jinlan Xu 1 Stéphane P.A. Bordas 5
1 Study Computer Science & Technology [Hangzhou]
2 State Key Laboratory of CAD &CG [Zhejiang]
3 AROMATH - AlgebRe, geOmetrie, Modelisation et AlgoriTHmes
CRISAM - Inria Sophia Antipolis - Méditerranée , National and Kapodistrian University of Athens
4 ISM - Institute of Structural Mechanics [Weimar]
5 Research Unit in Engineering Sciences [Luxembourg]
Abstract : In this paper, we propose a general framework for constructing IGA-suitable planar B-spline param-eterizations from given complex CAD boundaries. Instead of the computational domain bounded by four B-spline curves, planar domains with high genus and more complex boundary curves are considered. Firstly, some pre-processing operations including Bézier extraction and subdivision are performed on each boundary curve in order to generate a high-quality planar parameterization; then a robust planar domain partition framework is proposed to construct high-quality patch-meshing results with few singularities from the discrete boundary formed by connecting the end points of the resulting boundary segments. After the topology information generation of quadrilateral decomposition , the optimal placement of interior Bézier curves corresponding to the interior edges of the quadrangulation is constructed by a global optimization method to achieve a patch-partition with high quality. Finally, after the imposition of C 1 /G 1-continuity constraints on the interface of neighboring Bézier patches with respect to each quad in the quadrangulation, the high-quality Bézier patch parameterization is obtained by a local optimization method to achieve uniform and orthogonal iso-parametric structures while keeping the continuity conditions between patches. The efficiency and robustness of the proposed method are demonstrated by several examples which are compared to results obtained by the skeleton-based parameterization approach.
Keywords : isogeometric analysis analysis-suitable planar parameterization global/local optimization domain partition
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Submitted on : Monday, October 2, 2017 - 11:14:14 AM
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Gang Xu, Ming Li, Bernard Mourrain, Timon Rabczuk, Jinlan Xu, et al.. Constructing IGA-suitable planar parameterization from complex CAD boundary by domain partition and global/local optimization. Computer Methods in Applied Mechanics and Engineering, Elsevier, 2018, 328, pp.175 - 200. ⟨10.1016/j.cma.2017.08.052⟩. ⟨hal-01599319⟩

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