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

Gang Xu, Ming Li, Bernard Mourrain, Timon Rabczuk, Jinlan Xu, Stéphane P.A. Bordas

Research output: Contribution to journalArticle

37 Citations (Scopus)

Abstract

In this paper, we propose a general framework for constructing IGA-suitable planar B-spline parameterizations 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 C1∕G1-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.

Original languageEnglish
Pages (from-to)175-200
Number of pages26
JournalComputer Methods in Applied Mechanics and Engineering
Volume328
DOIs
Publication statusPublished - 2018 Jan 1
Externally publishedYes

Fingerprint

computer aided design
Parameterization
parameterization
partitions
Computer aided design
optimization
Splines
splines
curves
continuity
Global optimization
subdivisions
preprocessing
musculoskeletal system
Topology
Decomposition
topology
decomposition
Processing

Keywords

  • Analysis-suitable planar parameterization
  • Domain partition
  • Global/local optimization
  • Isogeometric analysis

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications

Cite this

Constructing IGA-suitable planar parameterization from complex CAD boundary by domain partition and global/local optimization. / Xu, Gang; Li, Ming; Mourrain, Bernard; Rabczuk, Timon; Xu, Jinlan; Bordas, Stéphane P.A.

In: Computer Methods in Applied Mechanics and Engineering, Vol. 328, 01.01.2018, p. 175-200.

Research output: Contribution to journalArticle

Xu, Gang ; Li, Ming ; Mourrain, Bernard ; Rabczuk, Timon ; Xu, Jinlan ; Bordas, Stéphane P.A. / Constructing IGA-suitable planar parameterization from complex CAD boundary by domain partition and global/local optimization. In: Computer Methods in Applied Mechanics and Engineering. 2018 ; Vol. 328. pp. 175-200.
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