Exact conversion from Bézier tetrahedra to Bézier hexahedra

Gang Xu, Yaoli Jin, Zhoufang Xiao, Qing Wu, Bernard Mourrain, Timon Rabczuk

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Modeling and computing of trivariate parametric volumes is an important research topic in the field of three-dimensional isogeometric analysis. In this paper, we propose two kinds of exact conversion approaches from Bézier tetrahedra to Bézier hexahedra with the same degree by reparametrization technique. In the first method, a Bézier tetrahedron is converted into a degenerate Bézier hexahedron, and in the second approach, a non-degenerate Bézier tetrahedron is converted into four non-degenerate Bézier hexahedra. For the proposed methods, explicit formulas are given to compute the control points of the resulting tensor–product Bézier hexahedra. Furthermore, in the second method, we prove that tetrahedral spline solids with Ck-continuity can be converted into a set of tensor–product Bézier volumes with Gk-continuity. The proposed methods can be used for the volumetric data exchange problems between different trivariate spline representations in CAD/CAE. Several experimental results are presented to show the effectiveness of the proposed methods.

Original languageEnglish
Pages (from-to)154-165
Number of pages12
JournalComputer Aided Geometric Design
Volume62
DOIs
Publication statusPublished - 2018 May 1
Externally publishedYes

Fingerprint

Triangular pyramid
Splines
Computer aided engineering
Electronic data interchange
Trivariate
Computer aided design
Tensor Product
Spline
Hexahedron
Isogeometric Analysis
Reparametrization
Dimensional Analysis
Data Exchange
Control Points
Explicit Formula
Three-dimensional
Computing
Experimental Results
Modeling

Keywords

  • Bézier hexahedra
  • Bézier tetrahedra
  • Isogeometric analysis
  • Reparameterization
  • Volumetric modeling

ASJC Scopus subject areas

  • Modelling and Simulation
  • Automotive Engineering
  • Aerospace Engineering
  • Computer Graphics and Computer-Aided Design

Cite this

Exact conversion from Bézier tetrahedra to Bézier hexahedra. / Xu, Gang; Jin, Yaoli; Xiao, Zhoufang; Wu, Qing; Mourrain, Bernard; Rabczuk, Timon.

In: Computer Aided Geometric Design, Vol. 62, 01.05.2018, p. 154-165.

Research output: Contribution to journalArticle

Xu, G, Jin, Y, Xiao, Z, Wu, Q, Mourrain, B & Rabczuk, T 2018, 'Exact conversion from Bézier tetrahedra to Bézier hexahedra', Computer Aided Geometric Design, vol. 62, pp. 154-165. https://doi.org/10.1016/j.cagd.2018.03.022
Xu, Gang ; Jin, Yaoli ; Xiao, Zhoufang ; Wu, Qing ; Mourrain, Bernard ; Rabczuk, Timon. / Exact conversion from Bézier tetrahedra to Bézier hexahedra. In: Computer Aided Geometric Design. 2018 ; Vol. 62. pp. 154-165.
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