Exact conversion from Bézier tetrahedra to Bézier hexahedra

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

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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
Publication statusPublished - 2018 May

Bibliographical note

Funding Information:
This research was supported by the National Natural Science Foundation of China under Grant Nos. 61772163 , 61761136010 , 61472111 , Zhejiang Provincial Natural Science Foundation of China under Grant Nos. LQ16F020005 , LR16F020003 , and the Graduate Scientific Research Foundation of Hangzhou Dianzi University .

Publisher Copyright:
© 2018 Elsevier B.V.


  • 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


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