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Exact conversion from Bézier tetrahedra to Bézier hexahedra

Abstract : Modeling and computing of trivariate parametric volumes is an important research topic in the field of three-dimensional isogeo-metric 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 C k-continuity can be converted into a set of tensor-product Bézier volumes with G k-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.
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Submitted on : Tuesday, November 27, 2018 - 11:53:53 AM
Last modification on : Thursday, November 26, 2020 - 3:50:03 PM
Long-term archiving on: : Thursday, February 28, 2019 - 2:27:02 PM

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Gang Xu, Yaoli Jin, Zhoufang Xiao, Qing Wu, Bernard Mourrain, et al.. Exact conversion from Bézier tetrahedra to Bézier hexahedra. Computer Aided Geometric Design, Elsevier, 2018, 62, pp.154 - 165. ⟨10.1016/j.cagd.2018.03.022⟩. ⟨hal-01936167⟩

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