5 research outputs found
Constructing IGA-suitable planar parameterization from complex CAD boundary by domain partition and global/local optimization
In this paper, we propose a general framework for constructing IGA-suitable
planar B-spline parameterizations from given complex CAD boundaries consisting
of a set of B-spline curves. Instead of forming the computational domain by a
simple boundary, planar domains with high genus and more complex boundary
curves are considered. Firstly, some pre-processing operations including
B\'ezier 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 B\'ezier 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 B\'ezier patches
with respect to each quad in the quadrangulation, the high-quality B\'ezier
patch parameterization is obtained by a C1-constrained 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
Exact conversion from BĂ©zier tetrahedra to BĂ©zier hexahedra
International audienceModeling 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 BĂ©zier tetrahedra to BĂ©zier hexahedra with the same degree by reparametrization technique. In the first method, a BĂ©zier tetrahedron is converted into a degenerate BĂ©zier hexahedron, and in the second approach, a non-degenerate BĂ©zier tetrahedron is converted into four non-degenerate BĂ©zier hexahedra. For the proposed methods, explicit formulas are given to compute the control points of the resulting tensor-product BĂ©zier 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 BĂ©zier 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