Loop detection in surface patch intersections
Computer Aided Geometric Design
Shape preserving least-squares approximation by polynomial parametric spline curves
Computer Aided Geometric Design
Computer Aided Geometric Design - Special issue dedicated to Paul de Faget de Casteljau
Preventing Self-Intersection under Free-Form Deformation
IEEE Transactions on Visualization and Computer Graphics
Volumetric parameterization and trivariate B-spline fitting using harmonic functions
Computer Aided Geometric Design
Optimal analysis-aware parameterization of computational domain in isogeometric analysis
GMP'10 Proceedings of the 6th international conference on Advances in Geometric Modeling and Processing
Parameterization of contractible domains using sequences of harmonic maps
Proceedings of the 7th international conference on Curves and Surfaces
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In the isogeometric analysis framework, a computational domain is exactly described using the same representation as the one employed in the CAD process. For a CAD object, various computational domains can be constructed with the same shape but with different parameterizations; however one basic requirement is that the resulting parameterization should have no self-intersections. Moreover we will show, with an example of a 3D thermal conduction problem, that different parameterizations of a computational domain have different impacts on the simulation results and efficiency in isogeometric analysis. In this paper, a linear and easy-to-check sufficient condition for the injectivity of a trivariate B-spline parameterization is proposed. For problems with exact solutions, we will describe a shape optimization method to obtain an optimal parameterization of a computational domain. The proposed injective condition is used to check the injectivity of the initial trivariate B-spline parameterization constructed by discrete Coons volume method, which is a generalization of the discrete Coons patch method. Several examples and comparisons are presented to show the effectiveness of the proposed method. During the refinement step, the optimal parameterization can achieve the same accuracy as the initial parameterization but with less degrees of freedom.