High-quality construction of analysis-suitable trivariate NURBS solids by reparameterization methods

Gang Xu (1) , Bernard Mourrain (2) , André Galligo (2)

1 College of computer - Hangzhou Dianzi University
2 GALAAD - Geometry, algebra, algorithms

High-quality volumetric parameterization of computational domain plays an important role in three-dimensional isogeometric analysis. Reparameterization technique can improve the distribution of isoparametric curves/surfaces without changing the geometry. In this paper, using the reparameterization method, we investigate the high-quality construction of analysis-suitable NURBS volumetric parameterization. Firstly, we introduce the concept of volumetric reparameterization, and propose an optimal Möbis transformations to improve the quality of isoparametric structure based on a new uniformity metric. Secondly, from given boundary NURBS surfaces, we present a two-stage scheme to construct the analysis-suitable volumetric parameterization: in the first step, uniformity-improved reparameterization is performed on the boundary surfaces to achieve high-quality isoparametric structure without changing the shape; in the second step, from a new variational harmonic metric and the reparameterized boundary surfaces, we construct the optimal inner control points and weights to achieve an analysis-suitable NURBS solid. Several examples with complicated geometry are presented to illustrate the effectiveness of proposed methods.

Domaines: Ingénierie assistée par ordinateur; Synthèse d'image et réalité virtuelle [cs.GR]

Gang Xu, Bernard Mourrain, André Galligo. High-quality construction of analysis-suitable trivariate NURBS solids by reparameterization methods. 2013. ⟨hal-00922544v1⟩