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T-spline Parameterization of 2D Geometries Based on the Meccano Method with a New T-mesh Optimization Algorithm

Lopez, J.I., M. Brovka, J.M. Escobar, J.M. Cascon, and R. Montenegro

22nd International Meshing Roundtable, Springer-Verlag, pp.57-74, October 13-16 2013

IMR
PROCEEDINGS

22nd International Meshing Roundtable
Orlando, FL
October 13-16,2013

University Institute for Intelligent Systems and Numerical Applications in Engineering, SIANI, University of Las Palmas de Gran Canaria, Spain
Department of Economics and History of Economics, Faculty of Economics and Management, University of Salamanca, Spain
Email: {jilopez,mbrovka,jmescobar,rmontenegro}@siani.es, casbar@usal.es

Summary
We present a new method, based on the idea of the meccano method and a novel T-mesh optimization procedure, to construct a T-spline parameterization of 2D geometries for the application of isogeometric analysis. The proposed method only demands a boundary representation of the geometry as input data. The algorithmobtains, as a result, high quality parametric transformation between 2D objects and the parametric domain, the unit square. First, we define a parametric mapping between the input boundary of the object and the boundary of the parametric domain. Then, we build a T-mesh adapted to the geometric singularities of the domain in order to preserve the features of the object boundary with a desired tolerance. The key of the method lies in defining an isomorphic transformation between the parametric and physical T-mesh finding the optimal position of the interior nodes by applying a new T-mesh untangling and smoothing procedure. Bivariate T-spline representation is calculated by imposing the interpolation conditions on points sited both on the interior and on the boundary of the geometry. The efficacy of the proposed technique is shown in several examples.

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