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Engineering with Computers
Published in: Engineering with Computers 4/2014

01-10-2014 | Original Article

A new method for T-spline parameterization of complex 2D geometries

Authors: M. Brovka, J. I. López, J. M. Escobar, J. M. Cascón, R. Montenegro

Published in: Engineering with Computers | Issue 4/2014

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Abstract

We present a new strategy, 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 algorithm obtains, 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 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 in the interior and on the boundary of the geometry. The efficacy of the proposed technique is shown in several examples. Also we present some results of the application of isogeometric analysis in a geometry parameterized with this technique.
previous article Conformal parameterization for multiply connected domains: combining finite elements and complex analysis
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Appendix
Available only for authorised users
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Metadata
Title
A new method for T-spline parameterization of complex 2D geometries
Authors
M. Brovka
J. I. López
J. M. Escobar
J. M. Cascón
R. Montenegro
Publication date
01-10-2014
Publisher
Springer London
Published in
Engineering with Computers / Issue 4/2014
Print ISSN: 0177-0667
Electronic ISSN: 1435-5663
DOI
https://doi.org/10.1007/s00366-013-0336-8

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