A new approach to solid modeling with trivariate T-splines based on mesh optimization |
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| Authors: | JM Escobar JM Cascón E Rodríguez R Montenegro |
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| Affiliation: | 1. University of Las Palmas de Gran Canaria, University Institute for Intelligent Systems and Numerical Applications in Engineering (SIANI), Spain;2. University of Salamanca, Department of Economics and History of Economics, Faculty of Economics and Management, Spain;1. Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX 78712, USA;2. Institute of Mechanics and Advanced Materials, School of Engineering, Cardiff University, Queen’s Buildings, The Parade, Cardiff CF24 3AA, Wales, UK;3. Department of Computer Science, Brigham Young University, Provo, UT 84602, USA;4. Department of Civil and Environmental Engineering, Brigham Young University, Provo, UT 84602, USA;1. Research Training Group 1462, Bauhaus-Universität Weimar, Weimar, Germany;2. Institute of Structural Mechanics, Bauhaus-Universität Weimar, Weimar, Germany;3. School of Civil Engineering, University of Tehran, Tehran, Iran;1. Institute for Computational Engineering and Sciences, The University of Texas at Austin, TX, USA;2. Department of Civil Engineering and Architecture, University of Pavia, and IMATI-CNR, Pavia, Italy;3. Department of Civil and Environmental Engineering, Brigham Young University, Provo, USA;1. Istituto di Matematica Applicata e Tecnologie Informatiche ‘E. Magenes’ del CNR, via Ferrata 1, 27100, Pavia, Italy;2. Dipartimento di Matematica, Università di Pavia, via Ferrata 1, 27100, Pavia, Italy |
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| Abstract: | We present a new method to construct a trivariate T-spline representation of complex genus-zero solids for the application of isogeometric analysis. The proposed technique only demands a surface triangulation of the solid as input data. The key of this method lies in obtaining a volumetric parameterization between the solid and the parametric domain, the unitary cube. To do that, an adaptive tetrahedral mesh of the parametric domain is isomorphically transformed onto the solid by applying a mesh untangling and smoothing procedure. The control points of the trivariate T-spline are calculated by imposing the interpolation conditions on points sited both on the inner and on the surface of the solid. The distribution of the interpolating points is adapted to the singularities of the domain in order to preserve the features of the surface triangulation. |
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