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Interactive deformable models with quadratic bases in Bernstein–Bézier-form

Weber, Daniel and Kalbe, Thomas and Stork, André and Fellner, Dieter W. and Goesele, Michael (2011):
Interactive deformable models with quadratic bases in Bernstein–Bézier-form.
In: The Visual Computer, 27 (6-8), pp. 473-483, [Article]

Abstract

We present a physically based interactive simulation technique for de formable objects. Our method models the geometry as well as the displacements using quadratic basis functions in Bernstein–Bézier form on a tetrahedral finite element mesh. The Bernstein–Bézier formulation yields significant advantages compared to approaches using the monomial form. The implementation is simplified, as spatial derivatives and integrals of the displacement field are obtained analytically avoiding the need for numerical evaluations of the elements’ stiffness matrices. We introduce a novel traversal accounting for adjacency in order to accelerate the reconstruction of the global matrices. We show that our proposed method can compensate the additional effort introduced by the co-rotational formulation to a large extent. We validate our approach on several models and demonstrate new levels of accuracy and performance in comparison to current state-of-the-art.

Item Type: Article
Erschienen: 2011
Creators: Weber, Daniel and Kalbe, Thomas and Stork, André and Fellner, Dieter W. and Goesele, Michael
Title: Interactive deformable models with quadratic bases in Bernstein–Bézier-form
Language: English
Abstract:

We present a physically based interactive simulation technique for de formable objects. Our method models the geometry as well as the displacements using quadratic basis functions in Bernstein–Bézier form on a tetrahedral finite element mesh. The Bernstein–Bézier formulation yields significant advantages compared to approaches using the monomial form. The implementation is simplified, as spatial derivatives and integrals of the displacement field are obtained analytically avoiding the need for numerical evaluations of the elements’ stiffness matrices. We introduce a novel traversal accounting for adjacency in order to accelerate the reconstruction of the global matrices. We show that our proposed method can compensate the additional effort introduced by the co-rotational formulation to a large extent. We validate our approach on several models and demonstrate new levels of accuracy and performance in comparison to current state-of-the-art.

Journal or Publication Title: The Visual Computer
Volume: 27
Number: 6-8
Divisions: 20 Department of Computer Science
20 Department of Computer Science > Graphics, Capture and Massively Parallel Computing
20 Department of Computer Science > Interactive Graphics Systems
Date Deposited: 24 Nov 2017 17:42
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