A Line/Trimmed NURBS Surface Intersection Algorithm Using Matrix Representations

Jingjing Shen 1 Laurent Busé 2 Pierre Alliez 3 Neil Dodgson 1
2 AROMATH - AlgebRe, geOmetrie, Modelisation et AlgoriTHmes
CRISAM - Inria Sophia Antipolis - Méditerranée , National and Kapodistrian University of Athens
3 TITANE - Geometric Modeling of 3D Environments
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : We contribute a reliable line/surface intersection method for trimmed NURBS surfaces, based on a novel matrix-based implicit representation and numerical methods in linear algebra such as singular value decomposition and the computation of generalized eigenvalues and eigenvectors. A careful treatment of degenerate cases makes our approach robust to intersection points with multiple pre-images. We then apply our intersection algorithm to mesh NURBS surfaces through Delaunay refinement. We demonstrate the added value of our approach in terms of accuracy and treatment of degenerate cases, by providing comparisons with other intersection approaches as well as a variety of meshing experiments.
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Jingjing Shen, Laurent Busé, Pierre Alliez, Neil Dodgson. A Line/Trimmed NURBS Surface Intersection Algorithm Using Matrix Representations. Computer Aided Geometric Design, Elsevier, 2016, 48, pp.1-16. ⟨10.1016/j.cagd.2016.07.002⟩. ⟨hal-01268109v2⟩

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