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Isotropic triangle meshing of NURBS model

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NURBS is a mathematical model that has become a standard in the modeling community for generating and representing curves and surfaces. For some specific applications such as computational engineering or real-time rendering, the NURBS surfaces must be converted into isotropic triangle surface meshes. Such conversion is still a scientific challenge and current mesh generators suffer from a lack of control on the shape and size of the mesh elements, as well as of topological guarantees.

This project devises a reliable algorithm for meshing NURBS surfaces, using generic meshing framework of the CGAL library. The meshing is based on Delaunay triangulations. It consists of sampling a point set on the NURBS surface to initialize the triangulation and then refining it until all mesh elements meet some user-specified criteria. The core idea of the refinement process is to insert new points that are the intersections between the NURBS surface and line segments (the dual Voronoi edges of Delaunay triangles). We present a reliable and efficient line/NURBS intersection oracle based on the matrix representation of NURBS surfaces and methods in numerical linear algebra (matrix kernel, singular value decomposition, eigen-computation).

This talk is part of the Rainbow Group Seminars series.

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