Come Lebreton -- 3D Delaunay Meshing of NURBS Models through Matrix Representations
13 December 2017 –
3D Delaunay Meshing of NURBS Models through Matrix Representations Come Lebreton Most often the industry, be it aerospace, mechanical, civil engineering, has recourse to C(omputer) A(ided) D(esign) to conceive their products. To optimize the functionality of these products (efficiency, cost...), it goes into a loop of : simulating the behaviour of the model given different environmental settings, and go back to CAD, to change the shape, properties of the elements and simulate the model again. Since most of the simulation in the industry is not based directly on the CAD model, there is a crucial step between the design and the simulation : the meshing process. As a matter of fact, the meshing technique most commonly used is a front advancing technique, and can be simplified by : taking separately each of the surfaces constituting the model, converting them to polyhedral (triangles most often) surfaces, fixing the connections between the surfaces, and meshing inside the set of polyhedral surfaces. The fixing part can be truly annoying, and these methods are patched all over with heuristics. We propose a switch in the meshing paradigm, consisting in meshing directly the complete object, by issuing intersection requests. This has been tested before(Bursayev, Dey), yet, not with an intersection routine providing enough robustness. To achieve that, we use the already implemented CGAL meshing algorithm, that is generic in the sense it is blind to the type of the surface defining the object. All it requires is a module to answer intersections requests with the surface. We implemented the algorithm proposed by [Shen and Buse] for solving intersections with the NURBS surfaces. To ensure that the connection between surfaces is sealed, we implemented a roughly identical algorithm to the protection algorithm proposed by [Bursayev, Levine, Dey].