FINITE-ELEMENT MESH GENERATION FROM CONSTRUCTIVE-SOLID-GEOMETRY MODELS

The paper discusses automatic finite-element mesh generation from a constructive-solid-geometry model of a 3D solid object with curved faces. It is argued that, to derive a geometrically accurate mesh for such an object, much information about the object's boundary elements (faces, edges, and vertices) must be available, and a fruitful approach to dealing with this is presented. First, it is shown why the mesh-generation procedure requires a boundary representation for the derivation of an accurate mesh. The derivation of a mesh from a CSG model thus proceeds in two steps. The first is boundary evaluation of the CSG model, which entails its conversion into a B-Tep by computation of the boundary elements of the object. The second step is the generation of a tetrahedral mesh from this B-rep. The faces of the primitives in the CSG model have a dual representation: as rational Bezier patches, and as algebraic surfaces. In the B-rep, faces are represented as trimmed rational Bezier patches. All the computations on edges and faces are reduced to 2D. The FE meshing of the B-rep is then performed by triangulation of the faces, followed by tetrahedrization of the interior of the solid.