Approaches to Discretization of 3D Surfaces

Daniel Rypl

Department of Structural Mechanics
Faculty of Civil Engineering
Czech Technical University in Prague
Thákurova 7, 166 29 Prague, Czech Republic


Automation and robustness of the mesh generation is of primary importance for the integration of the finite element method with design processes in the framework of computer aided design and engineering. The presented work is concerned with various approaches to the design and implementation of reliable algorithms for automatic discretization of 3D surfaces. Initially, the triangulation of 3D parametric surfaces using both the direct and indirect approaches is investigated. A concrete implementation based on the advancing front technique is presented including demonstration on numerous examples. The direct approach is then extended to discrete surfaces described by unstructured triangular grids of arbitrary topology. The concrete implementation based again on the advancing front technique is accompanied by the discussion of several numerical aspect and presented on several examples. Finally, the generation of mixed quad-dominant and all-quadrilateral meshes on 3D surfaces using the developed advancing front based triangulation kernel is investigated and the proposed concept is presented on a set of examples.