The model is described by a boundary representation consisting of free form entities - vertices, curves, surfaces, and regions. The tensor product polynomial entities (namely the rational Bezier entities) have been employed. In this approach, each region is bounded by six surfaces, boundary each of which is formed by four curves, each of which is in turn given by two vertices. The advantage of this model representation consists in the existence of a unique mapping between the parametric and real spaces of each of the model entities. This significantly contributes to a unified handling of individual model entities. On the other hand, restrictions on the model topology result in some reduction of modelling flexibility. Since the same or similar type of the geometrical description is used in many CAD systems a natural and consistent interface (at least in terms of the geometric description) between the modeller and the mesh generator is supported.

Two levels of the mesh size specification are considered - the local and the global level. The local mesh size specification consists of two parts. Firstly, the required mesh size specification is used to explicitly prescribe the mesh size at individual model entities. To further improve the mesh size control, local mesh control vertices fixed to model entities via parametric coordinates have been introduced. Secondly, a curvature based mesh size control is employed to enable an accurate representation of model entities by their discretization even if no particular mesh size is required. It is based on the ratio between the appropriate mesh size and the radius of curvature at a given location. The global mesh size specification utilizes a background parametric tree with the mesh size specification at nodes and linear interpolation over the tree cells.

*Daniel Rypl
2005-12-03*