The model is described by the 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 existence of unique mapping between the
parametric and real spaces of each of the model entities. This
significantly contributes to unified handling of individual model
entities. On the other hand, the restriction on the model topology
results in some reduction of modeling flexibility.
Since the same or similar type of geometrical description is used in
many CAD systems a natural and consistent interface (at least in terms
of geometric description) between the modeler and the mesh generator
Two levels of mesh size specification are considered - local mesh size specification and global mesh size specification. The local mesh size specification consists of two parts. Firstly, 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, curvature based mesh size control is employed to enable accurate representation of model entities by their discretization even if no particular mesh size is required and is based on the ratio between the appropriate mesh size and radius of curvature at a given location. The global mesh size specification utilizes a background parametric tree with mesh size specification at nodes and linear interpolation over the tree cells (quadrants, octants).