Three levels of mesh size specification are considered - the global mesh size specification, local mesh size specification, and adaptive mesh size specification. The global mesh size specification uses global weight functions to control the mesh size description over a domain. The local mesh size specification concept prescribes the desired mesh size variation on individual model entities. In the adaptive mesh size specification strategy, various mesh size sources (typically a background mesh) built according to the preceding problem analysis are used. Only the local mesh size control is directly related to the underlying model.
The local mesh size specification consists of two parts - the required mesh size specification and the curvature-based mesh size control. The former concept is used to explicitly prescribe the mesh size at individual model entities. The mesh size specification is stored at each vertex and at each control point of any curve or surface. These values are used to extract the mesh size specification at any location on a curve or surface. Moreover, each model entity (except vertices) stores an upper bound limit on the mesh size which is not allowed to be exceeded. Similar expressions to the ones describing the geometry of rational Bezier curves and surfaces are used to interpolate the local mesh size specification at control points over the curve or surface. The mesh size extracted from a curve mesh size specification has the form
The curvature-based mesh size control is employed to enable an accurate representation of a curve or surface by its discretization even if no particular mesh size is required. The criterion is based on the ratio between the appropriate mesh size and the radius of curvature at a given location on the curve or surface. The radius of the first (flexural) curvature on a parameterized curve is given by