The same set of geometrical operations as described in Section Geometrical Operations (Sequential Mesh Generation) has been adopted. In order to enable forming of a region bounded by surfaces of orders that are lower than the orders of the region itself, the set has been extended by surface expansion (Fig. 3.1). The expansion is accomplished separately in each direction using the same approach as for the curve expansion. Thus the expansion of a rational Bezier surface of degrees and in each parametric direction, respectively, given by a set of control points with corresponding weights to a surface of degree and given by control points and weights is governed by the relations
(3.3) |
(3.4) |
(3.5) |
(3.6) |
(3.7) |
(3.8) |
Note that the set of the geometrical operations could be further extended by curve, surface, and region extraction from a region.
Daniel Rypl
2005-12-07