The generic problem defined in Section 6.1.3 can be sub-structured in several smaller (also very generic) problems which lead to fairly independent functional modules that perform operations on common data. These modules are combined in a simple multi-step sequence that solves the generic problem. The characteristic decomposition of the entire task into smaller tasks is essential for the architectural features and flexibility of VORONOI.
The key concept to overcome any of the grid/geometry consistency problems rigorously is to treat equally grid and geometry points by merging the set of geometry points and the set of grid points and by finally (re-)triangulating the resulting point cloud. This means that before the actual triangulation is performed, all the geometrical boundary information and the connectivity information of the old grid(s) has been thrown away! Hence a special method must ensure that the geometrical edges are reproduced during the triangulation.
Adding input, output, and interpolation steps, we obtain the following
basic re-gridding algorithm
.
The Algorithm 6.4 may be compared with the transcript of a VORONOI run shown in Figure 6.4, where 1) 2) 3) correspond to the Input step, 4) 5) correspond to the Refinement step, 6) is the Triangulation, 7) 8) correspond to the Segmentation step, and 9) is the Output step (including the interpolation).
Figure: Transcript of a VORONOI run for a 200 point self-test example
