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The problem of building a constrained Delaunay triangulation (CDT) at different levels of resolution is considered for the hierarchical description of topographic surfaces. The surface is approximated at each level by a network of planar triangular faces having vertices at a subset of surface-specific points, such as peaks, pits, or passes, and including edges that describe surface-specific lines, such as ridges or valleys. Each approximation is built based on a Delaunay triangulation of the data points that includes the given constraint segments. A dynamic algorithm for constrained Delaunay triangulation is proposed. The algorithm is based on the stepwise refinement of a CDT by the incremental insertion of points and constraint segments.>
Floriani et al. (2003) studied this question.