Greedy cuts: an advancing front terrain triangulation algorithm

We propose advancing-front techniques for the problem of simplification of dense digitized terrain models. While most simplification algorithms have been based on either incremental refinement or decimation techniques, our Greedy-Cuts algorithms use a simple triangulationgrowth procedure. They work by taking greedy cuts (“bites”) out of a simple closed polygon that bounds a connected component of the yet-to-be triangulated region. The method begins with a large polygon, bounding the whole extent of the terrain to be triangulated, and works its way inward, performing at each step one of three basic operations: ear cutting, greedy biting, and edge splitting. In this paper, we present both the basic Greedy-Cuts framework (which has been introduced in our earlier paper) and a new enhancement of the Greedy-Cuts method that improves the quality of the resulting triangulation. This improvement is made possible through the maintenance of two “fronts”, a real front and a virtual front, that bound between them a region of the terrain that has only a tentative triangulation. By allowing simple local operations (edge collapses and edge flips) in the tentative triangulation, we are able to avoid many of the artifacts of the basic Greedy-Cuts advancing-front technique, while not significantly affecting memory usage or running time. Our implementation of Greedy-Cuts, as well as its multi-front enhancement is publicly available in the GcTin system. We give experimental evidence of the effectiveness of the multi-front enhancement to the Greedy-Cuts method and show that our method is competitive with current algorithms in terms of running time. One of the major advantages of our implementation is that it requires very little memory beyond that for the input height array.