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A modified longest side bisection triangulation

Fast and efficient exploration of large terrains in a virtual reality manner requires different levels of detail to speedup processing of terrain parts in background. Thus, the triangulation refinement problem has become an important issue in processing terrain data. The longest side bisection of triangles is one possible way to subdivide a triangle in a couple of subtriangles. In the larger context of triangulations, this subdivision can be seen as an approach of the triangulation refinement problem. This particular triangulation refinement yields a strong hierarchical triangulation, which itself is an approach of a multiresolution model for terrain surfaces. In its pure form, the longest side bisection of a triangle (assume is a smallest angle in ) and its descendants only produces triangles whose smallest angles are always greater or equal to . In this paper we show that with a small modification, the lower bound on the smallest angles can be increased to , without increasing the total number of subtriangles produced in two consecutive refinement steps. Even the new vertices inserted in the triangulation are exactly the same.