Abstract
This paper introduces a 2-dimensional triangulation scheme based on a topological triangulation that approximates a given domain X within a specified Hausdorff distance from X. The underlying space of the resulting good quality triangulation is homeomorphic to X and contains either equilateral triangles or right angled triangles with 30‡, 60‡ and 90‡ angles. For a particular range of approximation tolerance, the number of triangles in the triangulation produced by the method is O(t log2 t) where t is the number of triangles in an optimal triangulation where the optimum is taken over bounded aspect ratio triangulations satisfying a certain boundary condition with respect to X. The method can also produce a quadrangulation of X having similar properties. Relevant implementation issues and results are discussed.
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© 1997 Springer-Verlag Berlin Heidelberg
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Dey, T.K., Roy, A., Shah, N.R. (1997). Approximating geometric domains through topological triangulations. In: Ramesh, S., Sivakumar, G. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1997. Lecture Notes in Computer Science, vol 1346. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0058019
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DOI: https://doi.org/10.1007/BFb0058019
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