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On the computation of zone and double zone diagrams. (arXiv:1208.3124v4 [cs.CG] UPDATED)

来源于:arXiv
Classical objects in computational geometry are defined by explicit relations. Several years ago the pioneering works of T. Asano, J. Matou\v{s}ek and T. Tokuyama introduced "implicit computational geometry" in which the geometric objects are defined by implicit relations involving sets. An important member in this family is called "a zone diagram". The implicit nature of zone diagrams implies, as already observed in the original works, that their computation is a challenging task. In a continuous setting this task has been addressed (briefly) only by these authors in the Euclidean plane with point sites. We discuss the possibility to compute zone diagrams in a wide class of spaces and also shed new light on their computation in the original setting. The class of spaces, which is introduced here, includes, in particular, Euclidean spheres and finite dimensional strictly convex normed spaces. Sites of a general form are allowed and it is shown that a generalization of the iterative meth 查看全文>>