Towards Compatible Triangulations
نویسندگان
چکیده
منابع مشابه
Compatible triangulations and point partitions by series-triangular graphs
We introduce series-triangular graph embeddings and show how to partition point sets with them. This result is then used to prove an upper bound on the number of Steiner points needed to obtain compatible triangulations of point sets. The problem is generalized to finding compatible triangulations for more than two point sets and we show that such triangulations can be constructed with only a l...
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Two vertex-labelled polygons are compatible if they have the same clockwise cyclic ordering of vertices. The definition extends to polygonal regions (polygons with holes) and to triangulations—for every face, the clockwise cyclic order of vertices on the boundary must be the same. It is known that every pair of compatible n-vertex polygonal regions can be extended to compatible triangulations b...
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For a given point set S (in general position), two pointed pseudo-triangulations are compatible if their union is plane. We show that for any set S there exist two maximally disjoint compatible pointed pseudotriangulations, that is, their union is a triangulation of S. In contrast, we show that there are point sets S and pointed pseudo-triangulations T such that there exists no pointed pseudo-t...
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Two planar triangulations with a correspondence between two vertex sets are compatible (isomorphic) if they are topologically equivalent. This work presents a simple and robust method for morphing two compatible planar triangulations with identical convex boundaries that locally preserves the intrinsic geometric properties of triangles throughout the morph. The method is based on the barycentri...
متن کاملOn Compatible Triangulations of Simple Polygons
It is well known that, given two simple n-sided polygons, it may not be possible to triangulate the two polygons in a compatible fashion, if one's choice of triangulation vertices is restricted to polygon corners. Is it always possible to produce compatible triangulations if additional vertices inside the polygon are allowed? We give a positive answer and construct a pair of such triangu-lation...
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