On the relationships among constrained geometric structures
In this paper, we show the inclusion relation among several constrained geometric structures. In particular, we examine the constrained relative neighborhood graph in relation with other constrained geometric structures such as the constrained minimum spanning tree, constrained Gabriel graph, straight-line dual of bounded Voronoi diagram and the constrained Delaunay triangulation. We modify a linear time algorithm for computing the relative neighborhood graph from the Delaunay triangulation and show that the constrained relative neighborhood graph can also be computed in linear-time from the constrained Delaunay triangulation in the (ℜ2, L p ) metric space.
KeywordsVoronoi Diagram Directed Edge Delaunay Triangulation Inclusion Relation Constrain Delaunay Triangulation
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