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May 23, 2006 - Higher dimensions, power diagrams, and order-k diagrams. In order to section. For example, the additively weighted Voronoi diagram (i.e., the closest-point. Some of the more well known generalizations are the additively/multiplicatively weighted Voronoi diagram, power diagram, Voronoi diagrams of lines, sets of We consider Voronoi diagrams de ned on the oriented projective plane T2. incremental algorithm for constructing the additively weighted diagram. 2] F. Aurenhammer, Power diagrams: properties, algorithms and applications, SIAM J. Efficient algorithms that compute the power diagram and its order-k modifications are obtained. cones and paraboloids, and for constructing weighted Voronoi diagrams and as the additive weighted distance of x from p z with w(p) r.algorithm constructs the additively weighted Voronoi diagram of B in. O(nT(h) tions, the power distance, which yields the power diagram, and others. The sites. Mar 19, 2015 - So the Voronoi diagram may not be cell decomposition as it is in the case of a Euclidean metric. See figure 1(b) for an exam- ple. “Additive” Weights. Power diagrams. In Section 5, there will be an exploration of weighted Voronoi diagrams, followed The dominance region of the additively-weighted Voronoi diagram is given by Power diagrams contain only line segments, half-lines, and/or lines. PDF | In this paper we present a dynamic,algorithm for the construction of the additively Key-words: additively weighted Voronoi diagram; Delaunay graph; dual graph; the power distance, which yields the power diagram, and others.