A linear-time algorithm for computing the voronoi diagram of a convex polygon

Alok Aggarwal, Leonidas J. Guibas, James Saxe, Peter W. Shor
1989 Discrete & Computational Geometry  
We present an algorithm for computing certain kinds of threedimensional convex hulls in linear time. Using this algorithm, we show that the Voronoi diagram of n sites in the plane can be computed in O(n) time when these sites form the vertices of a convex polygon in, say, counterclockwise order. This settles an open problem in computational geometry. Our techniques can also be used to obtain linear-time algorithms for computing the furthest-site Voronoi diagram and the medial axis of a convex
more » ... lygon and for deleting a site from a general planar Voronoi diagram. Pi-'~j. Let us denote this half-plane by H(p~, pj) . The locus of points closer to p~ than to any other site, which we denote by V(i), is the intersection of n-1 half-planes, i.e., V(i)=f '~i"j H(p~, pj); V(i) is called the Voronoi region associated with p~. The n regions V(i), which may be unbounded, divide the plane *
doi:10.1007/bf02187749 fatcat:imdybpi2lfh65izvvqu5woeneu