Simultaneous edge flips for convex subdivisions
نویسندگان
چکیده
It has been shown that one triangulation of a set of points can be converted to any other triangulation of the same set of points by a sequence of edge flip operations. In this paper we consider a tesselation of a set of points consisting of convex cells, a convex subdivision, and explore the notion of flipping edges from one convex subdivision of the points to another, where both subdivisions use the same number of edges. It is easy to construct examples of a convex subdivision where no single edge can be flipped so that the convexity of all cells of the subdivision is maintained. At the CCCG in 2003 Ferran Hurtado asked whether there exists a convex subdivision for which the size of the minimal simultaneous edge flip is linear with respect to the number of edges. In the paper we construct such a subdivision.
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