منابع مشابه
Balanced triangulations
Motivated by applications in numerical analysis, we investigate balanced triangulations, i.e. triangulations where all angles are strictly larger than π/6 and strictly smaller than π/2, giving the optimal lower bound for the number of triangles in the case of the square. We also investigate platonic surfaces, where we find for each one its respective optimal bound. In particular, we settle (aff...
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Regular triangulations of products of lattice polytopes are constructed with the additional property that the dual graphs of the triangulations are bipartite. Such triangulations are instrumental in deriving lower bounds for the number of real roots of certain sparse polynomial systems by recent results of Soprunova and Sottile (Adv. Math., to appear). Special attention is paid to the cube case.
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Regular triangulations of products of lattice polytopes are constructed with the additional property that the dual graphs of the triangulations are bipartite. Special attention is paid to the cube case. Such triangulations are instrumental in deriving lower bunds for the number of real roots of certain sparse polynomial systems by recent results of Soprunova and Sottile [21].
متن کاملCounting triangulations of balanced subdivisions of convex polygons
We compute the number of triangulations of a convex k-gon each of whose sides is subdivided by r − 1 points. We find explicit formulas and generating functions, and we determine the asymptotic behaviour of these numbers as k and/or r tend to infinity. We connect these results with the question of finding the planar set of n points in general position that has the minimum possible number of tria...
متن کاملDynamic Ray Shooting and Shortest Paths in Planar Subdivisions via Balanced Geodesic Triangulations
We give new methods for maintaining a data structure that supports ray-shooting and shortest-path queries in a dynamically changing connected planar subdivision S . Our approach is based on a new dynamic method for maintaining a balanced decomposition of a simple polygon via geodesic triangles. We maintain such triangulations by viewing their dual trees as balanced trees. We show that rotations...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2013
ISSN: 0012-365X
DOI: 10.1016/j.disc.2013.05.017