A new polynomial-time algorithm for linear programming
Combinatorica
A linear-time algorithm for computing the Voronoi diagram of a convex polygon
Discrete & Computational Geometry
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Convex drawings of graphs in two and three dimensions (preliminary version)
Proceedings of the twelfth annual symposium on Computational geometry
Tutte's barycenter method applied to isotopies
Computational Geometry: Theory and Applications - Special issue on the thirteenth canadian conference on computational geometry - CCCG'01
Pseudotriangulations from Surfaces and a Novel Type of Edge Flip
SIAM Journal on Computing
Kinetic collision detection between two simple polygons
Computational Geometry: Theory and Applications
Allocating Vertex π-Guards in Simple Polygons via Pseudo-Triangulations
Discrete & Computational Geometry
Acute Triangulations of Polygons
Discrete & Computational Geometry
Embedding 3-polytopes on a small grid
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Discrete laplace operators: no free lunch
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
A Discrete Laplace–Beltrami Operator for Simplicial Surfaces
Discrete & Computational Geometry
Planar minimally rigid graphs and pseudo-triangulations
Computational Geometry: Theory and Applications - Special issue on the 19th annual symposium on computational geometry - SoCG 2003
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We consider the pair (p i ,f i ) as a force with two-dimensional direction vector f i applied at the point p i in the plane. For a given set of forces we ask for a non-crossing geometric graph on the points p i that has the following property: There exists a weight assignment to the edges of the graph, such that for every p i the sum of the weighted edges (seen as vectors) around p i yields *** f i . As additional constraint we restrict ourselves to weights that are non-negative on every edge that is not on the convex hull of the point set. We show that (under a generic assumption) for any reasonable set of forces there is exactly one pointed pseudo-triangulation that fulfils the desired properties. Our results will be obtained by linear programming duality over the PPT-polytope. For the case where the forces appear only at convex hull vertices we show that the pseudo-triangulation that resolves the load can be computed as weighted Delaunay triangulation. Our observations lead to a new characterization of pointed pseudo-triangulations, structures that have been proven to be extremely useful in the design and analysis of efficient geometric algorithms. As an application, we discuss how to compute the maximal locally convex function for a polygon whose corners lie on its convex hull.