
A CGAL implementation of the Straight Skeleton of a - DMA-FI
... instants of the events) and constructions (for bisectors and events). As with most geometric algorithms, its correctness can be made a exclusive function of its predicates if these are chosen carefully. In our case, the fundamental predicates are the relative ordering of events. It suffices that the ...
... instants of the events) and constructions (for bisectors and events). As with most geometric algorithms, its correctness can be made a exclusive function of its predicates if these are chosen carefully. In our case, the fundamental predicates are the relative ordering of events. It suffices that the ...
Solution
... 1. a1 a2 a3 and a3 a2 a1 are two three-digit decimal numbers, with a1 , a3 being different non-zero digits. The squares of these numbers are five-digit numbers b1 b2 b3 b4 b5 and b5 b4 b3 b2 b1 respectively. Find all such threedigit numbers. Solution. Assume a1 > a3 > 0. As the square of a1 a2 a3 mu ...
... 1. a1 a2 a3 and a3 a2 a1 are two three-digit decimal numbers, with a1 , a3 being different non-zero digits. The squares of these numbers are five-digit numbers b1 b2 b3 b4 b5 and b5 b4 b3 b2 b1 respectively. Find all such threedigit numbers. Solution. Assume a1 > a3 > 0. As the square of a1 a2 a3 mu ...
Alternating Paths through Disjoint Line Segments
... Michael Hoffmann and Csaba D. Tóth Institute for Theoretical Computer Science ...
... Michael Hoffmann and Csaba D. Tóth Institute for Theoretical Computer Science ...
Minimal tangent visibility graphs
... hull of the obstacles are edges of any pseudo-triangulation. A pseudo-triangulation of a collection of six obstacles is depicted in Fig. 3. L e m m a 2.1. The bounded free faces of any pseudo-triangulation are pseudotriangles. Proof. Let B be a family of noncrossing bitangents containing the bitange ...
... hull of the obstacles are edges of any pseudo-triangulation. A pseudo-triangulation of a collection of six obstacles is depicted in Fig. 3. L e m m a 2.1. The bounded free faces of any pseudo-triangulation are pseudotriangles. Proof. Let B be a family of noncrossing bitangents containing the bitange ...
LESSON 4-1: CONGRUENT FIGURES/POLYGONS
... POLYGON: A polygon is a closed plane figure formed by three or more segments. Each segment intersects exactly two other segments, but only at their endpoints, and no two segments with a common endpoint are collinear. The vertices of the polygon are the endpoints of the sides. When naming a polygon, ...
... POLYGON: A polygon is a closed plane figure formed by three or more segments. Each segment intersects exactly two other segments, but only at their endpoints, and no two segments with a common endpoint are collinear. The vertices of the polygon are the endpoints of the sides. When naming a polygon, ...
Steinitz's theorem

In polyhedral combinatorics, a branch of mathematics, Steinitz's theorem is a characterization of the undirected graphs formed by the edges and vertices of three-dimensional convex polyhedra: they are exactly the (simple) 3-vertex-connected planar graphs (with at least four vertices). That is, every convex polyhedron forms a 3-connected planar graph, and every 3-connected planar graph can be represented as the graph of a convex polyhedron. For this reason, the 3-connected planar graphs are also known as polyhedral graphs. Steinitz's theorem is named after Ernst Steinitz, who submitted its first proof for publication in 1916. Branko Grünbaum has called this theorem “the most important and deepest known result on 3-polytopes.”The name ""Steinitz's theorem"" has also been applied to other results of Steinitz: the Steinitz exchange lemma implying that each basis of a vector space has the same number of vectors, the theorem that if the convex hull of a point set contains a unit sphere, then the convex hull of a finite subset of the point contains a smaller concentric sphere, and Steinitz's vectorial generalization of the Riemann series theorem on the rearrangements of conditionally convergent series.↑ ↑ 2.0 2.1 ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑