Placing the largest similar copy of a convex polygon among polygonal obstacles
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Checking geometric programs or verification of geometric structures
Proceedings of the twelfth annual symposium on Computational geometry
Checking the convexity of polytopes and the planarity of subdivision
WADS '97 Selected papers presented at the international workshop on Algorithms and data structure
3-Dimensional Euclidean Voronoi Diagrams of Lines with a Fixed Number of Orientations
SIAM Journal on Computing
Pre-triangulations and liftable complexes
Proceedings of the twenty-second annual symposium on Computational geometry
The voronoi diagram of three lines
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
On the computation of an arrangement of quadrics in 3D
Computational Geometry: Theory and Applications - Special issue on the 19th European workshop on computational geometry - EuroCG 03
An exact and efficient approach for computing a cell in an arrangement of quadrics
Computational Geometry: Theory and Applications - Special issue on robust geometric algorithms and their implementations
Flip Algorithm for Segment Triangulations
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
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Given a set S of line segments in the plane, we introduce a new family of partitions of the convex hull of S called segment triangulations of S. The set of faces of such a triangulation is a maximal set of disjoint triangles that cut S at, and only at, their vertices. Surprisingly, several properties of point set triangulations extend to segment triangulations. Thus, the number of their faces is an invariant of S. In the same way, if S is in general position, there exists a unique segment triangulation of S whose faces are inscribable in circles whose interiors do not intersect S. This triangulation, called segment Delaunay triangulation, is dual to the segment Voronoi diagram. The main result of this paper is that the local optimality which characterizes point set Delaunay triangulations [10] extends to segment Delaunay triangulations. A similar result holds for segment triangulations with same topology as the Delaunay one.