Three-dimensional triangulations from local transformations
SIAM Journal on Scientific and Statistical Computing
Placing the largest similar copy of a convex polygon among polygonal obstacles
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Construction of three-dimensional Delaunay triangulations using local transformations
Computer Aided Geometric Design
Graph of triangulations of a convex polygon and tree of triangulations
Computational Geometry: Theory and Applications
Mental imagery in program design and visual programming
International Journal of Human-Computer Studies - Best of empirical studies of programmers 7
Pseudotriangulations from Surfaces and a Novel Type of Edge Flip
SIAM Journal on Computing
Pre-triangulations and liftable complexes
Proceedings of the twenty-second annual symposium on Computational geometry
Counting and Enumerating Pointed Pseudotriangulations with the Greedy Flip Algorithm
SIAM Journal on Computing
Triangulations of line segment sets in the plane
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
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Given a set Sof disjoint line segments in the plane, which we call sites, a segment triangulation of Sis a partition of the convex hull of Sinto sites, edges, and faces. The set of faces is a maximal set of disjoint triangles such that the vertices of each triangle are on three distinct sites. The segment Delaunay triangulation of Sis the segment triangulation of Swhose faces are inscribable in circles whose interiors do not intersect S. It is dual to the segment Voronoi diagram. The aim of this paper is to show that any given segment triangulation can be transformed by a finite sequence of local improvements in a segment triangulation that has the same topology as the segment Delaunay triangulation. The main difference with the classical flip algorithm for point set triangulations is that local improvements have to be computed on non convex regions. We overcome this difficulty by using locally convex functions.