Journal ArticleDOI
Simultaneous edge flipping in triangulations
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This work generalizes the operation of flipping an edge in a triangulation to that of flipping several edges simultaneously, finding an optimal upper bound on the number of simultaneous flips that are needed to transform a Triangulation into another.Abstract:
We generalize the operation of flipping an edge in a triangulation to that of flipping several edges simultaneously. Our main result is an optimal upper bound on the number of simultaneous flips that are needed to transform a triangulation into another. Our results hold for triangulations of point sets and for polygons.read more
Citations
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Journal ArticleDOI
Enumerating Order Types for Small Point Sets with Applications
TL;DR: A complete and reliable data base for all possible order types of size n=10 or less is established and substantiate the usefulness of the data base by applying it to several problems in computational and combinatorial geometry.
Journal ArticleDOI
Flips in planar graphs
Prosenjit Bose,Ferran Hurtado +1 more
TL;DR: This work overviews both the combinatorial perspective and the geometric perspective of edge flips in planar graphs, highlighting the similarities and differences of the two settings.
BookDOI
Algorithm Theory - SWAT 2004
Torben Hagerup,Jyrki Katajainen +1 more
TL;DR: An overview of the results achieved on cache-oblivious algorithms and data structures since the seminal paper by Frigo et al. in 1999 is given.
Journal ArticleDOI
A lower bound on the number of triangulations of planar point sets
TL;DR: It is shown that the number of straight-edge triangulations exhibited by any set of n points in general position in the plane is bounded from below by Ω(2.33n).
Topologic and geometric constraint-based hexahedral mesh generation
TL;DR: This dissertation focuses on delineating known constraints associated with hexahedral meshes and formulating these constraints utilizing the dual of thehexahedral mesh, and shows that hexahedrahedral mesh generation can be viewed as an optimization problem.
References
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Journal ArticleDOI
Reverse search for enumeration
David Avis,Komei Fukuda +1 more
TL;DR: This paper develops the reverse search technique in a general framework and shows its broader applications to various problems in operations research, combinatorics, and geometry, and proposes new algorithms for listing.
Voronoi diagrams and Delaunay triangulations
TL;DR: The Voronoi diagram of a set of sites partitions space into regions one per site the region for a site s consists of all points closer to s than to any other site as discussed by the authors.
Book ChapterDOI
Voronoi diagrams and Delaunay triangulations
TL;DR: The Voronoi diagrams and Delaunay triangulations have been rediscovered or applied in many areas of math ematics and the natural sciences and are central topics in computational geometry with hundreds of papers discussing algorithms and extensions.
Journal ArticleDOI
Rotation distance, triangulations, and hyperbolic geometry
Daniel D. Sleator,Daniel D. Sleator,Daniel D. Sleator,Robert E. Tarjan,William P. Thurston,William P. Thurston,William P. Thurston +6 more
TL;DR: In this paper, the authors established a tight bound of In 6 on the maximum rotation distance between two A2-node trees for all large n, using volumetric arguments in hyperbolic 3-space.