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Flip Distance Between Triangulations of a Simple Polygon is NPComplete
 EXTENDED ABSTRACT IN PROC. 29 TH EUROCG
, 2013
"... Let T be a triangulation of a simple polygon. A flip in T is the operation of removing one diagonal of T and adding a different one such that the resulting graph is again a triangulation. The flip distance between two triangulations is the smallest number of flips required to transform one triangul ..."
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Cited by 5 (1 self)
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show that computing the flip distance between two triangulations of a simple polygon is NPcomplete. This complements a recent result that shows APXhardness of determining the flip distance between two triangulations of a planar point set.
Flip distance between two triangulations of a point set is NPcomplete
 IN CANADIAN CONFERENCE ON COMPUTATIONAL GEOMETRY (CCCG
, 2012
"... Given two triangulations of a convex polygon, computing the minimum number of flips required to transform one to the other is a longstanding open problem. It is not known whether the problem is in P or NPcomplete. We prove that two natural generalizations of the problem are NPcomplete, namely co ..."
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Cited by 5 (1 self)
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Given two triangulations of a convex polygon, computing the minimum number of flips required to transform one to the other is a longstanding open problem. It is not known whether the problem is in P or NPcomplete. We prove that two natural generalizations of the problem are NPcomplete, namely
ReTiling Polygonal Surfaces
 Computer Graphics
, 1992
"... This paper presents an automatic method of creating surface models at several levels of detail from an original polygonal description of a given object. Representing models at various levels of detail is important for achieving high frame rates in interactive graphics applications and also for speed ..."
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Cited by 448 (3 self)
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This paper presents an automatic method of creating surface models at several levels of detail from an original polygonal description of a given object. Representing models at various levels of detail is important for achieving high frame rates in interactive graphics applications and also
Polygonization of Implicit Surfaces
, 1988
"... This paper discusses a numerical technique that approximates an implicit surface with a polygonal representation. The implicit function is adaptively sampled as it is surrounded by a spatial partitioning. The partitioning is represented by an octree, which may either converge to the surface or track ..."
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Cited by 432 (5 self)
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This paper discusses a numerical technique that approximates an implicit surface with a polygonal representation. The implicit function is adaptively sampled as it is surrounded by a spatial partitioning. The partitioning is represented by an octree, which may either converge to the surface
A Volumetric Method for Building Complex Models from Range Images
, 1996
"... A number of techniques have been developed for reconstructing surfaces by integrating groups of aligned range images. A desirable set of properties for such algorithms includes: incremental updating, representation of directional uncertainty, the ability to fill gaps in the reconstruction, and robus ..."
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Cited by 1018 (18 self)
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with one range image at a time, we first scanconvert it to a distance function, then combine this with the data already acquired using a simple additive scheme. To achieve space efficiency, we employ a runlength encoding of the volume. To achieve time efficiency, we resample the range image to align
Primitives for the manipulation of general subdivisions and the computations of Voronoi diagrams
 ACM Tmns. Graph
, 1985
"... The following problem is discussed: Given n points in the plane (the sites) and an arbitrary query point 4, find the site that is closest to q. This problem can be solved by constructing the Voronoi diagram of the given sites and then locating the query point in one of its regions. Two algorithms ar ..."
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Cited by 543 (11 self)
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are given, one that constructs the Voronoi diagram in O(n log n) time, and another that inserts a new site in O(n) time. Both are based on the use of the Voronoi dual, or Delaunay triangulation, and are simple enough to be of practical value. The simplicity of both algorithms can be attributed
The Digital Michelangelo Project: 3D Scanning of Large Statues
, 2000
"... We describe a hardware and software system for digitizing the shape and color of large fragile objects under nonlaboratory conditions. Our system employs laser triangulation rangefinders, laser timeofflight rangefinders, digital still cameras, and a suite of software for acquiring, aligning, merg ..."
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Cited by 488 (8 self)
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We describe a hardware and software system for digitizing the shape and color of large fragile objects under nonlaboratory conditions. Our system employs laser triangulation rangefinders, laser timeofflight rangefinders, digital still cameras, and a suite of software for acquiring, aligning
Improved Approximation Algorithms for Maximum Cut and Satisfiability Problems Using Semidefinite Programming
 Journal of the ACM
, 1995
"... We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds the solution ..."
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Cited by 1231 (13 self)
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We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds
Multiresolution Analysis of Arbitrary Meshes
, 1995
"... In computer graphics and geometric modeling, shapes are often represented by triangular meshes. With the advent of laser scanning systems, meshes of extreme complexity are rapidly becoming commonplace. Such meshes are notoriously expensive to store, transmit, render, and are awkward to edit. Multire ..."
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Cited by 605 (16 self)
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. Multiresolution analysis offers a simple, unified, and theoretically sound approach to dealing with these problems. Lounsbery et al. have recently developed a technique for creating multiresolution representations for a restricted class of meshes with subdivision connectivity. Unfortunately, meshes encountered
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