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@string{prl = {Phys. Rev. Lett.}} |
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@string{rmp = {Rev. Mod. Phys.}} |
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@article{Dey:2003ts, |
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Abstract = {There are many scientific and engineering applications where an automatic detection of shape dimension from sample data is necessary. Topological dimensions of shapes constitute an important global feature of them. We present a Voronoi-based dimension detection algorithm that assigns a dimension to a sample point which is the topological dimension of the manifold it belongs to. Based on this dimension detection, we also present an algorithm to approximate shapes of arbitrary dimension from their samples. Our empirical results with data sets in three dimensions support our theory.}, |
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Address = {175 FIFTH AVE, NEW YORK, NY 10010 USA}, |
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Author = {Dey, TK and Giesen, J and Goswami, S and Zhao, WL}, |
64 |
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Date = {APR 2003}, |
65 |
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Date-Added = {2010-11-04 11:11:29 -0400}, |
66 |
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Date-Modified = {2010-11-04 11:11:29 -0400}, |
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Doi = {DOI 10.1007/s00454-002-2838-9}, |
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Journal = {Discrete \& Computational Geometry}, |
69 |
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Pages = {419-434}, |
70 |
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Publisher = {SPRINGER-VERLAG}, |
71 |
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Timescited = {3}, |
72 |
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Title = {Shape dimension and approximation from samples}, |
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Volume = {29}, |
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Year = {2003}, |
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/s00454-002-2838-9}} |
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@article{EDELSBRUNNER:1994oq, |
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Abstract = {Frequently, data in scientific computing is in its abstract form a finite point set in space, and it is sometimes useful or required to compute what one might call the ''shape'' of the set. For that purpose, this article introduces the formal notion of the family of alpha-shapes of a finite point set in R3. Each shape is a well-defined polytope, derived from the Delaunay triangulation of the point set, with a parameter alpha is-an-element-of R controlling the desired level of detail. An algorithm is presented that constructs the entire family of shapes for a given set of size n in time O(n2), worst case. A robust implementation of the algorithm is discussed, and several applications in the area of scientific computing are mentioned.}, |
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Address = {1515 BROADWAY, NEW YORK, NY 10036}, |
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Author = {EDELSBRUNNER, H and MUCKE, EP}, |
81 |
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Date = {JAN 1994}, |
82 |
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Date-Added = {2010-11-04 11:11:14 -0400}, |
83 |
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Date-Modified = {2010-11-04 11:11:14 -0400}, |
84 |
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Journal = {Acm Transactions On Graphics}, |
85 |
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Keywords = {COMPUTATIONAL GRAPHICS; DELAUNAY TRIANGULATIONS; GEOMETRIC ALGORITHMS; POINT SETS; POLYTOPES; ROBUST IMPLEMENTATION; SCIENTIFIC COMPUTING; SCIENTIFIC VISUALIZATION; SIMPLICIAL COMPLEXES; SIMULATED PERTURBATION; 3-DIMENSIONAL SPACE}, |
86 |
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Pages = {43-72}, |
87 |
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Publisher = {ASSOC COMPUTING MACHINERY}, |
88 |
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Timescited = {270}, |
89 |
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Title = {3-DIMENSIONAL ALPHA-SHAPES}, |
90 |
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Volume = {13}, |
91 |
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Year = {1994}} |
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@article{EDELSBRUNNER:1995cj, |
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Abstract = {Efficient algorithms are described for computing topological, combinatorial, and metric properties of the union of finitely many spherical balls in R(d) These algorithms are based on a simplicial complex dual to a decomposition of the union of balls using Voronoi cells, and on short inclusion-exclusion formulas derived from this complex. The algorithms are most relevant in R(3) where unions of finitely many balls are commonly used as models of molecules.}, |
95 |
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Address = {175 FIFTH AVE, NEW YORK, NY 10010}, |
96 |
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Author = {EDELSBRUNNER, H}, |
97 |
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Date = {APR-JUN 1995}, |
98 |
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Date-Added = {2010-11-04 11:11:14 -0400}, |
99 |
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Date-Modified = {2010-11-04 11:11:14 -0400}, |
100 |
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Journal = {Discrete \& Computational Geometry}, |
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Pages = {415-440}, |
102 |
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Publisher = {SPRINGER VERLAG}, |
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Timescited = {65}, |
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Title = {THE UNION OF BALLS AND ITS DUAL SHAPE}, |
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Volume = {13}, |
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Year = {1995}} |
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@article{Barber96, |
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Author = {C.~B. Barber and D.~P. Dobkin and H.~T. Huhdanpaa}, |
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Year = {1980}, |
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/BF00977785}} |
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@article{EDELSBRUNNER:1994oq, |
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Abstract = {Frequently, data in scientific computing is in its abstract form a finite point set in space, and it is sometimes useful or required to compute what one might call the ''shape'' of the set. For that purpose, this article introduces the formal notion of the family of alpha-shapes of a finite point set in R3. Each shape is a well-defined polytope, derived from the Delaunay triangulation of the point set, with a parameter alpha is-an-element-of R controlling the desired level of detail. An algorithm is presented that constructs the entire family of shapes for a given set of size n in time O(n2), worst case. A robust implementation of the algorithm is discussed, and several applications in the area of scientific computing are mentioned.}, |
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Address = {1515 BROADWAY, NEW YORK, NY 10036}, |
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Author = {EDELSBRUNNER, H and MUCKE, EP}, |
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Date = {JAN 1994}, |
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Date-Added = {2010-10-27 12:32:43 -0400}, |
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Date-Modified = {2010-10-27 12:32:43 -0400}, |
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Journal = {Acm Transactions On Graphics}, |
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Keywords = {COMPUTATIONAL GRAPHICS; DELAUNAY TRIANGULATIONS; GEOMETRIC ALGORITHMS; POINT SETS; POLYTOPES; ROBUST IMPLEMENTATION; SCIENTIFIC COMPUTING; SCIENTIFIC VISUALIZATION; SIMPLICIAL COMPLEXES; SIMULATED PERTURBATION; 3-DIMENSIONAL SPACE}, |
105 |
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Pages = {43-72}, |
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Publisher = {ASSOC COMPUTING MACHINERY}, |
107 |
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Timescited = {270}, |
108 |
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Title = {3-DIMENSIONAL ALPHA-SHAPES}, |
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Volume = {13}, |
110 |
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Year = {1994}} |
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@misc{Qhull, |
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Date-Added = {2010-10-21 12:05:09 -0400}, |
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Date-Modified = {2010-10-21 12:05:09 -0400}, |
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Title = {Aspects of Structural Glass Transitions}, |
1949 |
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Volume = {I}, |
1950 |
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Year = 1989, |
1951 |
< |
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1951 |
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1952 |
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@article{Lewis91, |
1954 |
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Author = {L.~J. Lewis}, |