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Primitives for the manipulation of general subdivisions and the computations of Voronoi diagrams

by Leonidas Guibas, Jorge Stolfi - 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 ..."
Abstract - Cited by 534 (11 self) - Add to MetaCart
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

Algebraic Decision Diagrams and their Applications

by R. Iris Bahar, Erica A. Frohm, Charles M. Gaona, Gary D. Hachtel, Enrico Macii, Abelardo Pardo, Fabio Somenzi , 1993
"... In this paper we present theory and experiments on the Algebraic Decision Diagrams (ADD's). These diagrams extend BDD's by allowing values from an arbitrary finite domain to be associated with the terminal nodes. We present a treatment founded in boolean algebras and discuss algorithms and ..."
Abstract - Cited by 321 (18 self) - Add to MetaCart
In this paper we present theory and experiments on the Algebraic Decision Diagrams (ADD's). These diagrams extend BDD's by allowing values from an arbitrary finite domain to be associated with the terminal nodes. We present a treatment founded in boolean algebras and discuss algorithms

Diagrams

by Ricky Ini Liu, Ricky Ini Liu , 2010
"... The algebra of symmetric functions, the representation theory of the symmetric group, and the geometry of the Grassmannian are related to each other via Schur functions, Specht modules, and Schubert varieties, all of which are indexed by partitions and their Young diagrams. We will generalize these ..."
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these objects to allow for not just Young diagrams but arbitrary collections of boxes or, equally well, bipartite graphs. We will then provide evidence for a conjecture that the relation between the areas described above can be extended to these general diagrams. In particular, we will prove the conjecture

The hyperbolic Voronoi diagram in arbitrary dimension

by Frank Nielsen, Richard Nock , 2014
"... We show that in the Klein projective ball model of hyperbolic space, the hyperbolic Voronoi diagram is affine and amounts to clip a corresponding power diagram, requiring however al-gebraic arithmetic. By considering the lesser-known Beltrami hemisphere model of hyperbolic geometry, we overcome the ..."
Abstract - Cited by 1 (1 self) - Add to MetaCart
We show that in the Klein projective ball model of hyperbolic space, the hyperbolic Voronoi diagram is affine and amounts to clip a corresponding power diagram, requiring however al-gebraic arithmetic. By considering the lesser-known Beltrami hemisphere model of hyperbolic geometry, we overcome

The Voronoi diagram of three arbitrary lines in R³

by Hazel Everett, Christian Gillot, Daniel Lazard, Sylvain Lazard, Marc Pouget
"... In this paper we study the Voronoi diagram of lines in R³. The Voronoi diagram of three lines in general position was studied in [14]. In this paper we complete this work by presenting a complete characterization of the Voronoi diagram of three arbitrary lines in R³. As in the general case, we prove ..."
Abstract - Cited by 1 (0 self) - Add to MetaCart
In this paper we study the Voronoi diagram of lines in R³. The Voronoi diagram of three lines in general position was studied in [14]. In this paper we complete this work by presenting a complete characterization of the Voronoi diagram of three arbitrary lines in R³. As in the general case, we

k-Voronoi diagrams computing in arbitrary domains

by Rubén Cárdenes , Simon K Warfield , Andrea J U Mewes , Juan Ruiz-Alzola - In Proc. IEEE International Conference on Image Processing , 2003
"... ABSTRACT We propose a novel algorithm to compute Voronoi diagrams of order k in arbitrary 2D and 3D domains. The algorithm is based on a fast ordered propagation distance transformation called occlusion points propagation geodesic distance transformation (OPPGDT) which is robust and linear in the d ..."
Abstract - Cited by 1 (0 self) - Add to MetaCart
ABSTRACT We propose a novel algorithm to compute Voronoi diagrams of order k in arbitrary 2D and 3D domains. The algorithm is based on a fast ordered propagation distance transformation called occlusion points propagation geodesic distance transformation (OPPGDT) which is robust and linear

Verification of Arithmetic Circuits with Binary Moment Diagrams

by Randal E. Bryant, Yirng-An Chen - IN PROCEEDINGS OF THE 32ND ACM/IEEE DESIGN AUTOMATION CONFERENCE , 1995
"... Binary Moment Diagrams (BMDs) provide a canonical representations for linear functions similar to the way Binary Decision Diagrams (BDDs) represent Boolean functions. Within the class of linear functions, we can embed arbitrary functions from Boolean variables to integer values. BMDs can thus model ..."
Abstract - Cited by 110 (10 self) - Add to MetaCart
Binary Moment Diagrams (BMDs) provide a canonical representations for linear functions similar to the way Binary Decision Diagrams (BDDs) represent Boolean functions. Within the class of linear functions, we can embed arbitrary functions from Boolean variables to integer values. BMDs can thus model

Phase diagram of the . . .

by Jesper Lykke Jacobsen, Jesús Salas , 2007
"... We study the zero-temperature partition function of the Potts antiferromagnet (i.e., the chromatic polynomial) on a torus using a transfer-matrix approach. We consider square- and triangular-lattice strips with fixed width L, arbitrary length N, and fully periodic boundary conditions. On the mathema ..."
Abstract - Cited by 4 (3 self) - Add to MetaCart
We study the zero-temperature partition function of the Potts antiferromagnet (i.e., the chromatic polynomial) on a torus using a transfer-matrix approach. We consider square- and triangular-lattice strips with fixed width L, arbitrary length N, and fully periodic boundary conditions

THE DISCRETE GEODESIC PROBLEM

by Joseph S. B. Mitchell, David M. Mount, Christos H. Papadimitriou , 1987
"... We present an algorithm for determining the shortest path between a source and a destination on an arbitrary (possibly nonconvex) polyhedral surface. The path is constrained to lie on the surface, and distances are measured according to the Euclidean metric. Our algorithm runs in time O(n log n) and ..."
Abstract - Cited by 180 (1 self) - Add to MetaCart
We present an algorithm for determining the shortest path between a source and a destination on an arbitrary (possibly nonconvex) polyhedral surface. The path is constrained to lie on the surface, and distances are measured according to the Euclidean metric. Our algorithm runs in time O(n log n

A linear time algorithm for computing exact Euclidean distance transforms of binary images in arbitrary dimensions

by Calvin R. Maurer, Rensheng Qi, Vijay Raghavan, Senior Member - IEEE Transactions on Pattern Analysis and Machine Intelligence , 2003
"... Abstract—A sequential algorithm is presented for computing the exact Euclidean distance transform (DT) of a k-dimensional binary image in time linear in the total number of voxelsN. The algorithm, which is based on dimensionality reduction and partial Voronoi diagram construction, can be used for co ..."
Abstract - Cited by 101 (3 self) - Add to MetaCart
Abstract—A sequential algorithm is presented for computing the exact Euclidean distance transform (DT) of a k-dimensional binary image in time linear in the total number of voxelsN. The algorithm, which is based on dimensionality reduction and partial Voronoi diagram construction, can be used
Results 1 - 10 of 941