Results 241 to 250 of about 388,744 (284)
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Journal of Algorithms, 1988
Given a set of n points in the plane, two points are said to be rectangularly visible if the orthogonal rectangle with the two points as opposite vertices has no other point of the set in its interior. It is shown that all pairs of rectangularly visible points in a set of size n can be determined in O(n log n\(+k)\) time, where k is the number of ...
Mark H. Overmars, Derick Wood
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Given a set of n points in the plane, two points are said to be rectangularly visible if the orthogonal rectangle with the two points as opposite vertices has no other point of the set in its interior. It is shown that all pairs of rectangularly visible points in a set of size n can be determined in O(n log n\(+k)\) time, where k is the number of ...
Mark H. Overmars, Derick Wood
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Rectangular Codes and Rectangular Algebra
1999We investigate general properties of rectangular codes. The class of rectangular codes includes all linear, group, and many nongroup codes. We define a basis of a rectangular code. This basis gives a universal description of a rectangular code. In this paper the rectangular algebra is defined.
Vladimir Sidorenko +2 more
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Proceedings of the twenty-fifth annual symposium on Computational geometry, 2009
Raisz [3] introduced rectangular cartograms in 1934 as a way of visualizing spatial information, such as population or economic strength, of a set of regions like countries or states. Rectangular cartograms represent geographic regions by rectangles; the positioning and adjacencies of the rectangles are chosen according to their geographic locations ...
Mark de Berg +3 more
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Raisz [3] introduced rectangular cartograms in 1934 as a way of visualizing spatial information, such as population or economic strength, of a set of regions like countries or states. Rectangular cartograms represent geographic regions by rectangles; the positioning and adjacencies of the rectangles are chosen according to their geographic locations ...
Mark de Berg +3 more
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Journal of Symbolic Logic, 1998
AbstractWe prove that every rectangularly dense diagonal-free cylindric algebra is representable. As a corollary, we give finite, sound and complete axiomatizations for the finite-variable fragments of first order logic without equality and for multi-dimensional modal S5-logic.
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AbstractWe prove that every rectangularly dense diagonal-free cylindric algebra is representable. As a corollary, we give finite, sound and complete axiomatizations for the finite-variable fragments of first order logic without equality and for multi-dimensional modal S5-logic.
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Rectangular Parallelepipeds in Ellipsoids
SIAM Review, 1996The authors give short elementary proofs for some geometric facts. We give an example: Let \(A\) be a real \(n\times n\) symmetric matrix with distinct eigenvalues. A general quadric is given by \(\langle Ax, x\rangle=1\). Then any rectangular parallelepiped inscribed in the quadric has its sides parallel to the principal axes of the quadric.
J. Duncan, D. Khavinson, H. Shapiro
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GUARDING RECTANGULAR PARTITIONS
International Journal of Computational Geometry & Applications, 2009A rectangular partition is a partition of a rectangle into non-overlapping rectangles, such that no four rectangles meet at a common point. A vertex guard is a guard located at a vertex of the partition (i.e., at a corner of a rectangle); it guards the rectangles that meet at this vertex.
Yefim Dinitz +2 more
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Rectangularity Versus Piecewise Rectangularity of Product Spaces
Canadian Mathematical Bulletin, 1987AbstractWe shall discuss relations between rectangularity and piecewise rectangularity of product spaces. In particular, we show that for each positive integer n there exists an n-dimensional, collectionwise normal, non-piecewise rectangular product X × Y which satisfies the inequality dim (X × Y) ≤ dim X + dim Y.
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On the Number of Rectangular Tilings
IEEE Transactions on Image Processing, 2006Adaptive multiscale representations via quadtree splitting and two-dimensional (2-D) wavelet packets, which amount to space and frequency decompositions, respectively, are powerful concepts that have been widely used in applications. These schemes are direct extensions of their one-dimensional counterparts, in particular, by coupling of the two ...
D. Xu, Minh N. Do
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Eccentric electrophoretic motion of a rectangular particle in a rectangular microchannel
Journal of Colloid and Interface Science, 2010Understanding of the effects of the boundary - the channel walls - on the electrophoretic motion of particles in microchannels is very important. This paper developed an analytical solution of the electrophoretic mobility for eccentric motion of a rectangular particle in a rectangular microchannel.
Dongquing, Li, Yasaman, Daghighi
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Parallel Computing, 2005
In this paper, we propose a variation of honeycomb meshes. A honeycomb rectangular disk HReD(m, n) is obtained from the honeycomb rectangular mesh HReM(m, n) by adding a boundary cycle. A honeycomb rectangular disk HReD(m, n) is a 3-regular planar graph. It is obvious that the honeycomb rectangular mesh HReM(m, n) is a subgraph of HReD(m, n).
Yuan-Hsiang Teng +2 more
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In this paper, we propose a variation of honeycomb meshes. A honeycomb rectangular disk HReD(m, n) is obtained from the honeycomb rectangular mesh HReM(m, n) by adding a boundary cycle. A honeycomb rectangular disk HReD(m, n) is a 3-regular planar graph. It is obvious that the honeycomb rectangular mesh HReM(m, n) is a subgraph of HReD(m, n).
Yuan-Hsiang Teng +2 more
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