The Experts below are selected from a list of 60 Experts worldwide ranked by ideXlab platform
Masahiko Shizawa - One of the best experts on this subject based on the ideXlab platform.
-
Invertible affine transformations on Integer Coordinate system â general theory inn- dimensional space
Systems and Computers in Japan, 2007Co-Authors: Masahiko ShizawaAbstract:This paper considers a Lattice represented by Integer Coordinates in n-dimensional space (digital lattice). On the digital lattice, an automorphism is constructed by a newly proposed theory and algorithm, to enable the approximation of the arbitrarily given equivolume affine transformation. The equivolume affine transformation is a general affine transformation that satisfies the condition of volume invariance, and is characterized by the determinant of the representation matrix having an absolute value of 1. An equivolume affine transformation in n-dimensional space can represent any combination of reflection, rotation, equivolume expansion/contraction and skew deformation
-
invertible affine transformations on Integer Coordinate system general theory in n dimensional space
Systems and Computers in Japan, 1993Co-Authors: Masahiko ShizawaAbstract:This paper considers a Lattice represented by Integer Coordinates in n-dimensional space (digital lattice). On the digital lattice, an automorphism is constructed by a newly proposed theory and algorithm, to enable the approximation of the arbitrarily given equivolume affine transformation. The equivolume affine transformation is a general affine transformation that satisfies the condition of volume invariance, and is characterized by the determinant of the representation matrix having an absolute value of 1. An equivolume affine transformation in n-dimensional space can represent any combination of reflection, rotation, equivolume expansion/contraction and skew deformation
E.m. Arkin - One of the best experts on this subject based on the ideXlab platform.
-
FOCS - Computing a shortest k-link path in a polygon
Proceedings. 33rd Annual Symposium on Foundations of Computer Science, 1992Co-Authors: J.s.b. Mitchell, C. Piatko, E.m. ArkinAbstract:The authors consider the problem of finding a shortest polygonal path from s to t within a simple polygon P, subject to the restriction that the path have at most k links (edges). They give an algorithm to compute a k-link path with length at most (1 + epsilon ) times the length of a shortest k-link path, for any error tolerance epsilon >0. The algorithm runs in time O(n/sup 3/k/sup 3/ log (Hk/ epsilon /sup 1/k/)), where N is the largest Integer Coordinate among the n vertices of P. They also study the more general problem of approximating shortest k-link paths in polygons with holes. In this case, they give an algorithm that returns a path with at most 2k links and length at most that of a shortest k-link path; the running time is O(kE/sup 2/), where E is the number of edges in the visibility graph. Finally, they study the bicriteria path problem in which the two criteria are link length and 'total turn' (the integral of mod Delta theta mod along a path). They obtain in an exact polynomial-time algorithm for polygons with holes. >
-
Computing a shortest k-link path in a polygon
Proceedings. 33rd Annual Symposium on Foundations of Computer Science, 1992Co-Authors: J.s.b. Mitchell, C. Piatko, E.m. ArkinAbstract:The authors consider the problem of finding a shortest polygonal path from s to t within a simple polygon P, subject to the restriction that the path have at most k links (edges). They give an algorithm to compute a k-link path with length at most (1 + epsilon ) times the length of a shortest k-link path, for any error tolerance epsilon >0. The algorithm runs in time O(n/sup 3/k/sup 3/ log (Hk/ epsilon /sup 1/k/)), where N is the largest Integer Coordinate among the n vertices of P. They also study the more general problem of approximating shortest k-link paths in polygons with holes. In this case, they give an algorithm that returns a path with at most 2k links and length at most that of a shortest k-link path; the running time is O(kE/sup 2/), where E is the number of edges in the visibility graph. Finally, they study the bicriteria path problem in which the two criteria are link length and 'total turn' (the integral of mod Delta theta mod along a path). They obtain in an exact polynomial-time algorithm for polygons with holes.
J.s.b. Mitchell - One of the best experts on this subject based on the ideXlab platform.
-
FOCS - Computing a shortest k-link path in a polygon
Proceedings. 33rd Annual Symposium on Foundations of Computer Science, 1992Co-Authors: J.s.b. Mitchell, C. Piatko, E.m. ArkinAbstract:The authors consider the problem of finding a shortest polygonal path from s to t within a simple polygon P, subject to the restriction that the path have at most k links (edges). They give an algorithm to compute a k-link path with length at most (1 + epsilon ) times the length of a shortest k-link path, for any error tolerance epsilon >0. The algorithm runs in time O(n/sup 3/k/sup 3/ log (Hk/ epsilon /sup 1/k/)), where N is the largest Integer Coordinate among the n vertices of P. They also study the more general problem of approximating shortest k-link paths in polygons with holes. In this case, they give an algorithm that returns a path with at most 2k links and length at most that of a shortest k-link path; the running time is O(kE/sup 2/), where E is the number of edges in the visibility graph. Finally, they study the bicriteria path problem in which the two criteria are link length and 'total turn' (the integral of mod Delta theta mod along a path). They obtain in an exact polynomial-time algorithm for polygons with holes. >
-
Computing a shortest k-link path in a polygon
Proceedings. 33rd Annual Symposium on Foundations of Computer Science, 1992Co-Authors: J.s.b. Mitchell, C. Piatko, E.m. ArkinAbstract:The authors consider the problem of finding a shortest polygonal path from s to t within a simple polygon P, subject to the restriction that the path have at most k links (edges). They give an algorithm to compute a k-link path with length at most (1 + epsilon ) times the length of a shortest k-link path, for any error tolerance epsilon >0. The algorithm runs in time O(n/sup 3/k/sup 3/ log (Hk/ epsilon /sup 1/k/)), where N is the largest Integer Coordinate among the n vertices of P. They also study the more general problem of approximating shortest k-link paths in polygons with holes. In this case, they give an algorithm that returns a path with at most 2k links and length at most that of a shortest k-link path; the running time is O(kE/sup 2/), where E is the number of edges in the visibility graph. Finally, they study the bicriteria path problem in which the two criteria are link length and 'total turn' (the integral of mod Delta theta mod along a path). They obtain in an exact polynomial-time algorithm for polygons with holes.
Masahiko Shizawa Member - One of the best experts on this subject based on the ideXlab platform.
-
invertible affine transformations on Integer Coordinate system general theory in n dimensional space
Systems and Computers in Japan, 2007Co-Authors: Masahiko Shizawa MemberAbstract:This paper considers a lattice represented by Integer Coordinates in n-dimensional space (digital lattice). On the digital lattice, an automorphism is constructed by a newly proposed theory and algorithm, to enable the approximation of the arbitrarily given equivolume affine transformation. The equivolume affine transformation is a general affine transformation that satisfies the condition of volume invariance, and is characterized by the determinant of the representation matrix having an absolute value of 1. An equivolume affine transformation in n-dimensional space can represent any combination of reflection, rotation, equivolume expansion/contraction and skew deformation. These transformations often are employed as fundamental transformations in the handling of geometrical information in computers. This paper discusses first the geometrical characters of equivolume affine transformations. It then defines the fundamental reflection, skew and translations. It is shown that the equivolume affine transformation in n-dimensional space can be decomposed into the product of (n2-1) fundamental skew transformations, n fundamental translations and a finite number of fundamental reflections. For the fundamental transformation, one-to-one Integer approximation is defined, and a systematic method is proposed to evaluate the upper bound of the approximation error. With the proposed error estimation method, an algorithm is proposed to determine the decomposition suppressing the error in the overall system. One advantage of this theory is that it is no longer necessary to preserve the geometrical information before transformation in the computer, which has been commonplace up to now in computer programming.
C. Piatko - One of the best experts on this subject based on the ideXlab platform.
-
FOCS - Computing a shortest k-link path in a polygon
Proceedings. 33rd Annual Symposium on Foundations of Computer Science, 1992Co-Authors: J.s.b. Mitchell, C. Piatko, E.m. ArkinAbstract:The authors consider the problem of finding a shortest polygonal path from s to t within a simple polygon P, subject to the restriction that the path have at most k links (edges). They give an algorithm to compute a k-link path with length at most (1 + epsilon ) times the length of a shortest k-link path, for any error tolerance epsilon >0. The algorithm runs in time O(n/sup 3/k/sup 3/ log (Hk/ epsilon /sup 1/k/)), where N is the largest Integer Coordinate among the n vertices of P. They also study the more general problem of approximating shortest k-link paths in polygons with holes. In this case, they give an algorithm that returns a path with at most 2k links and length at most that of a shortest k-link path; the running time is O(kE/sup 2/), where E is the number of edges in the visibility graph. Finally, they study the bicriteria path problem in which the two criteria are link length and 'total turn' (the integral of mod Delta theta mod along a path). They obtain in an exact polynomial-time algorithm for polygons with holes. >
-
Computing a shortest k-link path in a polygon
Proceedings. 33rd Annual Symposium on Foundations of Computer Science, 1992Co-Authors: J.s.b. Mitchell, C. Piatko, E.m. ArkinAbstract:The authors consider the problem of finding a shortest polygonal path from s to t within a simple polygon P, subject to the restriction that the path have at most k links (edges). They give an algorithm to compute a k-link path with length at most (1 + epsilon ) times the length of a shortest k-link path, for any error tolerance epsilon >0. The algorithm runs in time O(n/sup 3/k/sup 3/ log (Hk/ epsilon /sup 1/k/)), where N is the largest Integer Coordinate among the n vertices of P. They also study the more general problem of approximating shortest k-link paths in polygons with holes. In this case, they give an algorithm that returns a path with at most 2k links and length at most that of a shortest k-link path; the running time is O(kE/sup 2/), where E is the number of edges in the visibility graph. Finally, they study the bicriteria path problem in which the two criteria are link length and 'total turn' (the integral of mod Delta theta mod along a path). They obtain in an exact polynomial-time algorithm for polygons with holes.