26 research outputs found
Sixteen space-filling curves and traversals for d-dimensional cubes and simplices
This article describes sixteen different ways to traverse d-dimensional space
recursively in a way that is well-defined for any number of dimensions. Each of
these traversals has distinct properties that may be beneficial for certain
applications. Some of the traversals are novel, some have been known in
principle but had not been described adequately for any number of dimensions,
some of the traversals have been known. This article is the first to present
them all in a consistent notation system. Furthermore, with this article, tools
are provided to enumerate points in a regular grid in the order in which they
are visited by each traversal. In particular, we cover: five discontinuous
traversals based on subdividing cubes into 2^d subcubes: Z-traversal (Morton
indexing), U-traversal, Gray-code traversal, Double-Gray-code traversal, and
Inside-out traversal; two discontinuous traversals based on subdividing
simplices into 2^d subsimplices: the Hill-Z traversal and the Maehara-reflected
traversal; five continuous traversals based on subdividing cubes into 2^d
subcubes: the Base-camp Hilbert curve, the Harmonious Hilbert curve, the Alfa
Hilbert curve, the Beta Hilbert curve, and the Butz-Hilbert curve; four
continuous traversals based on subdividing cubes into 3^d subcubes: the Peano
curve, the Coil curve, the Half-coil curve, and the Meurthe curve. All of these
traversals are self-similar in the sense that the traversal in each of the
subcubes or subsimplices of a cube or simplex, on any level of recursive
subdivision, can be obtained by scaling, translating, rotating, reflecting
and/or reversing the traversal of the complete unit cube or simplex.Comment: 28 pages, 12 figures. v2: fixed a confusing typo on page 12, line
Intensive hypercube communication Prearranged communication in link-bound machines,
Hypercube algorithms are developed for a variety of communication-intensive tasks such as transposing a matrix, histogramming, sending a (long) message from one node to another, broadcasting a message from one node to all others, broadcasting a message from each node to all others, and exchanging messages between nodes via a fixed permutation. The algorithm for exchanging via a fixed permutation can be viewed as a deterministic analog of Valiant's randomized routing. The algorithms are for link-bound hypercubes in which local processing time is ignored, communication time predominates, message headers are not needed because all nodes know the task being performed, and all nodes can use all communication links simultaneously. Through systematic use of techniques such as pipelining, hatching, variable packet sizing, symmetrizing, and completing, for all these problems algorithms which achieve a time with an optimal highest-order term are obtained.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/28830/1/0000664.pd
Computational methods and software systems for dynamics and control of large space structures
This final report on computational methods and software systems for dynamics and control of large space structures covers progress to date, projected developments in the final months of the grant, and conclusions. Pertinent reports and papers that have not appeared in scientific journals (or have not yet appeared in final form) are enclosed. The grant has supported research in two key areas of crucial importance to the computer-based simulation of large space structure. The first area involves multibody dynamics (MBD) of flexible space structures, with applications directed to deployment, construction, and maneuvering. The second area deals with advanced software systems, with emphasis on parallel processing. The latest research thrust in the second area, as reported here, involves massively parallel computers
Technology 2000, volume 1
The purpose of the conference was to increase awareness of existing NASA developed technologies that are available for immediate use in the development of new products and processes, and to lay the groundwork for the effective utilization of emerging technologies. There were sessions on the following: Computer technology and software engineering; Human factors engineering and life sciences; Information and data management; Material sciences; Manufacturing and fabrication technology; Power, energy, and control systems; Robotics; Sensors and measurement technology; Artificial intelligence; Environmental technology; Optics and communications; and Superconductivity