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Results for “Convex hull”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

A fast adaptive convex hull algorithm on two-dimensional processor arrays with a reconfigurable BUS system

A bus system that can change dynamically to suit computational needs is referred to as reconfigurable. We present a fast adaptive convex hull algorithm on a two-dimensional processor array with a reconfigurable bus system (2-D PARBS, for short). Specifically, we show that computing the convex hull of a planar set of n points taken O(log n/log m) time on a 2-D PARBS of size mn x n with 3 less than or equal to m less than or equal to n. Our result implies that the convex hull of n points in the plane can be computed in O(1) time in a 2-D PARBS of size n(exp 1.5) x n.

Olariu, S.↗
NASA NTRS1991

Rule groupings in expert systems using nearest neighbour decision rules, and convex hulls

Expert System shells are lacking in many areas of software engineering. Large rule based systems are not semantically comprehensible, difficult to debug, and impossible to modify or validate. Partitioning a set of rules found in CLIPS (C Language Integrated Production System) into groups of rules which reflect the underlying semantic subdomains of the problem, will address adequately the concerns stated above. Techniques are introduced to structure a CLIPS rule base into groups of rules that inherently have common semantic information. The concepts involved are imported from the field of A.I., Pattern Recognition, and Statistical Inference. Techniques focus on the areas of feature selection, classification, and a criteria of how 'good' the classification technique is, based on Bayesian Decision Theory. A variety of distance metrics are discussed for measuring the 'closeness' of CLIPS rules and various Nearest Neighbor classification algorithms are described based on the above metric.

Anastasiadis, Stergios↗
NASA NTRS1998

Worst case estimation of homology design by convex analysis

The methodology of homology design is investigated for optimum design of advanced structures. for which the achievement of delicate tasks by the aid of active control system is demanded. The proposed formulation of homology design, based on the finite element sensitivity analysis, necessarily requires the specification of external loadings. The formulation to evaluate the worst case for homology design caused by uncertain fluctuation of loadings is presented by means of the convex model of uncertainty, in which uncertainty variables are assigned to discretized nodal forces and are confined within a conceivable convex hull given as a hyperellipse. The worst case of the distortion from objective homologous deformation is estimated by the Lagrange multiplier method searching the point to maximize the error index on the boundary of the convex hull. The validity of the proposed method is demonstrated in a numerical example using the eleven-bar truss structure.

Yoshikawa, N.↗
NASA NTRS2012

Rapid Process to Generate Beam Envelopes for Optical System Analysis

The task of evaluating obstructions in the optical throughput of an optical system requires the use of two disciplines, and hence, two models: optical models for the details of optical propagation, and mechanical models for determining the actual structure that exists in the optical system. Previous analysis methods for creating beam envelopes (or cones of light) for use in this obstruction analysis were found to be cumbersome to calculate and take significant time and resources to complete. A new process was developed that takes less time to complete beam envelope analysis, is more accurate and less dependent upon manual node tracking to create the beam envelopes, and eases the burden on the mechanical CAD (computer-aided design) designers to form the beam solids. This algorithm allows rapid generation of beam envelopes for optical system obstruction analysis. Ray trace information is taken from optical design software and used to generate CAD objects that represent the boundary of the beam envelopes for detailed analysis in mechanical CAD software. Matlab is used to call ray trace data from the optical model for all fields and entrance pupil points of interest. These are chosen to be the edge of each space, so that these rays produce the bounding volume for the beam. The x and y global coordinate data is collected on the surface planes of interest, typically an image of the field and entrance pupil internal of the optical system. This x and y coordinate data is then evaluated using a convex hull algorithm, which removes any internal points, which are unnecessary to produce the bounding volume of interest. At this point, tolerances can be applied to expand the size of either the field or aperture, depending on the allocations. Once this minimum set of coordinates on the pupil and field is obtained, a new set of rays is generated between the field plane and aperture plane (or vice-versa). These rays are then evaluated at planes between the aperture and field, at a desired number of steps perceived necessary to build up the bounding volume or cone shape. At each plane, the ray coordinates are again evaluated using the convex hull algorithm to reduce the data to a minimal set. When all of the coordinates of interest are obtained for every plane of the propagation, the data is formatted into an xyz file suitable for FRED optical analysis software to import and create a STEP file of the data. This results in a spiral-like structure that is easily imported by mechanical CAD users who can then use an automated algorithm to wrap a skin around it and create a solid that represents the beam.

Howard, Joseph↗
NASA NTRS1976

Timesharing without synchronization

The capacity region of a multiple-access channel has recently been identified as the convex hull (barred K) of a certain set (K) of points in the first quadrant of the (R1,R2) plane. For a pair of rates in K, a more or less standard random-coding argument can be used to show the existence of a good pair of codes. But for points in barred K-K, it is apparently necessary for the two senders to use some form of time sharing to achieve the desired rates. However, in order to share time, at least one of the senders must have knowledge of the other's phase; and in many practical situations this knowledge does not exist. This paper investigates the problems which arise in coding for multiple-access channels when the senders cannot synchronize with each other.

Mceliece, R. J.↗
NASA NTRS1985

Some properties of n-dimensional triangulations

A number of mathematical results relevant to the problem of constructing a triangulation, i.e., a simplicial tessellation, of the convex hull of an arbitrary finite set of points in n-space are described. The principal results achieved are: (1) a set of n+2 points in n-space may be triangulated in at most 2 different ways; (2) the sphere test defined in this report selects a preferred one of these two triangulations; (3) a set of parameters is defined that permits the characterization and enumeration of all sets of n+2 points in n-space that are significantly different from the point of view of their possible triangulation; (4) the local sphere test induces a global sphere test property for a triangulation; and (5) a triangulation satisfying the global sphere property is dual to the n-dimensional Dirichlet tesselation, i.e., it is a Delaunay triangulation.

Lawson, C. L.↗
NASA NTRS1986

Properties of n-dimensional triangulations

This paper establishes a number of mathematical results relevant to the problem of constructing a triangulation, i.e., a simplical tessellation of the convex hull of an arbitrary finite set of points in n-space. The principal results of the present paper are: (1) a set of n + 2 points in n-space may be triangulated in at most 2 different ways; (2) the 'sphere test' defined in this paper selects a preferred one of these two triangulations; (3) a set of parameters is defined that permits the characterization and enumeration of all sets on n + 2 points in n-space that are significantly different from the point of view of their possible triangulations; and (4) the local sphere test induces a global sphere test property for a triangulation.

Lawson, Charles L.↗
NASA NTRS1990

The shape of Eros

Monte Carlo simulations are presently used to optimize estimation, ascertain associated errors, and guide bias-correction procedures, for the Eros polar silhouette convex hull that has been estimated from radar echo spectra. This hull is trapezoidal; this nonaxisymmetric shape may account for odd harmonics in Eros' echo spectral signature as a function of rotation phase. Additional constraints have been obtained for the figure of Eros through the inversion of the optical lightcurve to estimate the asteroid's two-dimensional average of the three-dimensional shape. This 'mean cross-section' and the polar silhouette exhibit similar elongations.

Ostro, S. J.↗
NASA NTRS1991

Surface reconstruction from scattered data through pruning of unstructured grids

This paper describes an algorithm for reconstructing a surface from a randomly digitized object. Scan data (treated as a cloud of points) is first tesselated out to its convex hull using Delaunay triangulation. The line-of-sight between each surface point and the scanning device is traversed, and any tetrahedra which are pierced by it are removed. The remaining tetrahedra form an approximate solid model of the scanned object. Due to the inherently limited resolution of any scan, this algorithm requires two additional procedures to produce a smooth, polyhedral surface: one process removes long, narrow tetrahedra which span indentations in the surface between digitized points; the other smooths sharp edges. The results for a moderately resolved sample body and a highly resolved aircraft are displayed.

Maksymiuk, C. M.↗
NASA NTRS1992

Recursive optimal pruning with applications to tree structured vector quantizers

A pruning algorithm of Chou et al. (1989) for designing optimal tree structures identifies only those codebooks which lie on the convex hull of the original codebook's operational distortion rate function. The authors introduce a modified version of the original algorithm, which identifies a large number of codebooks having minimum average distortion, under the constraint that, in each step, only modes having no descendents are removed from the tree. All codebooks generated by the original algorithm are also generated by this algorithm. The new algorithm generates a much larger number of codebooks in the middle- and low-rate regions. The additional codebooks permit operation near the codebook's operational distortion rate function without time sharing by choosing from the increased number of available bit rates. Despite the statistical mismatch which occurs when coding data outside the training sequence, these pruned codebooks retain their performance advantage over full search vector quantizers (VQs) for a large range of rates.

Kiang, Shei-Zein↗
NASA NTRS1992

Data reduction using cubic rational B-splines

A geometric method is proposed for fitting rational cubic B-spline curves to data that represent smooth curves including intersection or silhouette lines. The algorithm is based on the convex hull and the variation diminishing properties of Bezier/B-spline curves. The algorithm has the following structure: it tries to fit one Bezier segment to the entire data set and if it is impossible it subdivides the data set and reconsiders the subset. After accepting the subset the algorithm tries to find the longest run of points within a tolerance and then approximates this set with a Bezier cubic segment. The algorithm uses this procedure repeatedly to the rest of the data points until all points are fitted. It is concluded that the algorithm delivers fitting curves which approximate the data with high accuracy even in cases with large tolerances.

Chou, Jin J.↗
NASA NTRS1991

Efficient distance calculation using the spherically-extended polytope (s-tope) model

An object representation scheme which allows for Euclidean distance calculation is presented. The object model extends the polytope model by representing objects as the convex hull of a finite set of spheres. An algorithm for calculating distances between objects is developed which is linear in the total number of spheres specifying the two objects.

Hamlin, Gregory J.↗
NASA NTRS1992

Cartography of asteroids and comet nuclei from low resolution data

High resolution images of non-spherical objects, such as Viking images of Phobos and the anticipated Galileo images of Gaspra, lend themselves to conventional planetary cartographic procedures: control network analysis, stereophotogrammetry, image mosaicking in 2D or 3D, and airbrush mapping. There remains the problem of a suitable map projection for bodies which are extremely elongated or irregular in shape. Many bodies will soon be seen at lower resolution (5-30 pixels across the disk) in images from speckle interferometry, the Hubble Space Telescope, ground-based radar, distinct spacecraft encounters, and closer images degraded by smear. Different data with similar effective resolutions are available from stellar occultations, radar or lightcurve convex hulls, lightcurve modeling of albedo variations, and cometary jet modeling. With such low resolution, conventional methods of shape determination will be less useful or will fail altogether, leaving limb and terminator topography as the principal sources of topographic information. A method for shape determination based on limb and terminator topography was developed. It has been applied to the nucleus of Comet Halley and the jovian satellite Amalthea. The Amalthea results are described to give an example of the cartographic possibilities and problems of anticipated data sets.

Stooke, Philip J.↗
NASA NTRS1993

Two generalizations of Kohonen clustering

The relationship between the sequential hard c-means (SHCM), learning vector quantization (LVQ), and fuzzy c-means (FCM) clustering algorithms is discussed. LVQ and SHCM suffer from several major problems. For example, they depend heavily on initialization. If the initial values of the cluster centers are outside the convex hull of the input data, such algorithms, even if they terminate, may not produce meaningful results in terms of prototypes for cluster representation. This is due in part to the fact that they update only the winning prototype for every input vector. The impact and interaction of these two families with Kohonen's self-organizing feature mapping (SOFM), which is not a clustering method, but which often leads ideas to clustering algorithms is discussed. Then two generalizations of LVQ that are explicitly designed as clustering algorithms are presented; these algorithms are referred to as generalized LVQ = GLVQ; and fuzzy LVQ = FLVQ. Learning rules are derived to optimize an objective function whose goal is to produce 'good clusters'. GLVQ/FLVQ (may) update every node in the clustering net for each input vector. Neither GLVQ nor FLVQ depends upon a choice for the update neighborhood or learning rate distribution - these are taken care of automatically. Segmentation of a gray tone image is used as a typical application of these algorithms to illustrate the performance of GLVQ/FLVQ.

Bezdek, James C.↗
NASA NTRS1993

Approaches to high aspect ratio triangulations

In aerospace computational fluid dynamics calculations, high aspect ratio, or stretched, triangulations are necessary to adequately resolve the features of a viscous flow around bodies. In this paper, we explore alternatives to the Delaunay triangulation which can be used to generate high aspect ratio triangulations of point sets. The method is based on a variation of the lifting map concept which derives Delaunay triangulations from convex hull calculations.

Posenau, M.-A.↗
NASA NTRS1993

Certification of computational results

A conceptually novel and powerful technique to achieve fault detection and fault tolerance in hardware and software systems is described. When used for software fault detection, this new technique uses time and software redundancy and can be outlined as follows. In the initial phase, a program is run to solve a problem and store the result. In addition, this program leaves behind a trail of data called a certification trail. In the second phase, another program is run which solves the original problem again. This program, however, has access to the certification trail left by the first program. Because of the availability of the certification trail, the second phase can be performed by a less complex program and can execute more quickly. In the final phase, the two results are compared and if they agree the results are accepted as correct; otherwise an error is indicated. An essential aspect of this approach is that the second program must always generate either an error indication or a correct output even when the certification trail it receives from the first program is incorrect. The certification trail approach to fault tolerance is formalized and realizations of it are illustrated by considering algorithms for the following problems: convex hull, sorting, and shortest path. Cases in which the second phase can be run concurrently with the first and act as a monitor are discussed. The certification trail approach are compared to other approaches to fault tolerance.

Sullivan, Gregory F.↗