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A technique is presented for triangulation of NURBS surfaces. This technique is built upon an advancing front technique combined with grid point projection. This combined approach has been successfully implemented for structured and unstructured grids.
The introduced methodologies are successful in: a) Ising LIDAR features for photogrammetric geo-refererncing; b) Delivering a geo-referenced imagery of the same quality as point-based geo-referencing procedures; c) Taking advantage of the synergistic characteristics of spatial data acquisition systems. The triangulation output can be used for the generation of 3-D perspective views.
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Spherical triangle nets for approximating satellite position
A multi-year study and analysis of data from satellites launched specifically for geodetic purposes and from other satellites useful in geodetic studies was conducted. The program of work included theoretical studies and analysis for the geometric determination of station positions derived from photographic observations of both passive and active satellites and from range observations. The current status of data analysis, processing and results are examined.
Summary of the results of the Ohio State University geometric adjustment for the coordinates at 158 satellite tracking stations. In the solution the origin of the coordinate system is defined through the 'inner' adjustment procedure, whereas the orientation is through the Conventional International Origin and the Greenwich Mean Astronomical Meridian, both as defined by the Bureau International de l'Heure. The scale is implemented through Secor observations and weighted height constraints. Chord distances derived from C-band radar observations and from electronic distance measurements are also included, but they seem to have very little effect. The scale selected corresponds to a best fitting ellipsoid of a = 6,378,142 m and 1/f = 298.25. The average standard deviation of a single coordinate is 3.9 m.
An automated docking system must have a reliable method for determining range and orientation of the passive (target) vehicle with respect to the active vehicle. This method must also provide accurate information on the rates of change of range to and orientation of the passive vehicle. The method must be accurate within required tolerances and capable of operating in real time. The method being developed at Marshall Space Flight Center employs a single TV camera, a laser illumination system and a target consisting, in its minimal configuration, of three retro-reflectors. Two of the retro-reflectors are mounted flush to the same surface, with the third retro-reflector mounted to a post fixed midway between the other two and jutting at a right angle from the surface. For redundancy, two additional retroreflectors are mounted on the surface on a line at right angles to the line containing the first two retro-reflectors, and equally spaced on either side of the post. The target vehicle will contain a large target for initial acquisition and several smaller targets for close range.
This viewgraph presentation provides information on optimizing the travel distance between two points on a curved surface. The presentation addresses the single source shortest path problem, fast algorithms for estimating the eikonal equation, fast schemes and barrier theorems, and the discontinuous Galerkin method, including hyperbolic causality, finite element method, scalars, and marching the discontinuous Galerkin Eikonal approximation.
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A new laser-based optical sensor system that provides hazard detection for planetary rovers is presented. It is anticipated that the sensor can support safe travel at speeds up to 6cm/second for large (1m) rovers in full sunlight on Earth or Mars. The system overcomes limitations in an older design that require image differencing ot detect a laser stripe in full sun.
The Science Crew Operations and Utility Testbed (SCOUT) project is focused on the development of a rover vehicle that can be utilized by two crewmembers during extra vehicular activities (EVAs) on the moon and Mars. The current SCOUT vehicle can transport two suited astronauts riding in open cockpit seats. Among the aspects currently being developed is the cockpit design and layout. This process includes the identification of possible locations for a socket to which a crewmember could connect a portable life support system (PLSS) for recharging power, air, and cooling while seated in the vehicle. The spaces in which controls and connectors may be situated within the vehicle are constrained by the reach and vision capabilities of the suited crewmembers. Accordingly, quantification of the volumes within which suited crewmembers can both see and reach relative to the vehicle represents important information during the design process.
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Several paradigms for accessing CAD geometry during surface meshing for CFD are discussed. File translation, inconsistent geometry engines and non-native point construction are all identified as sources of non-robustness. The paper argues in favor of accessing CAD parts and assemblies in their native format, without translation, and for the use of CAD-native predicates and constructors in surface mesh generation. The discussion also emphasizes the importance of examining the computational requirements for exact evaluation of triangulation predicates during surface meshing. The native approach is demonstrated through an algorithm for the generation of closed manifold surface triangulations from CAD geometry. CAD parts and assemblies are used in their native format, and a part's native geometry engine is accessed through a modeler-independent application programming interface (API). In seeking a robust and fully automated procedure, the algorithm is based on a new physical space manifold triangulation technique specially developed to avoid robustness issues associated with poorly conditioned mappings. In addition, this approach avoids the usual ambiguities associated with floating-point predicate evaluation on constructed coordinate geometry in a mapped space. The technique is incremental, so that each new site improves the triangulation by some well defined quality measure. The algorithm terminates after achieving a prespecified measure of mesh quality and produces a triangulation such that no angle is less than a given angle bound, a or greater than pi - 2alpha. This result also sets bounds on the maximum vertex degree, triangle aspect-ratio and maximum stretching rate for the triangulation. In addition to the output triangulations for a variety of CAD parts, the discussion presents related theoretical results which assert the existence of such an angle bound, and demonstrate that maximum bounds of between 25 deg and 30 deg may be achieved in practice.
For a simultaneous adjustment of a large geodetic triangulation system, a semiiterative technique is modified and used successfully. In this semiiterative technique, known as the conjugate gradient (CG) method, original observation equations are used, and thus the explicit formation of normal equations is avoided, 'huge' computer storage space being saved in the case of triangulation systems. This method is suitable even for very poorly conditioned systems where solution is obtained only after more iterations. A detailed study of the CG method for its application to large geodetic triangulation systems was done that also considered constraint equations with observation equations. It was programmed and tested on systems as small as two unknowns and three equations up to those as large as 804 unknowns and 1397 equations. When real data (573 unknowns, 965 equations) from a 1858-km-long triangulation system were used, a solution vector accurate to four decimal places was obtained in 2.96 min after 1171 iterations (i.e., 2.0 times the number of unknowns).
Algorithms for the generation of 3D unstructured surface and volume grids are discussed. These algorithms are based on incremental insertion and local optimization. The present algorithms are very general and permit local grid optimization based on various measures of grid quality. This is very important; unlike the 2D Delaunay triangulation, the 3D Delaunay triangulation appears not to have a lexicographic characterization of angularity. (The Delaunay triangulation is known to minimize that maximum containment sphere, but unfortunately this is not true lexicographically). Consequently, Delaunay triangulations in three-space can result in poorly shaped tetrahedral elements. Using the present algorithms, 3D meshes can be constructed which optimize a certain angle measure, albeit locally. We also discuss the combinatorial aspects of the algorithm as well as implementational details.
We are concerned here with improving long range stereo by filtering image sequences. Traditionally, measurement errors from stereo camera systems have been approximated as 3-D Gaussians, where the mean is derived by triangulation and the covariance by linearized error propagation. However, there are two problems that arise when filtering such 3-D measurements. First, stereo triangulation suffers from a range dependent statistical bias; when filtering this leads to over-estimating the true range. Second, filtering 3-D measurements derived via linearized error propagation leads to apparent filter divergence; the estimator is biased to under-estimate range. To address the first issue, we examine the statistical behavior of stereo triangulation and show how to remove the bias by series expansion. The solution to the second problem is to filter with image coordinates as measurements instead of triangulated 3-D coordinates.
Investigations of triangulation nets and scaling are reported. Adjustment of the BC-4 worldwide geometric satellite triangulation net is described, along with procedures for correcting type II data and the contents of magnetic tapes containing data from the Pageos network. Computational steps for the further reduction of partially reduced satellite image plate coordinates are outlined. The problem of improving existing triangulation systems by means of satellite super-control points was studied. The SAO-69 geometric solution was scaled with C-band radar data, resulting in SAO and C-band adjustment compatible with one another in the Western Hemisphere. The North America solution NA-6, obtained from GEOS 1 data, was readjusted with new heights as constraints on all 30 optical stations and is referred to as the NA-8 solution.