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Oblique orthographic projections allow model to be viewed in any selected orientation specified by Euler-angle transformation. This transformation resolves coordinate system of model to principal plane on which display is to be plotted.
User and programer documentation is presented for two programs for automatic plotting of digital data. One of the programs generates oblique orthographic projections of three-dimensional numerical models and the other program generates contour plots of data distributed in an arbitrary planar region. A general description of the computational algorithms, user instructions, and complete listings of the programs is given. Several plots are included to illustrate various program options, and a single example is described to facilitate learning the use of the programs.
This Paper under-estimates answers to the following question under various constraints: If a geofencing algorithm uses a map projection to determine whether a position is inside/outside a polygon region, how far outside/inside the polygon can the point be and the algorithm determine that it is inside/outside (the opposite and therefore incorrect answer)? Geofencing systems for unmanned aircraft systems (UAS) often model stay-in and stay-out regions using 2D polygons with minimum and maximum altitudes. The vertices of the polygons are typically input as latitude-longitude pairs, and the edges as paths between adjacent vertices. There are numerous ways to generate these paths, resulting in numerous potential locations for the edges of stay-in and stay-out regions. These paths may be geodesics on a spherical model of the earth or geodesics on the WGS84 reference ellipsoid. In geofencing applications that use map projections, these paths are inverse images of straight lines in the projected plane. This projected plane may be a projection of a spherical earth model onto a tangent plane, called an orthographic projection. Alternatively, it may be a projection where the straight lines in the projected plane correspond to straight lines in the latitudelongitude coordinate system, also called a Plate Carr´ee projection. This paper estimates distances between different edge paths and an oracle path, which is a geodesic on either the spherical earth or the WGS84 ellipsoidal earth. This paper therefore estimates how far apart different edge paths can be rather than comparing their path lengths, which are not considered. Rather, the comparision is between the actual locations of the edges between vertices. For edges drawn using orthographic projections, this maximum distance increases as the distance from the polygon vertices to the projection point increases. For edges drawn using Plate Carr´ee projections, this maximum distance increases as the vertices become further from the equator. Distances between geodesics on a spherical earth and a WGS84 ellipsoidal earth are also analyzed, using the WGS84 ellipsoid as the oracle. Bounds on the 2D distance between a straight line and a great circle path, in an orthographically projected plane rather than on the surface of the earth, have been formally verified in the PVS theorem prover, meaning that they are mathematically correct in the absence of floating point errors.
This compact disk (CD) is part of the Clementine I high resolution (HiRes) camera lunar image mosaics developed by Malin Space Science Systems (MSSS). These mosaics were developed through calibration and semi-automated registration against the recently released geometrically and photometrically controlled Ultraviolet/Visible (UV/Vis) Basemap Mosaic, which is available through the PDS, as CD-ROM volumes CL_3001-3015. The HiRes mosaics are compiled from non-uniformity corrected, 750 nanometer ("D") filter high resolution observations from the HiRes imaging system onboard the Clementine Spacecraft. The geometric control is provided by the U.S. Geological Survey (USGS) Clementine Basemap Mosaic compiled from the 750 nm Ultraviolet/Visible Clementine imaging system. Calibration was achieved by removing the image nonuniformity largely caused by the HiRes system's light intensifier. Also provided are offset and scale factors, achieved by a fit of the HiRes data to the corresponding photometrically calibrated UV/Vis basemap that approximately transform the 8-bit HiRes data to photometric units. The mosaics on this CD are compiled from polar data (latitudes greater than 80 degrees), and are presented in the stereographic projection at a scale of 30 m/pixel at the pole, a resolution 5 times greater than that (150 m/pixel) of the corresponding UV/Vis polar basemap. This 5:1 scale ratio is in keeping with the sub-polar mosaic, in which the HiRes and UV/Vis mosaics had scales of 20 m/pixel and 100 m/pixel, respectively. The equal-area property of the stereographic projection made this preferable for the HiRes polar mosaic rather than the basemap's orthographic projection. Thus, a necessary first step in constructing the mosaic was the reprojection of the UV/Vis basemap to the stereographic projection. The HiRes polar data can be naturally grouped according to the orbital periapsis, which was in the south during the first half of the mapping mission and in the north during the second half. Images in each group have generally uniform intrinsic resolution, illumination, exposure and gain. Rather than mingle data from the two periapsis epochs, separate mosaics are provided for each, a total of 4 polar mosaics. The mosaics are divided into 100 square tiles of 2250 pixels (approximately 2.2 deg near the pole) on a side. Not all squares of this grid contain HiRes mosaic data, some inevitably since a square is not a perfect representation of a (latitude) circle, others due to the lack of HiRes data. This CD also contains ancillary data files that support the HiRes mosaic. These files include browse images with UV/Vis context stored in a Joint Photographic Experts Group (JPEG) format, index files ('imgindx.tab' and 'srcindx.tab') that tabulate the contents of the CD, and documentation files. For more information on the contents and organization of the CD volume set refer to the "FILES, DIRECTORIES AND DISK CONTENTS" section of this document. The image files are organized according to NASA's Planetary Data System (PDS) standards. An image file (tile) is organized as a PDS labeled file containing an "image object".
This compact disk (CD) is part of the Clementine I high resolution (HiRes) camera lunar image mosaics developed by Malin Space Science Systems (MSSS). These mosaics were developed through calibration and semi-automated registration against the recently released geometrically and photometrically controlled Ultraviolet/Visible (UV/Vis) Basemap Mosaic, which is available through the PDS, as CD-ROM volumes CL_3001-3015. The HiRes mosaics are compiled from non-uniformity corrected, 750 nanometer ("D") filter high resolution observations from the HiRes imaging system onboard the Clementine Spacecraft. The geometric control is provided by the U.S. Geological Survey (USGS) Clementine Basemap Mosaic compiled from the 750 nm Ultraviolet/Visible Clementine imaging system. Calibration was achieved by removing the image nonuniformity largely caused by the HiRes system's light intensifier. Also provided are offset and scale factors, achieved by a fit of the HiRes data to the corresponding photometrically calibrated UV/Vis basemap that approximately transform the 8-bit HiRes data to photometric units. The mosaics on this CD are compiled from polar data (latitudes greater than 80 degrees), and are presented in the stereographic projection at a scale of 30 m/pixel at the pole, a resolution 5 times greater than that (150 m/pixel) of the corresponding UV/Vis polar basemap. This 5:1 scale ratio is in keeping with the sub-polar mosaic, in which the HiRes and UV/Vis mosaics had scales of 20 m/pixel and 100 m/pixel, respectively. The equal-area property of the stereographic projection made this preferable for the HiRes polar mosaic rather than the basemap's orthographic projection. Thus, a necessary first step in constructing the mosaic was the reprojection of the UV/Vis basemap to the stereographic projection. The HiRes polar data can be naturally grouped according to the orbital periapsis, which was in the south during the first half of the mapping mission and in the north during the second half. Images in each group have generally uniform intrinsic resolution, illumination, exposure and gain. Rather than mingle data from the two periapsis epochs, separate mosaics are provided for each, a total of 4 polar mosaics. The mosaics are divided into 100 square tiles of 2250 pixels (approximately 2.2 deg near the pole) on a side. Not all squares of this grid contain HiRes mosaic data, some inevitably since a square is not a perfect representation of a (latitude) circle, others due to the lack of HiRes data. This CD also contains ancillary data files that support the HiRes mosaic. These files include browse images with UV/Vis context stored in a Joint Photographic Experts Group (JPEG) format, index files ('imgindx.tab' and 'srcindx.tab') that tabulate the contents of the CD, and documentation files. For more information on the contents and organization of the CD volume set refer to the "FILES, DIRECTORIES AND DISK CONTENTS" section of this document. The image files are organized according to NASA's Planetary Data System (PDS) standards. An image file (tile) is organized as a PDS labeled file containing an "image object".
This compact disk (CD) is part of the Clementine I high resolution (HiRes) camera lunar image mosaics developed by Malin Space Science Systems (MSSS). These mosaics were developed through calibration and semi-automated registration against the recently released geometrically and photometrically controlled Ultraviolet/Visible (UV/Vis) Basemap Mosaic, which is available through the PDS, as CD-ROM volumes CL_3001-3015. The HiRes mosaics are compiled from non-uniformity corrected, 750 nanometer ("D") filter high resolution observations from the HiRes imaging system onboard the Clementine Spacecraft. The geometric control is provided by the U. S. Geological Survey (USGS) Clementine Basemap Mosaic compiled from the 750 nm Ultraviolet/Visible Clementine imaging system. Calibration was achieved by removing the image nonuniformity largely caused by the HiRes system's light intensifier. Also provided are offset and scale factors, achieved by a fit of the HiRes data to the corresponding photometrically calibrated UV/Vis basemap that approximately transform the 8-bit HiRes data to photometric units. The mosaics on this CD are compiled from polar data (latitudes greater than 80 degrees), and are presented in the stereographic projection at a scale of 30 m/pixel at the pole, a resolution 5 times greater than that (150 m/pixel) of the corresponding UV/Vis polar basemap. This 5:1 scale ratio is in keeping with the sub-polar mosaic, in which the HiRes and UV/Vis mosaics had scales of 20 m/pixel and 100 m/pixel, respectively. The equal-area property of the stereographic projection made this preferable for the HiRes polar mosaic rather than the basemap's orthographic projection. Thus, a necessary first step in constructing the mosaic was the reprojection of the UV/Vis basemap to the stereographic projection. The HiRes polar data can be naturally grouped according to the orbital periapsis, which was in the south during the first half of the mapping mission and in the north during the second half. Images in each group have generally uniform intrinsic resolution, illumination, exposure and gain. Rather than mingle data from the two periapsis epochs, separate mosaics are provided for each, a total of 4 polar mosaics. The mosaics are divided into 100 square tiles of 2250 pixels (approximately 2.2 deg near the pole) on a side. Not all squares of this grid contain HiRes mosaic data, some inevitably since a square is not a perfect representation of a (latitude) circle, others due to the lack of HiRes data. This CD also contains ancillary data files that support the HiRes mosaic. These files include browse images with UV/Vis context stored in a Joint Photographic Experts Group (JPEG) format, index files ('imgindx.tab' and 'srcindx.tab') that tabulate the contents of the CD, and documentation files. For more information on the contents and organization of the CD volume set refer to the "FILES, DIRECTORIES AND DISK CONTENTS" section of this document. The image files are organized according to NASA's Planetary Data System (PDS) standards. An image file (tile) is organized as a PDS labeled file containing an "image object".
This compact disk (CD) is part of the Clementine I high resolution (HiRes) camera lunar image mosaics developed by Malin Space Science Systems (MSSS). These mosaics were developed through calibration and semi-automated registration against the recently released geometrically and photometrically controlled Ultraviolet/Visible (UV/Vis) Basemap Mosaic, which is available through the PDS, as CD-ROM volumes CL_3001-3015. The HiRes mosaics are compiled from non-uniformity corrected, 750 nanometer ("D") filter high resolution observations from the HiRes imaging system onboard the Clementine Spacecraft. The geometric control is provided by the U. S. Geological Survey (USGS) Clementine Basemap Mosaic compiled from the 750 nm Ultraviolet/Visible Clementine imaging system. Calibration was achieved by removing the image nonuniformity largely caused by the HiRes system's light intensifier. Also provided are offset and scale factors, achieved by a fit of the HiRes data to the corresponding photometrically calibrated UV/Vis basemap that approximately transform the 8-bit HiRes data to photometric units. The mosaics on this CD are compiled from polar data (latitudes greater than 80 degrees), and are presented in the stereographic projection at a scale of 30 m/pixel at the pole, a resolution 5 times greater than that (150 m/pixel) of the corresponding UV/Vis polar basemap. This 5:1 scale ratio is in keeping with the sub-polar mosaic, in which the HiRes and UV/Vis mosaics had scales of 20 m/pixel and 100 m/pixel, respectively. The equal-area property of the stereographic projection made this preferable for the HiRes polar mosaic rather than the basemap's orthographic projection. Thus, a necessary first step in constructing the mosaic was the reprojection of the UV/Vis basemap to the stereographic projection. The HiRes polar data can be naturally grouped according to the orbital periapsis, which was in the south during the first half of the mapping mission and in the north during the second half. Images in each group have generally uniform intrinsic resolution, illumination, exposure and gain. Rather than mingle data from the two periapsis epochs, separate mosaics are provided for each, a total of 4 polar mosaics. The mosaics are divided into 100 square tiles of 2250 pixels (approximately 2.2 deg near the pole) on a side. Not all squares of this grid contain HiRes mosaic data, some inevitably since a square is not a perfect representation of a (latitude) circle, others due to the lack of HiRes data. This CD also contains ancillary data files that support the HiRes mosaic. These files include browse images with UV/Vis context stored in a Joint Photographic Experts Group (JPEG) format, index files ('imgindx.tab' and 'srcindx.tab') that tabulate the contents of the CD, and documentation files. For more information on the contents and organization of the CD volume set refer to the "FILES, DIRECTORIES AND DISK CONTENTS" section of this document. The image files are organized according to NASA's Planetary Data System (PDS) standards. An image file (tile) is organized as a PDS labeled file containing an "image object".
A reference of moderately detailed eclipse predictions and maps for use by the professional astronomical community is provided. The general characteristics of every solar eclipse and a detailed set of cylindrical project world maps which show the umbral paths of every solar eclipse from 1901 to 2100 are presented. The geodetic path coordinates and local circumstance on the center line, and a series of orthographic projection maps which show the regions of visibility of both partial and central phases for every eclipse from 1986 through 2035 are also provided.
A complete catalog is presented, listing the general characteristics of every solar eclipse from 1901 through 2100. To complement this catalog, a detailed set of cylindrical projection world maps shows the umbral paths of every solar eclipse over the 200 year interval. Focusing in on the next 50 years, accurate geodetic path coordinates and local circumstances for the 71 central eclipses from 1987 through 2035 are tabulated. Finally, the geodetic paths of the umbral and penumbral shadows of all 109 solar eclipses in this period are plotted on orthographic projection maps of the Earth. Appendices are included which discuss eclipse geometry, eclipse frequency and occurrence, modern eclipse prediction and time determination. Finally, code for a simple Fortran program is given to predict the occurrence and characteristics of solar eclipses.
The present work presents preliminary efforts at a mathematical formulation of a photogrammetric method suitable for computerized processing. A theory is derived for the extraction of surface topography from stereometric pairs of photographs. The theory can be applied to either convergent or near-orthographic-projection stereo. Scene brightness is treated as a scalar function defined on a general surface embedded in ordinary three-dimensional space (the actual topography). Correspondence of points is based on adjustments leading to photometric equivalence, while the adjustments are based on the local value of the photometric gradient.
A computer program that uses a three-dimensional geometric technique for fitting a smooth surface to the component parts of an aircraft configuration is presented. The resulting surface equations are useful in performing various kinds of calculations in which a three-dimensional mathematical description is necessary. Programs options may be used to compute information for three-view and orthographic projections of the configuration as well as cross-section plots at any orientation through the configuration. The aircraft geometry input section of the program may be easily replaced with a surface point description in a different form so that the program could be of use for any three-dimensional surface equations.
Previous radar mappings of the Moon at 70 cm wavelength in the late 1960's by Thompson have been replaced with a new set of observations using the 430 MHz radar at the Arecibo Observatory, Puerto Rico. Radar resolution was reduced to 2 to 5 km radar cell size and a beam-sweep, limb-to-limb calibration was conducted. Advances in computer technology provided the principle means of improving lunar radar mapping at this wavelength. Observation techniques and data processing are described and scattering differences found in the orthographic projection of the radar data are discussed.
Total ozone data taken by the Nimbus-7 Total Ozone Mapping Spectrometer (TOMS) played a central role in the successful outcome of the 1987 Airborne Antarctic Ozone Experiment. The near-real-time TOMS total ozone observations were suppled within hours of real time to the operations center in Punta Arenas, Chile, over a telecommunications network designed specifically for this purpose. The TOMS data preparation and method of transfer over the telecommunications links are reviewed. This atlas includes a complete set of the near-real-time TOMS orbital overpass data over regions around the Palmer Peninsula of Antarctica for the period of August 8 through September 29, 1987. Also provided are daily polar orthographic projections of TOMS total ozone measurements over the Southern Hemisphere from August through November 1987. In addition, a chronology of the salient points of the experiment, along with some latitudinal cross sections and time series at locations of interest of the TOMS total ozone observations are presented. The TOMS total ozone measurements are evaluated along the flight tracks of each of the ER-2 and DC-8 missions during the experiment. The ozone hole is shown here to develop in a monotonic progression throughout late August and September. The minimum total ozone amount was found on 5 October, when its all-time lowest value of 109 DU is recorded. The hole remains well defined, but fills gradually from mid-October through mid-November. The hole's dissolution is observed here to begin in mid-November, when it elongates and begins to rotate. By the end of November, the south pole is no longer located within the ozone hole.
A robot system called RAMBO is being developed. It is equipped with a camera, which, given a sequence of simple tasks, can perform these tasks on a moving object. RAMBO is given a complete geometric model of the object. A low level vision module extracts and groups characteristic features in images of the object. The positions of the object are determined in a sequence of images, and a motion estimate of the object is obtained. This motion estimate is used to plan trajectories of the robot tool to relative locations nearby the object sufficient for achieving the tasks. More specifically, low level vision uses parallel algorithms for image enchancement by symmetric nearest neighbor filtering, edge detection by local gradient operators, and corner extraction by sector filtering. The object pose estimation is a Hough transform method accumulating position hypotheses obtained by matching triples of image features (corners) to triples of model features. To maximize computing speed, the estimate of the position in space of a triple of features is obtained by decomposing its perspective view into a product of rotations and a scaled orthographic projection. This allows the use of 2-D lookup tables at each stage of the decomposition. The position hypotheses for each possible match of model feature triples and image feature triples are calculated in parallel. Trajectory planning combines heuristic and dynamic programming techniques. Then trajectories are created using parametric cubic splines between initial and goal trajectories. All the parallel algorithms run on a Connection Machine CM-2 with 16K processors.
Because of the great environmental significance of ozone and to support continuing research at McMurdo, Syowa, and other Southern Hemisphere stations, the development of the 1988 ozone hole was monitored using data from the Nimbus-7 Total Ozone Mapping Spectrometer (TOMS) instrument, produced in near-real-time. This Atlas provides a complete set of daily polar orthographic projections of the TOMS total ozone measurements over the Southern Hemisphere for the period August 1 through November 17, 1988. Although total ozone in mini-holes briefly dropped below 150 DU in late August, the main ozone hole is seen to be much less pronounced than in 1987. Minimum values, observed in late September and early October 1988, were seldom less than 175 DU. Compared with the same period in 1987, when a pronounced ozone hole whose minimum value of 109 Dobson Units (DU) was the lowest total ozone ever observed, the 1988 ozone hole is displaced from the South Pole, opposing a persistent maximum with values consistently above 500 DU. Daily ozone values above selected Southern Hemisphere stations are presented, along with comparisons of the 1988 ozone distribution to that of other years.
Because of the great environmental significance of ozone and to support continuing research at the Antarctic and other Southern Hemisphere stations, the development of the 1989 ozone hole was monitored using data from the Nimbus-7 Total Ozone Mapping Spectrometer (TOMS) instrument, produced in near-real-time. This Atlas provides a complete set of daily polar orthographic projections of the TOMS total ozone measurements over the Southern Hemisphere for the period August 1 through November 30, 1989. The 1989 ozone hole developed in a manner similar to that of 1987, reaching a comparable depth in early October. This was in sharp contrast to the much weaker hole of 1988. The 1989 ozone hole remained at polar latitudes as it filled in November, in contrast to other recent years when the hole drifted to mid-latitudes before disappearing. Daily ozone values above selected Southern Hemisphere stations are presented, along with comparisons of the 1989 ozone distribution to that of other years.
The U.S. Bureau of Mines is developing a computer model to analyze the human factors aspect of mining machine operator compartments. The model will be used as a research tool and as a design aid. It will have the capability to perform the following: simulated anthropometric or reach assessment, visibility analysis, illumination analysis, structural analysis of the protective canopy, operator fatigue analysis, and computation of an ingress-egress rating. The model will make extensive use of graphics to simplify data input and output. Two dimensional orthographic projections of the machine and its operator compartment are digitized and the data rebuilt into a three dimensional representation of the mining machine. Anthropometric data from either an individual or any size population may be used. The model is intended for use by equipment manufacturers and mining companies during initial design work on new machines. In addition to its use in machine design, the model should prove helpful as an accident investigation tool and for determining the effects of machine modifications made in the field on the critical areas of visibility and control reach ability.
Interaction with tumbling objects will become more common as human activities in space expand. Attempting to interact with a large complex object translating and rotating in space, a human operator using only his visual and mental capacities may not be able to estimate the object motion, plan actions or control those actions. A robot system (RAMBO) equipped with a camera, which, given a sequence of simple tasks, can perform these tasks on a tumbling object, is being developed. RAMBO is given a complete geometric model of the object. A low level vision module extracts and groups characteristic features in images of the object. The positions of the object are determined in a sequence of images, and a motion estimate of the object is obtained. This motion estimate is used to plan trajectories of the robot tool to relative locations rearby the object sufficient for achieving the tasks. More specifically, low level vision uses parallel algorithms for image enhancement by symmetric nearest neighbor filtering, edge detection by local gradient operators, and corner extraction by sector filtering. The object pose estimation is a Hough transform method accumulating position hypotheses obtained by matching triples of image features (corners) to triples of model features. To maximize computing speed, the estimate of the position in space of a triple of features is obtained by decomposing its perspective view into a product of rotations and a scaled orthographic projection. This allows use of 2-D lookup tables at each stage of the decomposition. The position hypotheses for each possible match of model feature triples and image feature triples are calculated in parallel. Trajectory planning combines heuristic and dynamic programming techniques. Then trajectories are created using dynamic interpolations between initial and goal trajectories. All the parallel algorithms run on a Connection Machine CM-2 with 16K processors.