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Morphometrics of polygonal ground on Earth and Mars: Assessing formation mechanisms from orbit
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Limits on polygonal organization of boulders in the Martian northern lowlands
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Shape and Symmetry Determine Two-Dimensional Melting Transitions of Hard Regular Polygons
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Exposed Ice in the Northern Mid-Latitudes of Mars
Ice-Rich Layer: Polygonal features with dimensions of approximately 100 meters, bounded by cracks, are commonly observed on the martian northern plains. These features are generally attributed to thermal cracking of ice-rich sediments, in direct analogy to polygons in terrestrial polar regions. We mapped polygons in the northern mid-latitudes (30 to 65 N) using MOC and HiRISE images. Polygons are scattered across the northern plains, with a particular concentration in western Utopia Planitia. This region largely overlaps the Late Amazonian Astapus Colles unit, characterized by polygonal terrain and nested pits consistent with periglacial and thermokarst origins. Bright and Dark Polygonal Cracks: An examination of all MOC images (1997 through 2003) covering the study area demonstrated that, at latitudes of 55 to 65 N, most of the imaged polygons show bright bounding cracks. We interpret these bright cracks as exposed ice. Between 40 and 55 N, most of the imaged polygons show dark bounding cracks. These are interpreted as polygons from which the exposed ice has been removed by sublimation. The long-term stability limit for exposed ice, even in deep cracks, apparently lies near 55 N. Bright and Dark Spots: Many HiRISE and MOC frames showing polygons in the northern plains also show small numbers of bright and dark spots, particularly in western Utopia Planitia. Many of the spots are closely associated with collapse features suggestive of thermokarst. The spots range from tens to approximately 100 meters in diameter. The bright spots are interpreted as exposed ice, due to their prevalence on terrain mapped as ice rich. The dark spots are interpreted as former bright spots, which have darkened as the exposed ice is lost by sublimation. The bright spots may be the martian equivalents of pingos, ice-cored mounds found in periglacial regions on Earth. Terrestrial pingos from which the ice core has melted often collapse to form depressions similar to the martian dark spots. Future Observations: The SHARAD radar should be able to confirm the presence and measure the depth of the interpreted ice-rich layer that forms the Astapus Colles unit. If this layer is confirmed it will strengthen the interpretation of bright polygon cracks and bright spots as exposed ice. HiRISE images of the northern plains are showing unprecedented details of the polygonal cracks. Future HiRISE images that include bright spots, compared to MOC images taken years earlier, will illustrate the temporal stability of the spots. The CRISM spectrometer, with multiple spectral bands and a spatial resolution around 20 meters, should allow mineralogical identification of the material exposed in the polygonal bounding cracks and in the bright spots.
Generating a Simulated Fluid Flow Over an Aircraft Surface Using Anisotropic Diffusion
A fluid-flow simulation over a computer-generated aircraft surface is generated using a diffusion technique. The surface is comprised of a surface mesh of polygons. A boundary-layer fluid property is obtained for a subset of the polygons of the surface mesh. A pressure-gradient vector is determined for a selected polygon, the selected polygon belonging to the surface mesh but not one of the subset of polygons. A maximum and minimum diffusion rate is determined along directions determined using a pressure gradient vector corresponding to the selected polygon. A diffusion-path vector is defined between a point in the selected polygon and a neighboring point in a neighboring polygon. An updated fluid property is determined for the selected polygon using a variable diffusion rate, the variable diffusion rate based on the minimum diffusion rate, maximum diffusion rate, and angular difference between the diffusion-path vector and the pressure-gradient vector.
Generating a Simulated Fluid Flow over a Surface Using Anisotropic Diffusion
A fluid-flow simulation over a computer-generated surface is generated using a diffusion technique. The surface is comprised of a surface mesh of polygons. A boundary-layer fluid property is obtained for a subset of the polygons of the surface mesh. A gradient vector is determined for a selected polygon, the selected polygon belonging to the surface mesh but not one of the subset of polygons. A maximum and minimum diffusion rate is determined along directions determined using the gradient vector corresponding to the selected polygon. A diffusion-path vector is defined between a point in the selected polygon and a neighboring point in a neighboring polygon. An updated fluid property is determined for the selected polygon using a variable diffusion rate, the variable diffusion rate based on the minimum diffusion rate, maximum diffusion rate, and the gradient vector.
New Support for Hypotheses of an Ancient Ocean on Mars
A new analog for the giant polygons in the Chryse-Acidalia area suggests that those features may have formed in a major body of water - likely a Late Hesperian to Early Amazonian ocean. This analog -terrestrial polygons in subsea, passive margin basins derives from 3D seismic data that show similar-scale, polygonal fault systems in the subsurface of more than 50 terrestrial offshore basins. The terrestrial and martian polygons share similar sizes, basin-wide distributions, tectonic settings, and association with expected fine-grained sediments. Late Hesperian deposition from outflow floods may have triggered formation of these polygons, by providing thick, rapidly-deposited, fine-grained sediments necessary for polygonal fracturing. The restriction of densely occurring polygons to elevations below approx. -4000 m to -4100 m supports inferences that a body of water controlled their formation. Those same elevations appear to restrict occurrence of polygons in Utopia Planitia, suggesting that this analog may apply also to Utopia and that similar processes may have occurred across the martian lowlands.
Martian Oceans: Old Debate - New Insights
The possibility of an ancient ocean in the northern lowlands of Mars has been discussed for decades [1-14], but the subject remains controversial [15-20]. Among the many unique features of the northern lowlands is the extensive development of "giant polygons" - polygonal landforms that range from 1 to 20 km across. The kilometer-scale size of these features distinguishes them from a variety of smaller polygons (usually < 250 m) on Mars that have been compared to terrestrial analogs such as ice-wedge and desiccation features. However, until recently, geologists were aware of no examples of polygons on Earth comparable in scale to the giant polygons of Mars, so there were no good analogs from which to draw interpretations. That picture has changed with 3D seismic data acquired by the petroleum industry in exploration of offshore basins. The new data reveal kilometer-scale polygonal features in more than 50 offshore basins on Earth]. These features provide a credible analog for the giant polygons of Mars.
Computer-aided design file format for additive manufacturing and methods of file generation
A method of generating a tessellated output file comprising receiving a computer-aided design (CAD) model file defining a CAD model including a plurality of vertices, a plurality of curves, a plurality of surfaces, and at least one volume; generating base polygon data defining the CAD model for additive manufacturing, the base polygon data including a plurality of connected polygons, each polygon including a plurality of nodes, a plurality of edges, and a face; generating data for a vertex metadata container including a listing of CAD model vertices and one polygon node associated with each CAD model vertex; generating data for a curve metadata container including a listing of CAD model curves and at least one polygon edge associated with each CAD model curve; and generating data for a surface metadata container including a listing of CAD model surfaces and at least one polygon face associated with each CAD model surface.
Computer-aided design file format for additive manufacturing and methods of file generation
A tessellated output file format describing a computer-aided design (CAD) model including a plurality of vertices, a plurality of curves, a plurality of surfaces, and at least one volume, the tessellated output file format comprising base polygon data, a vertex metadata container, a curve metadata container, and a surface metadata container. The base polygon data defines the CAD model for additive manufacturing and includes a plurality of connected polygons, each polygon including a plurality of nodes, a plurality of edges, and a face. The vertex metadata container includes a listing of CAD model vertices and one polygon node associated with each CAD model vertex. The curve metadata container includes a listing of CAD model curves and at least one polygon edge associated with each CAD model curve. The surface metadata container includes a listing of CAD model surfaces and at least one polygon face associated with each CAD model surface.
Toroidal Single Wall Carbon Nanotubes in Fullerene Crop Circles
We investigate energetics and structure of circular and polygonal single wall carbon nanotubes (SWNTs) using large scale molecular simulations on NAS SP2, motivated by their unusual electronic and magnetic properties. The circular tori are formed by bending tube (no net whereas the polygonal tori are constructed by turning the joint of two tubes of (n, n), (n+1, n-1) and (n+2, n-2) with topological pentagon-heptagon defect, in which n =5, 8 and 10. The strain energy of circular tori relative to straight tube decreases by I/D(sup 2) where D is torus diameter. As D increases, these tori change from buckling to an energetically stable state. The stable tori are perfect circular in both toroidal and tubular geometry with strain less than 0. 03 eV/atom when D greater than 10, 20 and 40 nm for torus (5,5), (8,8) and (10, 10). Polygonal tori, whose strain is proportional to the number of defects and I/D are energetically stable even for D less than 10 nm. However, their strain is higher than that of perfect circular tori. In addition, the local maximum strain of polygonal tori is much higher than that of perfect circular tori. It is approx. 0.03 eV/atom or less for perfect circular torus (5,5), but 0.13 and 0.21 eV/atom for polygonal tori (6,4)/(5,5) and (7,3)/(5,5). Therefore, we conclude that the circular tori with no topological defects are more energetically stable and kinetically accessible than the polygonal tori containing the pentagon-heptagon defects for the laser-grown SWNTs and Fullerene crop circles.
Boundary to Constructive Solid Geometry Mappings: a Focus on 2-D Issues
The problem of converting boundary representation (B-rep) to constructive solid geometry representation (CSG-rep) (and vice versa) is discussed in two phases. The first phase entails finding a CSG-rep that defines the region bounded by a polygonal profile curve. The second phase utilizes the results of the first phase to find a CSG-rep for many non-polygonal profile curves. A mathematically concise representation of a region bounded by a polygonal is presented. Namely, any polygonal region bounded by an n sided polygon may be represented by a binary tree which has at most n planar halfspaces as leaves. A structure for this representation and an algorithm for calculating is discussed.
Binary space partitioning trees and their uses
Binary Space Partitioning (BSP) trees have some qualities that make them useful in solving many graphics related problems. The purpose is to describe what a BSP tree is, and how it can be used to solve the problem of hidden surface removal, and constructive solid geometry. The BSP tree is based on the idea that a plane acting as a divider subdivides space into two parts with one being on the positive side and the other on the negative. A polygonal solid is then represented as the volume defined by the collective interior half spaces of the solid's bounding surfaces. The nature of how the tree is organized lends itself well for sorting polygons relative to an arbitrary point in 3 space. The speed at which the tree can be traversed for depth sorting is fast enough to provide hidden surface removal at interactive speeds. The fact that a BSP tree actually represents a polygonal solid as a bounded volume also makes it quite useful in performing the boolean operations used in constructive solid geometry. Due to the nature of the BSP tree, polygons can be classified as they are subdivided. The ability to classify polygons as they are subdivided can enhance the simplicity of implementing constructive solid geometry.
Prospecting for Martian Ice from Orbit
Recent data from the Gamma-Ray Spectrometer (GRS) on Mars Odyssey indicate the presence of a hydrogen-rich layer tens of centimeters thick in high latitudes on Mars. This hydrogen-rich layer correlates to previously determined regions of ice stability. It has been suggested that the subsurface hydrogen is ice and constitutes 35 plus or minus 15% by weight near the north and south polar regions. This study constrains the location of subsurface ice deposits on the scale of kilometers or smaller by combining GRS data with surface features indicative of subsurface ice. The most recognizable terrestrial geomorphic indicators of subsurface ice, formed in permafrost and periglacial environments, include thermokarst pits, pingos, pseudocraters and patterned ground. Patterned ground features have geometric forms such as circles, polygons, stripes and nets. This study focuses on the polygonal form of patterned ground, selected for its discernable shape and subsurface implications. Polygonal features are typically demarcated by troughs, beneath which grow vertical ice-wedges. Ice-wedges form in thermal contraction cracks in ice-rich soil and grow with annual freezing and thawing events repeated over tens of years. Ice wedges exist below the depth of seasonal freeze-thaw. Terrestrial ice wedges can be several meters deep and polygons can be tens of meters apart, and, on rare occasions, up to 1 km. The crack spacing of terrestrial polygons is typically 3 to 10 times the crack depth.
Integration of Weather Avoidance and Traffic Separation
This paper describes a dynamic convective weather avoidance concept that compensates for weather motion uncertainties; the integration of this weather avoidance concept into a prototype 4-D trajectory-based Airborne Separation Assurance System (ASAS) application; and test results from a batch (non-piloted) simulation of the integrated application with high traffic densities and a dynamic convective weather model. The weather model can simulate a number of pseudo-random hazardous weather patterns, such as slow- or fast-moving cells and opening or closing weather gaps, and also allows for modeling of onboard weather radar limitations in range and azimuth. The weather avoidance concept employs nested "core" and "avoid" polygons around convective weather cells, and the simulations assess the effectiveness of various avoid polygon sizes in the presence of different weather patterns, using traffic scenarios representing approximately two times the current traffic density in en-route airspace. Results from the simulation experiment show that the weather avoidance concept is effective over a wide range of weather patterns and cell speeds. Avoid polygons that are only 2-3 miles larger than their core polygons are sufficient to account for weather uncertainties in almost all cases, and traffic separation performance does not appear to degrade with the addition of weather polygon avoidance. Additional "lessons learned" from the batch simulation study are discussed in the paper, along with insights for improving the weather avoidance concept. Introduction