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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 NTRS1993

A formational model for the polygonal terrains of Mars: Taking a crack at the genesis of the Martian polygons

The mechanism for the genesis of the polygonal terrains in Acidalia and Utopia Planitia has long been sought: however, no completely satisfying model was put forth that characterizes the evolution of these complexly patterned terrains. The polygons are roughly hexagonal but some are not entirely enclosed by fractures. These polygonal features range in widths from approximately 5 to 20 km. Several origins were proposed that describe the polygon borders as desiccation cracks, columnar jointing in a cooled lava, or frost-wedge features. These tension-induced cracking hypotheses were addressed by Pechmann, who convincingly disputes these mechanisms of formation based on scale magnitude difficulties and morphology. Pechmann suggests instead that the cracks delineating the 5-20-km-wide polygons on the northern plains of Mars are graben resulting from deep-seated, uniform, horizontal tension. The difficulty with this hypothesis is that no analogous polygonal forms are known to have originated by tectonism on Earth. McGill and Hills propose that the polygonal terrains on Mars resulted from either rapid desiccation of sediments or cooling of volcanics coupled with differential compaction of the material over a buried irregular topographic surface. They suggest that fracturing was enhanced over the areas of positive relief and was suppressed above the topographic lows. McGill and Hills suggest that the spacing of the topographic highs primarily controls the size of the Martian polygons and the physics of the shrinkage process is a secondary concern. Ray et. al. conducted a terrestrial study of patterned ground in periglacial areas of the U.S. to determine the process responsible for polygonal ground formation. They developed a model for polygon formation in which convection of seasonal melt water above a permafrost layer, driven by an unstable density stratification, differentially melts the permafrost interface, causing it to become undulatory.

Wenrich, M. L.↗
NASA NTRS1992

Origin of giant Martian polygons

Extensive areas of the Martian northern plains in Utopia and Acidalia planitiae are characterized by 'polygonal terrane'. Polygonal terrane consists of material cut by complex troughs defining a pattern resembling mudcracks, columnar joints, or frost-wedge polygons on earth. However, the Martian polygons are orders of magnitude larger than these potential earth analogues, leading to severe mechanical difficulties for genetic models based on simple analogy arguments. Plate-bending and finite element models indicate that shrinkage of desiccating sediment or cooling volcanics accompanied by differential compaction over buried topography can account for the stresses responsible for polygon troughs as well as the large size of the polygons. Although trough widths and depths relate primarily to shrinkage, the large scale of the polygonl pattern relates to the spacing between topographic elevations on the surface buried beneath polygonal terrane material. Geological relationships favor a sedimentary origin for polygonal terrane material, but our model is not dependent on the specific genesis. Our analysis also suggests that the polygons must have formed at a geologically rapid rate.

Mcgill, George E.↗
NASA NTRS2003

System and method for the adaptive mapping of matrix data to sets of polygons

A system and method for converting bitmapped data, for example, weather data or thermal imaging data, to polygons is disclosed. The conversion of the data into polygons creates smaller data files. The invention is adaptive in that it allows for a variable degree of fidelity of the polygons. Matrix data is obtained. A color value is obtained. The color value is a variable used in the creation of the polygons. A list of cells to check is determined based on the color value. The list of cells to check is examined in order to determine a boundary list. The boundary list is then examined to determine vertices. The determination of the vertices is based on a prescribed maximum distance. When drawn, the ordered list of vertices create polygons which depict the cell data. The data files which include the vertices for the polygons are much smaller than the corresponding cell data files. The fidelity of the polygon representation can be adjusted by repeating the logic with varying fidelity values to achieve a given maximum file size or a maximum number of vertices per polygon.

Burdon, David↗
NASA NTRS2020

Large-Scale Assessment of Polygon-Edge Boulder Clustering in the Martian Northern Lowlands

Two features evident in many images of the martian northern low-lands are polygonal fractures (especially northwards of 60°N) and meter-scale surface boulders. Since their first observation, several attempts have been made to classify and study these polygons as well as how the forces that form these polygons may modify the surface. Surface boulders have been used as a potential indicator of such modification, though current studies find evidence both for and against their association with the underlying polygons. Both these investigations are limited by the same fundamental challenge: map-ping the location of surface boulders manually is not practical at large scales. Here, we use the Martian Boulder Automatic Recognition System (MBARS) to provide image-wide assessments of boulder location and size, enabling large-scale assessment of boulder populations. To compare these boulder locations with the underlying polygons, we modified the 2-D Fourier analysis described by Orloff in 2013 to analyze boulder locations. When compared with Orloff’s observations of polygon scales, this provides an avenue for large-scale comparison of boulder-cluster scale and polygon scale.

Hood, Don R.↗
NASA NTRS1982

Conversion of raster coded images to polygonal data structures

A method is presented for converting polygons coded in raster data structures into conventional vector structures to allow the output of scanner-based data collection systems to be input directly to conventional geographic information systems. The method relies on topological principles to (1) uniquely label each polygon in the image and produce an output image in which each pixel is described by the label of the polygon to which it belongs; (2) create line segment components of polygon boundaries, with nodes labeled and the two adjacent polygons identified; and (3) traverse the polygon boundaries by connecting the appropriate adjacent line segments. The conversion capability makes it possible to design systems which automatically convert to the data structure most appropriate for a particular application.

Nichols, D. A.↗
NASA NTRS1984

Small-scale polygons on Mars

Polygonal-fracture patterns on the martian surface were discovered on Viking Orbiter images. The polygons are 2-20 km in diameter, much larger than those of known patterned ground on Earth. New observations show, however, that polygons exist on Mars that have diameters similar to those of ice-wedge polygons on Earth (generally a few meters to more than 100 m). Various explanations for the origin of these crustal features are examined; seasonal desiccation and thermal-contraction cracking in ice-rich ground. It is difficult to ascertain whether the polygons are forming today or are relics from the past. The crispness of some crack suggests a recent origin. On the other hand the absence of upturned edges (indicating actively forming ice wedges), the locally disintegrating ground, and a few possible superposed rayed craters indicate that the polygons are not forming at the present.

Lucchitta, B. K.↗
NASA NTRS1993

A model for the origin of Martian polygonal terrain

Extensive areas of the Martian northern plains in Utopia and Acidalia Planitiae are characterized by 'polygonal terrain.' Polygonal terrain consists of material cut by complex troughs defining a pattern resembling mudcracks, columnar joints, or frost-wedge polygons on the Earth. However, the Martian polygons are orders of magnitude larger than these potential Earth analogs, leading to severe mechanical difficulties for genetic models based on simple analogy arguments. Stratigraphic studies show that the polygonally fractured material in Utopia Planitia was deposited on a land surface with significant topography, including scattered knobs and mesas, fragments of ancient crater rims, and fresh younger craters. Sediments or volcanics deposited over topographically irregular surfaces can experience differential compaction producing drape folds. Bending stresses due to these drape folds would be superposed on the pervasive tensile stresses due to desiccation or cooling, such that the probability of fracturing is enhanced above buried topographic highs and suppressed above buried topographic lows. Thus it was proposed that the scale of the Martian polygons is controlled by the spacing of topographic highs on the buried surface rather than by the physics of the shrinkage process.

Mcgill, G. E.↗
NASA NTRS2019

Provably Correct Floating-Point Implementation of a Point-In-Polygon Algorithm

The problem of determining whether or not a point lies inside a given polygon occurs in many applications. In air traffic management concepts, a correct solution to the point-in-polygon problem is critical to geofencing systems for Unmanned Aerial Vehicles and in weather avoidance applications. Many mathematical methods can be used to solve the point-in-polygon problem. Unfortunately, a straightforward floating- point implementation of these methods can lead to incorrect results due to round-off errors. In particular, these errors may cause the control flow of the program to diverge with respect to the ideal real-number algorithm. This divergence potentially results in an incorrect point-in- polygon determination even when the point is far from the edges of the polygon. This paper presents a provably correct implementation of a point-in-polygon method that is based on the computation of the winding number. This implementation is mechanically generated from a source- to-source transformation of the ideal real-number specification of the algorithm. The correctness of this implementation is formally verified within the Frama-C analyzer, where the proof obligations are discharged using the Prototype Verification System (PVS).

Moscato, Mariano M.↗
NASA NTRS1981

Lineament and polygon patterns on Europa

A classification scheme is presented for the lineaments and associated polygonal patterns observed on the surface of Europa, and the frequency distribution of the polygons is discussed in terms of the stress-relief fracturing of the surface. The lineaments are divided on the basis of albedo, morphology, orientation and characteristic geometry into eight groups based on Voyager 2 images taken at a best resolution of 4 km. The lineaments in turn define a system of polygons varying in size from small reticulate patterns the limit of resolution to 1,000,000 sq km individuals. Preliminary analysis of polygon side frequency distributions reveals a class of polygons with statistics similar to those found in complex terrestrial terrains, particularly in areas of well-oriented stresses, a class with similar statistics around the antijovian point, and a class with a distribution similar to those seen in terrestrial tensional fracture patterns. Speculations concerning the processes giving rise to the lineament patterns are presented.

Pieri, D. C.↗
NASA NTRS1985

Origin of Martian Polygonal Terrain: Preliminary Results

The morphological characteristics of Martian polygonal terrain, and of the fractures defining the polygons were reviewed. The age relationships between the fractures defining the polygons and the material making up the polygonal terrain of Adamas Labyrinthus will be determined. This involves detailed mapping, with the relative ages of Key map units and the fractures determined by superposition and crater counts. The common occurrence of circular fracture patterns within the polygonal terrain is consistent with differential compaction over crater rims, and is easily accounted for by the tensile stresses that would be reasonably expected to occur in such places.

Mcgill, G. E.↗
NASA NTRS2002

Mola Topography Supports Drape-Folding Models for Polygonal Terrain of Utopia Planitia, Mars

One of the most important questions we ask about Mars is whether or not there have ever been large bodies of standing water on the surface. The polygonal terrains of Utopia and Acidalia Planitiae are located in the lowest parts of the northern lowlands, the most logical places for water to pond and sediments to accumulate. Showing that polygonal terrain is sedimentary in origin would represent strong evidence in favor of a northern ocean. A number of hypotheses for the origin of the giant martian polygons have been proposed, from the cooling of lava to frost wedging to the desiccation of wet sediments, but Pechman showed that none of these familiar processes could be scaled up to martian dimensions. Two models for polygon origin attempt to explain the scale of the martian polygons by postulating drape folding of a cover material, either sedimentary or volcanic, over an uneven, buried surface. The drape folding would produce bending stresses in the surface layers that increase the probability of Fracturing over drape anticlines and suppress the probability of fracturing over drape synclines. However, both models require an additional source of extensional strain to produce the total strain needed to produce the observed troughs.

McGill, George E.↗
NASA NTRS2017

Map Projection Induced Variations in Locations of Polygon Geofence Edges

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.

Neeley, Paula↗
NASA NTRS1984

Classical free-streamline flow over a polygonal obstacle

In classical Kirchhoff flow, an ideal incompressible fluid flows past an obstacle and around a motionless wake bounded by free streamlines. Since 1869 it has been known that in principle, the two-dimensional Kirchhoff flow over a polygonal obstacle can be determined by constructing a conformal map onto a polygon in the log-hodograph plane. In practice, however, this idea has rarely been put to use except for very simple obstacles, because the conformal mapping problem has been too difficult. This paper presents a practical method for computing flows over arbitrary polygonal obstacles to high accuracy in a few seconds of computer time. We achieve this high speed and flexibility by working with a modified Schwarz-Christoffel integral that maps onto the flow region directly rather than onto the log-hodograph polygon. This integral and its associated parameter problem are treated numerically by methods developed earlier by Trefethen for standard Schwarz-Christoffel maps.

Elcrat, A. R.↗
NASA NTRS1986

Classical free-streamline flow over a polygonal obstacle

In classical Kirchhoff flow, an ideal incompressible fluid flows past an obstacle and around a motionless wake bounded by free streamlines. Since 1869 it has been known that in principle, the two-dimensional Kirchhoff flow over a polygonal obstacle can be determined by constructing a conformal map onto a polygon in the log-hodograph plane. In practice, however, this idea has rarely been put to use except for very simple obstacles, because the conformal mapping problem has been too difficult. This paper presents a practical method for computing flows over arbitrary polygonal obstacles to high accuracy in a few seconds of computer time. We achieve this high speed and flexibility by working with a modified Schwarz-Christoffel integral that maps onto the flow region directly rather than onto the log-hodograph polygon. This integral and its associated parameter problem are treated numerically by methods developed earlier by Trefethen for standard Schwarz-Christoffel maps.

Elcrat, A. R.↗
NASA NTRS1986

A computational method to model radar return range in a polygonally based, computer-generated-imagery simulation

Described is a method for modeling a ground-mapping radar system for use in simulations where the terrain is in a polygonal form commonly used with computer generated imagery (CGI). The method employs a unique approach for rapidly rejecting polygons not visible to the radar to facilitate the real-time simulation of the radar return. This rapid rejection of the nonvisible polygons requires the precalculation and storage of a set of parameters that do not vary during the simulation. The calculation of a radar range as a function of the radar forward-looking angle to the CGI terrain is carried out only for the visible polygons. This method was used as part of a simulation for terrain-following helicopter operations on the vertical motion simulator at the NASA Ames Research Center. It proved to be an efficient means for returning real-time simulated radar range data.

Moran, F. J.↗
NASA NTRS2003

Global Characterization of Polygonally Fractured Terrain on Venus and Implications for a Climate Change Origin

On Earth, polygonal fractures with spacings of 1-100 cm form in lava flows that cool slowly under isotropic stress conditions. On Venus, polygonal fractures are observed with typical fracture spacings of 1-2 km, covering regions 10s to 100s of km across. These features have been proposed to form via cooling of lava flows or above subsurface intrusions, or due to surface cooling caused by climate change. A watershed algorithm was modified to search the entire Magellan image database autonomously for terrains with polygonal fractures. Here we characterize the 204 polygon terrains found using this method (including over 170 newly identified regions) with respect to size, morphology, stratigraphy, and geologic setting. These results are used to examine different models of origin.

Smrekar, S. E.↗
NASA NTRS2007

Some algorithms for polygons on a sphere.

A limited search for polygon algorithms for use in a new military training simulation that interfaces with several others produced only planar algorithms. To avoid having to implement several different sophisticated map projections to guarantee compatibility with all the other simulations, we opted to develop algorithms that work directly on a sphere. The first is an algorithm to compute the area of a polygon whose edges are segments of great circles. Since our model represents certain object locations as mathematical points, the second topic is whether a specified point is inside a specified polygon. Possibly pathological cases are identified and eliminated. When we realized that most political boundaries are actually rhumb lines, use of the Mercator projection equations seemed unavoidable. We then reasoned that if all the edges were short enough, lat-lon lines, great circle segments, and rhumb lines would be close enough to being identical that we could use whichever was most convenient. Thence, we looked at the relationship between the maximum distances between great circle segments and rhumb lines and between lat-lon lines and rhumb lines as functions of length, azimuth, and latitude. The final algorithm finds the area overlapped by two polygons. Again, potentially pathological cases are identified and eliminated.

Duquette, William H.↗
NASA NTRS2000

Small-Scale Polygons and the History of Ground Ice on Mars

This research has laid a foundation for continued study of permafrost polygons on Mars using the models and understanding discussed here. Further study of polygonal patterns on Mars is proceeding (under new funding) which is expected to reveal more results about the origin of observed martian polygons and what information they contain regarding the recent history of tile martian climate and of water ice on Mars.

Mellon, Michael T.↗