Too kink to be square? mapping satellite polygon footprints onto regular grids by tessellation
UNKNOWN
Kurosu, Thomas P.↗
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Results for “tessellation”
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Alternatives to Contour Visualizations for Power Systems Data
Electrical grids are geographical and topological structures whose voltage states are challenging to represent accurately and efficiently for visual analysis. The current common practice is to use colored contour maps, yet these can misrepresent the data. We examine the suitability of four alternative visualization methods for depicting voltage data in a geographically dense distribution system - Voronoi polygons, H3 tessellations, S2 tessellations, and a network-weighted contour map. We find that Voronoi tessellations and network-weighted contour maps more accurately represent the statistical distribution of the data than regular contour maps.
MATHEMATICS AND COMPUTING,POWER TRANSMISSION AND D↗
Alternatives to Contour Visualizations for Power Systems Data
Electrical grids are geographical and topological structures whose voltage states are challenging to represent accurately and efficiently for visual analysis. The current common practice is to use colored contour maps, yet these can misrepresent the data. We examine the suitability of four alternative visualization methods for depicting voltage data in a geographically dense distribution system-Voronoi polygons, H3 tessellations, S2 tessellations, and a network-weighted contour map. We find that Voronoi tessellations and network-weighted contour maps more accurately represent the statistical distribution of the data than regular contour maps.
MATHEMATICS AND COMPUTING↗
Generalised Primal-Dual Grids for Unstructured Co-Volume Schemes
The generation of high-quality staggered unstructured grids is considered, leading to the development of a new optimisation-based strategy designed to construct weighted 'Regular-Power' tessellations appropriate for co-volume type numerical discretisation techniques. This new framework aims to extend the conventional Delaunay-Voronoi primal-dual structure; seeking to assemble generalised orthogonal tessellations with enhanced geometric quality. The construction of these grids is motivated by the desire to improve the performance and accuracy of numerical methods based on unstructured co-volume type schemes, including various staggered grid techniques for the simulation of fluid dynamics and hyperbolic transport. In this study, a new hybrid optimisation strategy is proposed; seeking to optimise the geometry, topology and weights associated with general, two-dimensional Regular-Power tessellations using a combination of gradient-ascent and energy-based techniques. The performance of this new method is tested experimentally, with a range of complex, multi-resolution primal-dual grids generated for various coastal and regional ocean modelling applications.
power diagrams↗
Innovative Features of NASA's Celestial Mapping System to Support Exploration in the Lunar South Pole
Introduction: NASA's Celestial Mapping System (CMS) is developed to address the need for 3D tools for planetary science investigations, mission planning, in-situ operations, in a 3D-first design constructed around a unified view of a planetary globe. At present CMS provides many critical functionalities that include 1) Equipment planning and optimized placement on Lunar surface 2) Line of sight (visibility ) analysis 3) Powerful measurement tools based on 3D terrain with realistic 3D models to represent rovers, astronauts and equipment 4) Visualization of de-rived mapping products (e.g. resource maps), and 5) Data engine for hosting new observations that are not available in other contemporary lunar data tools. CMS is built on the foundation of powerful NASA WorldWind globe engines. In near future, users will be able to simultaneously deploy CMS onto multiple hardware configurations and platforms such as Windows, Linux, iOS and Android. The users will also have the flexibility to update to the latest imagery and terrain datasets as they are being acquired (in real time) before and/or during the exploration mission. CMS is also capable of consumption and analysis of data from locally hosted and external sources. It supports Open Geospatial Consorti-um (OGC) data and file standards, with current integrations of datasets from the Astrogeology Science Center of USGS which include global and local data acquired from NASA (LRO, Clementine, Lunar Orbiter) and JAXA (SELENE/Kaguya) with the capability of integrating more datasets. With development experience in both the end-user application and planetary engine side, CMS is also able to adapt to newer Lunar cartography standards as they develop and become recognized by international geospatial panels. Overcoming Polar Distortions: 3D geospatial applications traditionally suffer from significant distortion of imagery at the poles due to following reasons – 1) distortions in the source imagery 2) Incompatible tessellation algorithm on the poles 3) map projections. In the lunar context, with the focus on the South pole, this is not acceptable. The CMS team is researching ways to address polar distortion of imagery with new tessellation algorithms and by reprojecting the data using projections that are more accurate in polar scenarios. Figure1 shows the potential error introduced by different tessellation methods, represented by the red and green circles for Shoemaker crater. There is ~2 Km difference in the placement of the crater. Line of Sight Analysis and Traverse Planning: We have developed a built-in line of sight analysis (LOS) tool in CMS that analyzes the terrain profile and obstructions and provides the visibility of a given terrain for a remote observer. Figure 2 shows the viewshed analysis on the PSR in Nobile region. The PSR was created with help of HORUS generated images. The yellow pin shows the observer location outside the PSR. The yellow area shows the visible part of PSR. The obstructed area with no visibility for the observer is shown in red. This analysis was ex-tended further to set different heights for various observers and then perform the viewshed analysis. Combining the different visibility profiles can help designing improved traverses within the crater.
Geospatial Mapping↗
Innovative Features of NASA's Celestial Mapping System to Support Exploration in the Lunar South Pole
Introduction: NASA's Celestial Mapping System (CMS) is developed to address the need for 3D tools for planetary science investigations, mission planning, in-situ operations, in a 3D-first design constructed around a unified view of a planetary globe. At present CMS provides many critical functionalities that include 1) Equipment planning and optimized placement on Lunar surface 2) Line of sight (visibility ) analysis 3) Powerful measurement tools based on 3D terrain with realistic 3D models to represent rovers, astronauts and equipment 4) Visualization of de-rived mapping products (e.g. resource maps), and 5) Data engine for hosting new observations that are not available in other contemporary lunar data tools. CMS is built on the foundation of powerful NASA WorldWind globe engines. In near future, users will be able to simultaneously deploy CMS onto multiple hardware configurations and platforms such as Windows, Linux, iOS and Android. The users will also have the flexibility to update to the latest imagery and terrain datasets as they are being acquired (in real time) before and/or during the exploration mission. CMS is also capable of consumption and analysis of data from locally hosted and external sources. It supports Open Geospatial Consorti-um (OGC) data and file standards, with current integrations of datasets from the Astrogeology Science Center of USGS which include global and local data acquired from NASA (LRO, Clementine, Lunar Orbiter) and JAXA (SELENE/Kaguya) with the capability of integrating more datasets. With development experience in both the end-user application and planetary engine side, CMS is also able to adapt to newer Lunar cartography standards as they develop and become recognized by international geospatial panels. Overcoming Polar Distortions: 3D geospatial applications traditionally suffer from significant distortion of imagery at the poles due to following reasons – 1) distortions in the source imagery 2) Incompatible tessellation algorithm on the poles 3) map projections. In the lunar context, with the focus on the South pole, this is not acceptable. The CMS team is researching ways to address polar distortion of imagery with new tessellation algorithms and by reprojecting the data using projections that are more accurate in polar scenarios. Figure1 shows the potential error introduced by different tessellation methods, represented by the red and green circles for Shoemaker crater. There is ~2 Km difference in the placement of the crater. Line of Sight Analysis and Traverse Planning: We have developed a built-in line of sight analysis (LOS) tool in CMS that analyzes the terrain profile and obstructions and provides the visibility of a given terrain for a remote observer. Figure 2 shows the viewshed analysis on the PSR in Nobile region. The PSR was created with help of HORUS generated images. The yellow pin shows the observer location outside the PSR. The yellow area shows the visible part of PSR. The obstructed area with no visibility for the observer is shown in red. This analysis was ex-tended further to set different heights for various observers and then perform the viewshed analysis. Combining the different visibility profiles can help designing improved traverses within the crater.
Geospatial Mapping↗
Particle transport in Markov stochastic mixtures with spatial gradients
Markov geometries are a prototype class of stochastic media that are widely used to model complex disordered systems. In a series of recent works, we have shown that spatially homogeneous (but possibly non-isotropic) Poisson tessellations can be conveniently used in order to generate three-dimensional realizations of Markov media and thus characterize the features of particle transport e.g. in fragmented fuel elements following severe nuclear accidents or Rayleigh-Taylor turbulent mixing for inertial confinement fusion. In this paper we show that Poisson tessellations can be extended to take into account the presence of spatial gradients, which commonly occur in real-world applications due to material stratification. For this purpose, we will provide an explicit construction of spatially-non-homogeneous Poisson tessellations, fully characterize their statistical properties, and finally illustrate the behaviour of particle transport in such random media. (authors)
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
The Area Localized Coupled Model for Analytical Mean Flow Prediction in Arbitrary Wind Farm Geometries
This work introduces the area localized coupled (ALC) model, which extends the applicability of approaches that couple classical wake superposition models and atmospheric boundary layer models to wind farms with arbitrary layouts. Coupling wake and top–down boundary layer models is particularly challenging since the latter requires averaging over planform areas associated with turbine-specific regions of the flow that need to be specified. The ALC model uses Voronoi tessellation to define this local area around each turbine. A top–down description of a developing internal boundary layer is then applied over Voronoi cells upstream of each turbine to estimate the local mean velocity profile. Coupling between the velocity at hub-height based on this localized top–down model and a wake model is achieved by enforcing a minimum least-square-error in mean velocity in each cell. The wake model in the present implementation takes into account variations in wind farm inflow velocity and represents the wake profile behind each turbine as a super-Gaussian function that smoothly transitions between a top-hat shape in the region immediately following the turbine to a Gaussian profile downstream. Detailed comparisons to large-eddy simulation (LES) data from two different wind farms demonstrate the efficacy of the model in accurately predicting both wind farm power output and local turbine hub-height velocity for different wind farm geometries. These validations using data generated from two different LES codes demonstrate the model's versatility with respect to capturing results from different simulation setups and wind farm configurations.
49 EE - Wind and Water Power Program - Wind (EE-4W↗
Improved honeycomb and hyperhoneycomb lattice Hamiltonians for quantum simulations of non-Abelian gauge theories
Improved Kogut-Susskind Hamiltonians for quantum simulations of non-Abelian Yang-Mills gauge theories are developed for honeycomb (2+1D) and hyperhoneycomb (3+1D) spatial tessellations. This is motivated by the desire to identify lattices for quantum simulations that involve only 3-link vertices among the gauge field group spaces in order to reduce the complexity in applications of the plaquette operator. For the honeycomb lattice, we derive a classically 𝒪(𝑏 2 )-improved Hamiltonian, with 𝑏 being the lattice spacing. Tadpole improvement via the mean-field value of the plaquette operator is used to provide the corresponding quantum improvements. We have identified the (nonchiral) hyperhoneycomb as a candidate spatial tessellation for 3+1D quantum simulations of gauge theories, and determined the associated 𝒪(𝑏)-improved Hamiltonian.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Voronoi cell analysis: The shapes of particle systems
Many physical systems can be studied as collections of particles embedded in space, often evolving in time. Natural questions arise concerning how to characterize these arrangements—are they ordered or disordered? If they are ordered, how are they ordered and what kinds of defects do they possess? Voronoi tessellations, originally introduced to study problems in pure mathematics, have become a powerful and versatile tool for analyzing countless problems in pure and applied physics. Here we explain the basics of Voronoi tessellations and the shapes that they produce and describe how they can be used to characterize many physical systems.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
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.↗
Quantitative characterization of spatial distribution of particles in materials: Application to materials processing
Most engineering materials contain second phase particles or fibers which serve to reinforce the matrix phase. The effect of reinforcements on material properties is usually analyzed in terms of the average volume fraction and spacing of reinforcements, quantities which are global microstructural characteristics. However, material properties can also depend on local microstructural characteristics; for example, on how uniformly the reinforcing phase is distributed in the material. The analysis method will then be applied to a materials processing problem to discover how processing parameters can be selected to maximize redistribution of the reinforcing phase during processing. Several mathematical analysis methods could be adapted to the problem of characterizing the distribution of particles in materials. A tessellation-based method was selected. In the first phase of the investigation, a software package was written to automate the analysis. Typical results are shown. The analysis technique allows the degree to which particles are clustered together, the size and spacing of particle clusters, and the particle density in clusters to be found. The analysis methods were applied to computer-generated distributions and to a few real particle-containing materials. Methods for analyzing a nonuniform particle distribution in a material can be applied to two broad classes of materials science problems: understanding how the resulting particle distribution affects properties. The analysis method described is applied to a materials processing problem: how to select extrusion conditions to maximize the redistribution of reinforcing particles that are initially nonuniformly distributed. In addition, the tessellation-based method to analyze star distributions in spiral galaxies was adapted, illustrating the diverse types of problems to which the analysis method can be applied.
Parse, J. B.↗
An overview of the Kennedy Space Center robotics program
The KSC program has the ability to prove the soundness of a particular robotic concept on the ground before it is used in space. In this context, three (3) robotic systems are discussed: the tile robot (Tessellator); HFIR (High Efficiency Particulate Air (HEPA) Filter Inspection Robot); and ARID (Automatic Radiator Inspection Project). The Tessellator is a semi-autonomous robotic system used to rewaterproof and inspect thermal protection system tiles on the underside of the orbiter. The HFIR is used for autonomous inspection of HEPA filters located at the top of the LC 39 payload changeout rooms. The ARID is designed for autonomous inspection of orbiter radiators for damage while in the orbiter processing facility.
Rhodes, Eric L.↗
Unstructured 3D Delaunay mesh generation applied to planes, trains and automobiles
Technical issues associated with domain-tessellation production, including initial boundary node triangulation and volume mesh refinement, are presented for the 'TGrid' 3D Delaunay unstructured grid generation program. The approach employed is noted to be capable of preserving predefined triangular surface facets in the final tessellation. The capabilities of the approach are demonstrated by generating grids about an entire fighter aircraft configuration, a train, and a wind tunnel model of an automobile.
Blake, Kenneth R.↗
Watertight Anisotropic Surface Meshing Using Quadrilateral Patches
This paper presents a simple technique for generating anisotropic surface triangulations using unstructured quadrilaterals when the CAD entity can be mapped to a logical rectangle. Watertightness and geometric quality measures are maintained and are consistent with the CAPRI default tessellator. These triangulations can match user specified criteria for chord-height tolerance, neighbor triangle dihedral angle, and maximum triangle side length. This discrete representation has hooks back to the owning geometry and therefore can be used in conjunction with these entities to allow for easy enhancement or modification of the tessellation suitable for grid generation or other downstream applications.
Haimes, Robert↗
Component Fixturing Method
An end-configuration of components to be moved or positioned is first obtained. This end-configuration determines the relative positioning and orientation of the components with respect to each other when in a final, desired configuration. A folding pattern is then obtained that is formed by interior vertices defining corresponding tessellation facets. The folding pattern can be induced to transition from a first folded configuration to a second folded configuration. When in the second folded configuration mounting facets, which are a subset of the tessellation facets, are arranged by the geometry of the folding pattern into positions and orientations with respect to each other that correspond to the end-configuration of the components. A foldable structure is then obtained that folds in accordance with the folding pattern, and the components are affixed to their respective mounting facets.
Kling, Daniel↗
Three Dimensional Surface Redefinition Method for Computational Ice Accretion Solvers
Computational tools have been increasing in maturity and are thus commonly used in the engineering design process. Advancements in NASA’s current state of the art computational ice accretion tool are required to tackle the icing challenges of tomorrow. GlennICE, a next generation ice accretion solver, is under development at NASA to tackle these challenges. One of the elements of this migration is transitioning from a quasi-three dimensional strip theory based ice accretion methodology to a fully three dimensional methodology. This requires construction of a method to redefine or extrude a discretized or tessellated surface geometry based on the predicted volumetric ice growth for each tessellated surface triangle. This paper describes the methodology that is employed in the GlennICE software, and assesses the performance of the method in replicating a well defined analytical test case.
Computational↗
Three Dimensional Surface Redefinition Method for Computational Ice Accretion Solvers
Computational tools have been increasing in maturity and are thus commonly used in the engineering design process. Advancements in NASA’s current state of the art computational ice accretion tool are required to tackle the icing challenges of tomorrow. GlennICE, a next generation ice accretion solver, is under development at NASA to tackle these challenges. One of the elements of this migration is transitioning from a quasi-three dimensional strip theory based ice accretion methodology to a fully three dimensional methodology. This requires construction of a method to redefine or extrude a discretized or tessellated surface geometry based on the predicted volumetric ice growth for each tessellated surface triangle. This paper describes the methodology that is employed in the GlennICE software, and assesses the performance of the method in replicating a well definied analytical test case.
Computational↗