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NASA NTRS2010

ICER-3D Hyperspectral Image Compression Software

Software has been developed to implement the ICER-3D algorithm. ICER-3D effects progressive, three-dimensional (3D), wavelet-based compression of hyperspectral images. If a compressed data stream is truncated, the progressive nature of the algorithm enables reconstruction of hyperspectral data at fidelity commensurate with the given data volume. The ICER-3D software is capable of providing either lossless or lossy compression, and incorporates an error-containment scheme to limit the effects of data loss during transmission. The compression algorithm, which was derived from the ICER image compression algorithm, includes wavelet-transform, context-modeling, and entropy coding subalgorithms. The 3D wavelet decomposition structure used by ICER-3D exploits correlations in all three dimensions of sets of hyperspectral image data, while facilitating elimination of spectral ringing artifacts, using a technique summarized in "Improving 3D Wavelet-Based Compression of Spectral Images" (NPO-41381), NASA Tech Briefs, Vol. 33, No. 3 (March 2009), page 7a. Correlation is further exploited by a context-modeling subalgorithm, which exploits spectral dependencies in the wavelet-transformed hyperspectral data, using an algorithm that is summarized in "Context Modeler for Wavelet Compression of Hyperspectral Images" (NPO-43239), which follows this article. An important feature of ICER-3D is a scheme for limiting the adverse effects of loss of data during transmission. In this scheme, as in the similar scheme used by ICER, the spatial-frequency domain is partitioned into rectangular error-containment regions. In ICER-3D, the partitions extend through all the wavelength bands. The data in each partition are compressed independently of those in the other partitions, so that loss or corruption of data from any partition does not affect the other partitions. Furthermore, because compression is progressive within each partition, when data are lost, any data from that partition received prior to the loss can be used to reconstruct that partition at lower fidelity. By virtue of the compression improvement it achieves relative to previous means of onboard data compression, this software enables (1) increased return of hyperspectral scientific data in the presence of limits on the rates of transmission of data from spacecraft to Earth via radio communication links and/or (2) reduction in spacecraft radio-communication power and/or cost through reduction in the amounts of data required to be downlinked and stored onboard prior to downlink. The software is also suitable for compressing hyperspectral images for ground storage or archival purposes.

Xie, Hua↗
NASA NTRS2010

Context Modeler for Wavelet Compression of Spectral Hyperspectral Images

A context-modeling sub-algorithm has been developed as part of an algorithm that effects three-dimensional (3D) wavelet-based compression of hyperspectral image data. The context-modeling subalgorithm, hereafter denoted the context modeler, provides estimates of probability distributions of wavelet-transformed data being encoded. These estimates are utilized by an entropy coding subalgorithm that is another major component of the compression algorithm. The estimates make it possible to compress the image data more effectively than would otherwise be possible. The following background discussion is prerequisite to a meaningful summary of the context modeler. This discussion is presented relative to ICER-3D, which is the name attached to a particular compression algorithm and the software that implements it. The ICER-3D software is summarized briefly in the preceding article, ICER-3D Hyperspectral Image Compression Software (NPO-43238). Some aspects of this algorithm were previously described, in a slightly more general context than the ICER-3D software, in "Improving 3D Wavelet-Based Compression of Hyperspectral Images" (NPO-41381), NASA Tech Briefs, Vol. 33, No. 3 (March 2009), page 7a. In turn, ICER-3D is a product of generalization of ICER, another previously reported algorithm and computer program that can perform both lossless and lossy wavelet-based compression and decompression of gray-scale-image data. In ICER-3D, hyperspectral image data are decomposed using a 3D discrete wavelet transform (DWT). Following wavelet decomposition, mean values are subtracted from spatial planes of spatially low-pass subbands prior to encoding. The resulting data are converted to sign-magnitude form and compressed. In ICER-3D, compression is progressive, in that compressed information is ordered so that as more of the compressed data stream is received, successive reconstructions of the hyperspectral image data are of successively higher overall fidelity.

Kiely, Aaron↗
NASA NTRS2010

PPM Receiver Implemented in Software

A computer program has been written as a tool for developing optical pulse-position- modulation (PPM) receivers in which photodetector outputs are fed to analog-to-digital converters (ADCs) and all subsequent signal processing is performed digitally. The program can be used, for example, to simulate an all-digital version of the PPM receiver described in Parallel Processing of Broad-Band PPM Signals (NPO-40711), which appears elsewhere in this issue of NASA Tech Briefs. The program can also be translated into a design for digital PPM receiver hardware. The most notable innovation embodied in the software and the underlying PPM-reception concept is a digital processing subsystem that performs synchronization of PPM time slots, even though the digital processing is, itself, asynchronous in the sense that no attempt is made to synchronize it with the incoming optical signal a priori and there is no feedback to analog signal processing subsystems or ADCs. Functions performed by the software receiver include time-slot synchronization, symbol synchronization, coding preprocessing, and diagnostic functions. The program is written in the MATLAB and Simulink software system. The software receiver is highly parameterized and, hence, programmable: for example, slot- and symbol-synchronization filters have programmable bandwidths.

Gray, Andrew↗
NASA NTRS2010

Reception of Multiple Telemetry Signals via One Dish Antenna

A microwave aeronautical-telemetry receiver system includes an antenna comprising a seven-element planar array of receiving feed horns centered at the focal point of a paraboloidal dish reflector that is nominally aimed at a single aircraft or at multiple aircraft flying in formation. Through digital processing of the signals received by the seven feed horns, the system implements a method of enhanced cancellation of interference, such that it becomes possible to receive telemetry signals in the same frequency channel simultaneously from either or both of two aircraft at slightly different angular positions within the field of view of the antenna, even in the presence of multipath propagation. The present system is an advanced version of the system described in Spatio- Temporal Equalizer for a Receiving-Antenna Feed Array NPO-43077, NASA Tech Briefs, Vol. 34, No. 2 (February 2010), page 32. To recapitulate: The radio-frequency telemetry signals received by the seven elements of the array are digitized, converted to complex baseband form, and sent to a spatio-temporal equalizer that consists mostly of a bank of seven adaptive finite-impulse-response (FIR) filters (one for each element in the array) plus a unit that sums the outputs of the filters. The combination of the spatial diversity of the feedhorn array and the temporal diversity of the filter bank affords better multipath suppression performance than is achievable by means of temporal equalization alone. The FIR filter bank adapts itself in real time to enable reception of telemetry at a low bit error rate, even in the presence of frequency-selective multipath propagation like that commonly found at flight-test ranges. The combination of the array and the filter bank makes it possible to constructively add multipath incoming signals to the corresponding directly arriving signals, thereby enabling reductions in telemetry bit-error rates.

Mukai, Ryan↗
NASA NTRS2010

Space-Qualified Traveling-Wave Tube

The L-3 Communications Electron Technologies, Inc. Model 999HA traveling-wave tube (TWT), was developed for use as a high-power microwave amplifier for high-rate transmission of data and video signals from deep space to Earth (see figure). The 999HA is a successor to the 999H a non-space qualified TWT described in High-Power, High-Efficiency Ka-Band Traveling-Wave Tube (LEW-17900-1), NASA Tech Briefs, Vol. 31, No. 2 (February 2007), page 32. Operating in the 31.8-to-32.3 GHz frequency band, the 999HA has been shown to generate 252 W of continuous- wave output power at 62 percent overall power efficiency a 75-percent increase in output power over the 999H. The mass of the 999HA is 35 percent less than that of the 999H. Moreover, taking account of the elimination of a Faraday cage that is necessary for operation of the 999H but is obviated by a redesign of high-voltage feed-throughs for the 999HA, the overall reduction in mass becomes 57 percent with an 82 percent reduction in volume. Through a series of rigorous tests, the 999HA has been qualified for operation aboard spacecraft with a lifetime exceeding seven years. Offspring of the 999HA will fly on the Kepler and Lunar Reconnaissance Orbiter missions.

Wilson, Jeffrey D.↗
NASA NTRS2007

Software Compensates Electronic-Nose Readings for Humidity

A computer program corrects for the effects of humidity on the readouts of an array of chemical sensors (an "electronic nose"). To enable the use of this program, the array must incorporate an independent humidity sensor in addition to sensors designed to detect analytes other than water vapor. The basic principle of the program was described in "Compensating for Effects of Humidity on Electronic Noses" (NPO-30615), NASA Tech Briefs, Vol. 28, No. 6 (June 2004), page 63. To recapitulate: The output of the humidity sensor is used to generate values that are subtracted from the outputs of the other sensors to correct for contributions of humidity to those readings. Hence, in principle, what remains after corrections are the contributions of the analytes only. The outputs of the non-humidity sensors are then deconvolved to obtain the concentrations of the analytes. In addition, the humidity reading is retained as an analyte reading in its own right. This subtraction of the humidity background increases the ability of the software to identify such events as spills in which contaminants may be present in small concentrations and accompanied by large changes in humidity.

Zhou, Hanying↗
NASA NTRS2007

Extended-Range Ultrarefractive 1D Photonic Crystal Prisms

A proposal has been made to exploit the special wavelength-dispersive characteristics of devices of the type described in One-Dimensional Photonic Crystal Superprisms (NPO-30232) NASA Tech Briefs, Vol. 29, No. 4 (April 2005), page 10a. A photonic crystal is an optical component that has a periodic structure comprising two dielectric materials with high dielectric contrast (e.g., a semiconductor and air), with geometrical feature sizes comparable to or smaller than light wavelengths of interest. Experimental superprisms have been realized as photonic crystals having three-dimensional (3D) structures comprising regions of amorphous Si alternating with regions of SiO2, fabricated in a complex process that included sputtering. A photonic crystal of the type to be exploited according to the present proposal is said to be one-dimensional (1D) because its contrasting dielectric materials would be stacked in parallel planar layers; in other words, there would be spatial periodicity in one dimension only. The processes of designing and fabricating 1D photonic crystal superprisms would be simpler and, hence, would cost less than do those for 3D photonic crystal superprisms. As in 3D structures, 1D photonic crystals may be used in applications such as wavelength-division multiplexing. In the extended-range configuration, it is also suitable for spectrometry applications. As an engineered structure or artificially engineered material, a photonic crystal can exhibit optical properties not commonly found in natural substances. Prior research had revealed several classes of photonic crystal structures for which the propagation of electromagnetic radiation is forbidden in certain frequency ranges, denoted photonic bandgaps. It had also been found that in narrow frequency bands just outside the photonic bandgaps, the angular wavelength dispersion of electromagnetic waves propagating in photonic crystal superprisms is much stronger than is the angular wavelength dispersion obtained by use of conventional prisms and diffraction gratings and is highly nonlinear.

Ting, David Z.↗
NASA NTRS2007

Algorithm Plans Collision-Free Path for Robotic Manipulator

An algorithm has been developed to enable a computer aboard a robot to autonomously plan the path of the manipulator arm of the robot to avoid collisions between the arm and any obstacle, which could be another part of the robot or an external object in the vicinity of the robot. In simplified terms, the algorithm generates trial path segments and tests each segment for potential collisions in an iterative process that ends when a sequence of collision-free segments reaches from the starting point to the destination. The main advantage of this algorithm, relative to prior such algorithms, is computational efficiency: the algorithm is designed to make minimal demands upon the limited computational resources available aboard a robot. This path-planning algorithm utilizes a modified version of the collision-detection method described in "Improved Collision-Detection Method for Robotic Manipulator" (NPO-30356), NASA Tech Briefs, Vol. 27, No. 3 (June 2003), page 72. The method involves utilization of mathematical models of the robot constructed prior to operation and similar models of external objects constructed automatically from sensory data acquired during operation. This method incorporates a previously developed method, known in the art as the method of oriented bounding boxes (OBBs), in which an object is represented approximately, for computational purposes, by a box that encloses its outer boundary. Because many parts of a robotic manipulator are cylindrical, the OBB method has been extended in this method to enable the approximate representation of cylindrical parts by use of octagonal or other multiple-OBB assemblies denoted oriented bounding prisms (OBPs). A multiresolution OBB/OBP representation of the robot and its manipulator arm and a multiresolution OBB representation of external objects (including terrain) are constructed and used in a process in which collisions at successively finer resolutions are detected through computational detection of overlaps between the corresponding OBB and OBP models. For computational efficiency, the process is started at the coarsest resolution and stopped as soon as possible, preferably before reaching the finest resolution. At the coarsest resolution, there is a single OBB enclosing all relevant external objects and a single OBB enclosing the entire robot. At the next finer level of resolution, the coarsest-resolution OBB is divided into two OBBs, and so forth. If no collision is detected at the coarsest resolution, then there is no need for further computation to detect collisions. If a collision is detected at the coarsest resolution, then tests for collisions are performed at the next finer level of resolution. This process is continued to successively finer resolutions until either no more collisions are detected or the finest resolution is reached.

Backes, Paul↗
NASA NTRS2007

Analyzing Responses of Chemical Sensor Arrays

NASA is developing a third-generation electronic nose (ENose) capable of continuous monitoring of the International Space Station s cabin atmosphere for specific, harmful airborne contaminants. Previous generations of the ENose have been described in prior NASA Tech Briefs issues. Sensor selection is critical in both (prefabrication) sensor material selection and (post-fabrication) data analysis of the ENose, which detects several analytes that are difficult to detect, or that are at very low concentration ranges. Existing sensor selection approaches usually include limited statistical measures, where selectivity is more important but reliability and sensitivity are not of concern. When reliability and sensitivity can be major limiting factors in detecting target compounds reliably, the existing approach is not able to provide meaningful selection that will actually improve data analysis results. The approach and software reported here consider more statistical measures (factors) than existing approaches for a similar purpose. The result is a more balanced and robust sensor selection from a less than ideal sensor array. The software offers quick, flexible, optimal sensor selection and weighting for a variety of purposes without a time-consuming, iterative search by performing sensor calibrations to a known linear or nonlinear model, evaluating the individual sensor s statistics, scoring the individual sensor s overall performance, finding the best sensor array size to maximize class separation, finding optimal weights for the remaining sensor array, estimating limits of detection for the target compounds, evaluating fingerprint distance between group pairs, and finding the best event-detecting sensors.

Zhou, Hanying↗
NASA NTRS2007

Hybrid Automated Diagnosis of Discrete/Continuous Systems

A recently conceived method of automated diagnosis of a complex electromechanical system affords a complete set of capabilities for hybrid diagnosis in the case in which the state of the electromechanical system is characterized by both continuous and discrete values (as represented by analog and digital signals, respectively). The method is an integration of two complementary diagnostic systems: (1) beacon-based exception analysis for multi-missions (BEAM), which is primarily useful in the continuous domain and easily performs diagnoses in the presence of transients; and (2) Livingstone, which is primarily useful in the discrete domain and is typically restricted to quasi-steady conditions. BEAM has been described in several prior NASA Tech Briefs articles: "Software for Autonomous Diagnosis of Complex Systems" (NPO-20803), Vol. 26, No. 3 (March 2002), page 33; "Beacon-Based Exception Analysis for Multimissions" (NPO-20827), Vol. 26, No. 9 (September 2002), page 32; "Wavelet-Based Real-Time Diagnosis of Complex Systems" (NPO-20830), Vol. 27, No. 1 (January 2003), page 67; and "Integrated Formulation of Beacon-Based Exception Analysis for Multimissions" (NPO-21126), Vol. 27, No. 3 (March 2003), page 74. Briefly, BEAM is a complete data-analysis method, implemented in software, for real-time or off-line detection and characterization of faults. The basic premise of BEAM is to characterize a system from all available observations and train the characterization with respect to normal phases of operation. The observations are primarily continuous in nature. BEAM isolates anomalies by analyzing the deviations from nominal for each phase of operation. Livingstone is a model-based reasoner that uses a model of a system, controller commands, and sensor observations to track the system s state, and detect and diagnose faults. Livingstone models a system within the discrete domain. Therefore, continuous sensor readings, as well as time, must be discretized. To reason about continuous systems, Livingstone uses monitors that discretize the sensor readings using trending and thresholding techniques. In development of the a hybrid method, BEAM results were sent to Livingstone to serve as an independent source of evidence that is in addition to the evidence gathered by Livingstone standard monitors. The figure depicts the flow of data in an early version of a hybrid system dedicated to diagnosing a simulated electromechanical system. In effect, BEAM served as a "smart" monitor for Livingstone. BEAM read the simulation data, processed the data to form observations, and stored the observations in a file. A monitor stub synchronized the events recorded by BEAM with the output of the Livingstone standard monitors according to time tags. This information was fed to a real-time interface, which buffered and fed the information to Livingstone, and requested diagnoses at the appropriate times. In a test, the hybrid system was found to correctly identify a failed component in an electromechanical system for which neither BEAM nor Livingstone alone yielded the correct diagnosis.

Park, Han↗
NASA NTRS2007

Processing AIRS Scientific Data Through Level 2

The Atmospheric Infrared Spectrometer (AIRS) Science Processing System (SPS) is a collection of computer programs, denoted product generation executives (PGEs), for processing the readings of the AIRS suite of infrared and microwave instruments orbiting the Earth aboard NASA s Aqua spacecraft. AIRS SPS at an earlier stage of development was described in "Initial Processing of Infrared Spectral Data' (NPO-35243), NASA Tech Briefs, Vol. 28, No. 11 (November 2004), page 39. To recapitulate: Starting from level 0 (representing raw AIRS data), the PGEs and their data products are denoted by alphanumeric labels (1A, 1B, and 2) that signify the successive stages of processing. The cited prior article described processing through level 1B (the level-2 PGEs were not yet operational). The level-2 PGEs, which are now operational, receive packages of level-1B geolocated radiance data products and produce such geolocated geophysical atmospheric data products such as temperature and humidity profiles. The process of computing these geophysical data products is denoted "retrieval" and is quite complex. The main steps of the process are denoted microwave-only retrieval, cloud detection and cloud clearing, regression, full retrieval, and rapid transmittance algorithm.

Oliphant, Robert↗
NASA NTRS2007

Rapid and Quiet Drill

This describes aspects of the rapid and quiet drill (RAQD), which is a prototype apparatus for drilling concrete or bricks. The design and basic principle of operation of the RAQD overlap, in several respects, with those of ultrasonic/ sonic drilling and coring apparatuses described in a number of previous NASA Tech Briefs articles. The main difference is that whereas the actuation scheme of the prior apparatuses is partly ultrasonic and partly sonic, the actuation scheme of the RAQD is purely ultrasonic. Hence, even though the RAQD generates considerable sound, it is characterized as quiet because most or all of the sound is above the frequency range of human hearing.

Sherrit, Stewart↗
NASA NTRS2007

Modeling and Grid Generation of Iced Airfoils

SmaggIce Version 2.0 is a software toolkit for geometric modeling and grid generation for two-dimensional, singleand multi-element, clean and iced airfoils. A previous version of SmaggIce was described in Preparing and Analyzing Iced Airfoils, NASA Tech Briefs, Vol. 28, No. 8 (August 2004), page 32. To recapitulate: Ice shapes make it difficult to generate quality grids around airfoils, yet these grids are essential for predicting ice-induced complex flow. This software efficiently creates high-quality structured grids with tools that are uniquely tailored for various ice shapes. SmaggIce Version 2.0 significantly enhances the previous version primarily by adding the capability to generate grids for multi-element airfoils. This version of the software is an important step in streamlining the aeronautical analysis of ice airfoils using computational fluid dynamics (CFD) tools. The user may prepare the ice shape, define the flow domain, decompose it into blocks, generate grids, modify/divide/merge blocks, and control grid density and smoothness. All these steps may be performed efficiently even for the difficult glaze and rime ice shapes. Providing the means to generate highly controlled grids near rough ice, the software includes the creation of a wrap-around block (called the "viscous sublayer block"), which is a thin, C-type block around the wake line and iced airfoil. For multi-element airfoils, the software makes use of grids that wrap around and fill in the areas between the viscous sub-layer blocks for all elements that make up the airfoil. A scripting feature records the history of interactive steps, which can be edited and replayed later to produce other grids. Using this version of SmaggIce, ice shape handling and grid generation can become a practical engineering process, rather than a laborious research effort.

Vickerman, Mary B.↗
NASA NTRS2007

CHEM-Based Self-Deploying Planetary Storage Tanks

A document proposes self-deploying storage tanks, based on the cold elastic hibernated memory (CHEM) concept, to be used on remote planets. The CHEM concept, described in previous NASA Tech Briefs articles, involves the use of open-cell shape-memory-polymer (SMP) foam sandwich structures to make lightweight, space-deployable structures that can be compressed for storage and can later be expanded, then rigidified for use. A tank according to the proposal would be made of multiple SMP layers (of which at least one could be an SMP foam). The tank would be fabricated at full size in the rigid, deployed condition at ambient temperature, the SMP material(s) having been chosen so that ambient temperature would be below the SMP glass-transition temperature (T(sub g)). The tank would then be warmed to a temperature above T(sub g), where it would be compacted and packaged, then cooled to below T(sub g) and kept there during launch and transport to a distant planet. At the assigned position on the planet, the compacted tank would be heated above T(sub g) by the solar radiation making it rebound to its original size and shape. Finally, the tank would be rigidified through natural cooling to below T(sub g) in the planetary ambient environment.

Sokolowski, Witold↗
NASA NTRS2007

Tachometers Derived From a Brushless DC Motor

The upper part of the figure illustrates the major functional blocks of a direction-sensitive analog tachometer circuit based on the use of an unexcited two-phase brushless dc motor as a rotation transducer. The primary advantages of this circuit over many older tachometer circuits include the following: Its output inherently varies linearly with the rate of rotation of the shaft. Unlike some tachometer circuits that rely on differentiation of voltages with respect to time, this circuit relies on integration, which results in signals that are less noisy. There is no need for an additional shaft-angle sensor, nor is there any need to supply electrical excitation to a shaft-angle sensor. There is no need for mechanical brushes (which tend to act as sources of electrical noise). The underlying concept and electrical design are relatively simple. This circuit processes the back-electromagnetic force (back-emf) outputs of the two motor phases into a voltage directly proportional to the instantaneous rate (sign magnitude) of rotation of the shaft. The processing in this circuit effects a straightforward combination of mathematical operations leading to a final operation based on the well-known trigonometric identity (sin x)2 + (cos x)2 = 1 for any value of x. The principle of operation of this circuit is closely related to that of the tachometer circuit described in Tachometer Derived From Brushless Shaft-Angle Resolver (MFS-28845), NASA Tech Briefs, Vol. 19, No. 3 (March 1995), page 39. However, the present circuit is simpler in some respects because there is no need for sinusoidal excitation of shaftangle- resolver windings.

Howard, David E.↗
NASA NTRS2007

Wireless Measurement of Rotation and Displacement Rate

A magnetic field response sensor is designed to measure displacement or rotation rate without a physical connection to a power source, microprocessor, data acquisition equipment, or electrical circuitry. The sensor works with the magnetic field response recorder, which was described in Magnetic-Field-Response Measurement-Acquisition System, NASA Tech Briefs, Vol. 30, No. 6 (June 2006), page 28. These sensors are wirelessly powered and interrogated, and the measurement acquisition system and sensors are extremely lightweight.The response recorder uses oscillating magnetic fields to power the sensors. Once powered, the sensors respond with their own magnetic field. For displacement/ rotation measurements, the response recorder uses the sensor s response amplitude, which is dependent on the distance from the antenna. The recorder s antenna orientation and position are kept fixed, and the sampling period is constant.

Woodard, Stanley E.↗
NASA NTRS2006

Equipment for On-Wafer Testing From 220 to 325 GHz

A system of electronic instrumentation, constituting the equivalent of a two-port vector network analyzer, has been developed for use in on-wafer measurement of key electrical characteristics of semiconductor devices at frequencies from 220 to 325 GHz. A prior system designed according to similar principles was reported in Equipment for On-Wafer Testing at Frequencies Up to 220 GHz (NPO-20760), NASA Tech Briefs, Vol. 25, No. 11 (November 2001), page 42. As one would expect, a major source of difficulty in progressing to the present higher-frequency-range system was the need for greater mechanical precision as wavelengths shorten into the millimeter range, approaching the scale of mechanical tolerances of prior systems. The system (see figure) includes both commercial off-the-shelf and custom equipment. As in the system of the cited prior article, the equipment includes test sets that are extended versions of commercial network analyzers that function in a lower frequency range. The extension to the higher frequency range is accomplished by use of custom frequency-extension modules that contain frequency multipliers and harmonic mixers. On-wafer measurement is made possible by waveguide wafer probes that were custom designed and built for this wavelength range, plus an on-wafer calibration substrate designed for use with these probes. In this case, the calibration substrate was specially fabricated by laser milling. The system was used to make the first on-wafer measurements of a semiconductor device in the frequency range from 220 to 320 GHz. Some of the measurement results showed that the device had gain.

Samoska, Lorene↗
NASA NTRS2006

Software for Automated Generation of Cartesian Meshes

Cart3D is a collection of computer programs for generating Cartesian meshes [for computational fluid dynamics (CFD) and other applications] in volumes bounded by solid objects. Aspects of Cart3D at earlier stages of development were reported in "Robust and Efficient Generation of Cartesian Meshes for CFD" (ARC-14275), NASA Tech Briefs, Vol. 23, No. 8 (August 1999), page 30. The geometric input to Cart3D comprises surface triangulations like those commonly generated by computer-aided-design programs. Complexly shaped objects can be represented as assemblies of simpler ones. Cart3D deletes all portions of such an assembled object that are not on the exterior surface. Intersections between components are preserved in the resulting triangulation. A tie-breaking routine unambiguously resolves geometric degeneracies. Then taking the intersected surface triangulation as input, the volume mesh is generated through division of cells of an initially coarse hexahedral grid. Cells are subdivided to refine the grid in regions of increased surface curvature and/or increased flow gradients. Cells that become split into multiple unconnected regions by thin pieces of surface are identified.

Aftosmis, Michael J.↗