Basic Geometric Shapes Research Articles

An Investigation of Some Geometrical Shapes and Selection of Shielding and Lumped Resistors of Planar Dipole Antennas for GPR Applications Using FDTD

A ground-penetrating radar (GPR) antenna system is modeled using the three-dimensional finite-difference time-domain technique. This paper investigates some basic geometrical shapes for planar dipoles to find what shape gives the best performance for GPR applications. The antenna is resistor loaded and shielded by a rectangular conducting cavity to suit the application. The effect of adding a wave-absorbing coat to the shield is also studied. Furthermore, a genetic algorithm is used to optimize the cavity height and the resistor values

Far-field diffraction patterns of circular sectors and related apertures

In studies of scalar diffraction theory and experimental practice, the basic geometric shape of a circle is widely used as an aperture. Its Fraunhofer diffraction pattern has a simple mathematical expression easily determined by use of the Fourier-Bessel transform. However, it may require considerable mathematical effort to determine the far-field diffraction patterns of aperture shapes related to the circular geometry. From a computational point of view, the mathematical difficulties posed by other aperture geometries as well as more-general apertures with irregular shapes can be surpassed by means of optical setups or fast numerical algorithms. Unfortunately, no additional insight or information can be obtained from their exclusive application, as would be the case if mathematical formulas were available. The research presented here describes the far-field diffraction patterns of single-sector apertures as well as their extension to double symmetrical sectors and to sector wheels formed by interleaved transparent sectors of equal angular size; in each case, full or annular sectors are considered. The analytic solutions of their far-field amplitude distribution are given here in terms of a series of Bessel functions, some interesting properties are deduced from these solutions, and several examples are provided to illustrate graphically the results obtained from approximate numerical computations. Our results have been verified numerically with the fast-Fourier-transform algorithm and experimentally by means of a spherical wavefront-single-lens Fourier-transform architecture.

Application of Monte Carlo Simulation Method to the Nano-Scale Characterization by Scanning Electron Microscopy

Topographic imaging of materials by a scanning electron microscope (SEM), using the secondary electrons and backscattered electrons escaped from the surface under a primary electron beam bombardment as image signals, has been a very important technique in application to material sciences and the related fields. In this work we have developed a new parallel Monte Carlo simulation program to calculate SEM images especially for an inhomogeneous sample with a complex structure, which may be constructed with some basic geometrical shapes containing different materials. The ray-tracing arithmetic is employed to obtain the corrected electron flight step length for electrons across the interface of different zones containing distinct elements. We have done simulations for several specimens with artificial structures at the nm level. The results illustrate some new characters of image contrast, demonstrating the applicability of this image simulation technique to the characterization of nano-scale structure.

Trajectory Planning for Autonomous Aerospace Vehicles amid Known Obstacles and Conflicts

A discrete search strategy is presented for potential real-time generations of four-dimensional trajectories for a single autonomous aerospace vehicle amid known obstacles and conflicts. A model of autonomous operation isfirst developed. The problem of and requirements on real-time trajectory generations for autonomous aerospace vehicles are discussed. After an overview of various potential solution frameworks, a discrete search strategy is developed. In this strategy, a four-dimensional search space is defined and discretized. Potential obstacles and conflicts are represented by several basic geometric shapes and their combinations. Mathematical conditions are developed for a trajectory segment to be outside of an obstacle or conflict. Then, the A* search technique is used to obtain trajectory solutions, in which successor points are selected that avoid obstacles and conflicts and that satisfy dynamic motion constraints of the vehicle. A linear combination of flight distance and flight time is optimized in the trajectory generation process. A heuristic function that approximates this performance index is developed for the A * search procedure. Examples are provided that illustrate the application of the proposed method.

Is a Rectangle a Square? Developing Mathematical Vocabulary and Conceptual Understanding

Desiring to better encourage students' thinking and conceptual development, a fourth-grade teacher examines classroom discourse and written work during her students' analysis and description of basic geometric shapes.

Influences of dendrite morphologies and solid-back diffusion on macrosegregation in directionally solidified blade-like casting

A newly proposed solidification transport process (STP)-based micro-/macrosegregation model is used to investigate the influences of dendrite morphologies and solid-back diffusion (SBD) on macrosegregation behaviors in dendrite solidification of shaped castings. Via a unified micro-scale parameter, an arbitrary solidifying dendrite structure is reconstructed through the scalar production of a solid-fraction-dependent weighting coefficient vector and basic geometrical vector consisted of spherical, cylindrical, plate-like, inward cylindrical and inward spherical components. Computations are carried out on directionally solidified blade-like Al–4.5wt.%Cu castings with assumed different solid-diffusion-coefficients varying in eight orders of magnitude and different solid-phase morphologies including the five basic geometrical shapes and assumed equiaxed/columnar dendrites and granulated structures. The calculated results comparisons show that a solidification structure with a convex solid–liquid (S/L) interface tends to lighten the macrosegregation formation though the influences of the solid-phase morphologies on macrosegregation behaviors are less significant than that of solid-diffusion-coefficients.

Pressure Induced Cubic-to-Cubic Phase Transition in Monoolein Hydrated System

Synchrotron X-ray diffraction has been used to investigate structure, stability, and transformation of the Pn3m bicontinuous cubic phase in the monoolein−water system under hydrostatic pressure. As a first result, it appears that the full-hydration properties of monoolein are strongly related to the pressure. Moreover, the experimental results show the occurrence of a Pn3m to Ia3d cubic phase transition when the mechanical pressure increases to 1−1.2 kbar, depending on the water concentration. The underlying mechanism for the phase transition has been then explored in searching for relationships between the structural parameters derived from the two cubic phases. The emerging picture is a change in the basic geometrical shape of the monoolein molecule during compression. Moreover, the analysis of the position of the pivotal surface indicates that the interface is bending and stretching simultaneously as a function of pressure. Because the lipid concentration is rather low and the external pressure increas...

Detection and segmentation of generic shapes based on affine modeling of energy in eigenspace

This paper presents a novel approach for detection and segmentation of man made generic shapes in cluttered images. The set of shapes to be detected are members of affine transformed versions of basic geometric shapes such as rectangles, circles etc. The shape set is represented by its vectorial edge map transformed over a wide range of affine parameters. We use vectorial boundary instead of regular boundary to improve the robustness to noise, background clutter and partial occlusion. Our approach consists of a detection stage and a verification stage. In the detection stage, we first derive the energy from the principal eigenvectors of the set. Next, an a posteriori probability map of energy distribution is computed from the projection of the edge map representation in a vectorial eigen-space. Local peaks of the posterior probability map are located and indicate candidate detections. We use energy/probability based detection since we find that the underlying distribution is not Gaussian and resembles a hypertoroid. In the verification stage, each candidate is verified using a fast search algorithm based on a novel representation in angle space and the corresponding pose information of the detected shape is obtained. The angular representation used in the verification stage yields better results than a Euclidean distance representation. Experiments are performed in various interfering distortions, and robust detection and segmentation are achieved.

Automated image interpretation for integrated topology and shape optimization

A fully automated configuration optimization system (ACOS) for two-dimensional structures is proposed. The first stage of this system employs homogenization or material distribution methods to create a grey level image of a structure with minimum compliance. The second stage involves image interpretation that converts the grey level image to a parameterized structural model ready to undergo shape optimization. Several basic geometric shape templates are used to match holes of varied size and shape inside a structure. Two unique shape characteristics are defined and matching formulae that assign an appropriate template to a hole are provided. In the final stage, shape parameters are treated as design variables in a shape optimization that seeks a fine-tuned configuration and ensures satisfaction of all design constraints. Since human-machine interaction is not needed, ACOS increases the efficiency of the integrated topology and shape optimization for configuration designs. Three configuration design examples are provided.

514 FEM を用いたねじれ刃エンドミルの曲げ変形解析

This paper deals with the analysis of deflection of a square end mill using FEM. In FEM modeling the cross section under investigation is divided into eight nodes hexahedron elements based on basic geometrical shapes. The deflection of a tool caused by concentrated load is calculated by means of FEM. And the results of FEM analysis were compared with the analysis of deflection using moments of inertia of area.

Adsorption of Et3N and Bu3N from Toluene onto AgI in the Very Dilute Region: Surface Models and Cross-Sectional Areas

Adsorption isotherms for triethylamine and tributylamine solutions in toluene onto AgI in the very dilute region are presented and treated according to Everett, and Sircar and Myers models. An analysis of molecular orientation in the adsorbed phase and its consequences on the calculated cross-sectional areas for adsorbed molecules is performed, and a simple procedure to calculate cross-sectional areas along different molecular projections, based on basic geometrical shapes, is put forth. The proposed procedure is tested for the adsorption of alkanoic acids on silica and leads to results identical with Meyer's. For spherical molecules the values compare well with those of McClellan and Harnsberger. Finally, the contribution of these new cross-sectional values to attain a set of coherent quantities from the adsorption experiments is revealed.

Pictorial recognition of objects employing affine invariance in the frequency domain

Describes an efficient approach to pose invariant pictorial object recognition employing spectral signatures of image patches that correspond to object surfaces which are roughly planar. Based on singular value decomposition (SVD), the affine transform is decomposed into slant, tilt, swing, scale, and 2D translation. Unlike previous log-polar representations which were not invariant to slant, our log-log sampling configuration in the frequency domain yields complete affine invariance. The images are preprocessed by a novel model-based segmentation scheme that detects and segments objects that are affine-similar to members of a model set of basic geometric shapes. The segmented objects are then recognized by their signatures using multidimensional indexing in a pictorial dataset represented in the frequency domain. Experimental results with a dataset of 26 models show 100 percent recognition rates in a wide range of 3D pose parameters and imaging degradations: 0-360/spl deg/ swing and tilt, 0-82/spl deg/ of slant, more than three octaves in scale change, window-limited translation, high noise levels (0 dB), and significantly reduced resolution (1:5).

A flexible automated foam cutting system

Direct cutting of foam has the advantage of greater flexibility and reduced lead time over molding. This paper discusses the design and development of a flexible automated system for foam cutting that utilizes hot-wire cutters. The cutters are moved through the use of a five-axis gantry-type robot system equipped with a tool turret. A method for modeling the cut geometry, based on representing the three-dimensional cut shape as a combination of basic geometrical block shapes, is presented. This method gives the system flexibility to handle different workpiece geometries. A technique for generating the required cutting paths from the modeled geometry is also shown. The developed methodology was applied for the cutting of automotive seat cushions. The results show that the automated system significantly reduces the cutting time and produces cuts of improved quality.

Determination of porosity and particle size of natural bulk materials using image analysis

AbstractPorosity and particle volume are important properties of solids in numerous technical processes. Dehydration in food technology often leads to a decrease of particle size, combined with a change of porosity. Knowledge of the moisture dependence of these properties helps to avoid quality losses during drying. Common methods of porosity determination like mercury porosimetry or B.E.T. gas adsorption do not allow moisture variation. Therefore, a porosity evaluation method consisting of a combination of image analysis and gas displacement in a pycnometer is developed. Taking helium as the gas allows to measure open as well as encapsulated pore volume of the biological product. With particular consideration of basic geometrical particle shape of the investigated natural bulk materials, the disadvantage of image analysis being a two‐dimensional measuring method is limited. Experimental results are of high reproducibility and show good agreement with literature data and a standard porosimetry method. Particle size prediction derived from a combination of particle volume balance and estimated porosity shows good agreement between calculated and measured particle size, even under variation of moisture content. This comparison also indicates the high reliability of the presented porosity analysis.

The development of a microcomputer CAD/CAM and decision support system for the manufacturing of aerospace vehicles

Aircraft designing poses special problems in CAD (computer-aided design), because most CAD programs use basic geometric shapes as building blocks. Since it is difficult to describe aircraft components using basic geometric shapes, it is often necessary to input a large number of physical coordinates to describe the shape of aircraft components. By defining wings or fuselages using design parameters instead of physical coordinates, much time and energy is saved in the CAD process. A microcomputer program called AeroCAD was developed to simplify the aircraft design process. AeroCAD uses wing and fuselage design parameters as inputs. This makes it possible to design a wing or fuselage with a fraction of the values of conventional CAD programs. AeroCAD allows the user to build an aircraft from an existing database inventory of aircraft components; fuselage, wings, and tails. The inventory consists of components the user has previously created. The computer-generated aircraft can be rotated, translated, and scaled at the user's command. Another program was written so Numerical Control coding could be generated from AeroCAD's data base. This made it possible to manufacture a miniature aircraft. The milled model could then be used as a wind-tunnel model. AeroCAD was written for implementation on a microcomputer to take advantage of quick response times, ease of operation, printer output, and the ability to run AeroCAD on an inexpensive system. AeroCAD was written to have many useful features. The program can display normal color graphics or enhanced graphics on an IBM PC or PS/2.

Visual shape discrimination in the fiddler crab,Uca pugilator

Research into the visual shape discrimination abilities of compound‐eyed animals has almost exclusively been limited to insects, the crustaceans having been virtually ignored. The two groups have many dissimilarities, having primarily adapted in different habitats to different lifestyles. Differences may exist in visual systems and visually mediated behavior. Fiddler crabs (Uca pugilator), without training, differentially approached dissimilar silhouettes presented simultaneously, demonstrating visual discrimination between stationary, geometric shapes of equal‐area. The strength of response was ordered hierarchically: vertical rectangle, horizontal rectangle, triangle, square, circle. Basic geometric shapes were used to facilitate replication and comparison with research findings from other species.

Three-dimensional phonetic alphabet

A phonetic alphabet for communicating with dolphins, porpoises and whales inlcludes three basic geometric shapes, various combinations of which are used to represent speech sounds. The alphabet consists of eighteen symbols which may be understood by animals trained to identify these symbols with words by using their innate echolocation sensory capabilities, and may also be understood visually by human trainers.

Procedure for obtaining aerodynamic properties of spacecraft

A numerical procedure for calculating free-molecular aerodynamic coefficients for a large class of spacecraft configurations is presented. This involves modeling the spacecraft via the use of basic geometric shapes. The surface of each shape is numerically divided into small elemental areas. Overall coefficients are determined by summing force contributions from each of the exposed surface elements. Surface shielding is accounted for through the use of a shadow-projection technique and simple geometric relationships. Forces on elemental areas are determined by using the gas-surface interaction model attributed to Schaaf and Chambre with experimental momentum accommodation data. The procedure is implemented as a computer program. To illustrate the use and accuracy of this procedure, it is applied to the complex Skylab configuration. Results are compared with analytical predictions from a previous study.

The efficacy of solar conversion in a polar environment

A simple optical model of the polar environment is proposed. The unique properties of this polar model are shown to give equal significance to direct and scattered solar radiation. The influence of this model on the design of solar collectors for the arctic environment are discussed. The results of this analysis are applied to several basic geometric shapes with regard to their use as arctic shelters.

A Study in the Variation of Types of Computer Drawings Obtainable by Small Program Changes

1. A digital computer can make a drawing by a point-bypoint procedure. Given the initial location of a series of points describing a basic geometrical shape or basic unit, a computer program can direct the computer to develop a drawing from it. This initial point information may be a long list of graphical coordinates of points if the basic shape is complex. However, if the list is very short,