Set Of Parallel Planes Research Articles

Методы расчета радиоголограмм объемных объектов

A method for calculating holograms for volumetric objects based on the representation of objects in the form of ensembles of virtual point sources distributed on a set of parallel planes has been proposed. The proposed method is the development of the well-known method in which objects are represented as ensemble of real point scatterers. The possibilities of the proposed method are demonstrated by calculating a hologram of a fragment of a sphere, on which 1000 points are randomly selected, at which radiation emanating from the center of the sphere is scattered. The choice of a fragment of a sphere as an object under study is due to the fact that when calculating its hologram, phase errors inherent in approximate calculations are most pronounced. The calculations were performed for the frequency range of 2...100 GHz, the sphere radius of 0.5 m, a two-dimensional hologram size of 0.65×0.65 m, and a pixel count of 512×512. It is shown that, in comparison with the known method, the proposed method makes it possible to calculate the amplitude of a hologram with satisfactory accuracy if virtual sources are placed on parallel planes in an amount of more than 64 pieces. In the case of objects that require representation in the form of an ensemble of point scatterers in the amount of more than 1000 pieces, the calculation of their holograms by the proposed method turns out to be much more efficient than the known method.

Path Planning for Laser Cladding Robot on Artificial Joint Surface Based on Topology Reconstruction

Artificial joint surface coating is a hot issue in the interdisciplinary fields of manufacturing, materials and biomedicine. Due to the complex surface characteristics of artificial joints, there are some problems with efficiency and precision in automatic cladding path planning for coating fabrication. In this study, a path planning method for a laser cladding robot for artificial joints surface was proposed. The key of this method was the topological reconstruction of the artificial joint surface. On the basis of the topological relation, a set of parallel planes were used to intersect the CAD model to generate a set of continuous, directed and equidistant surface transversals on the artificial joint surface. The arch height error method was used to extract robot interpolation points from surface transversal lines according to machining accuracy requirements. The coordinates and normal vectors of interpolation points were used to calculate the position and pose of the robot tool center point (TCP). To ensure that the laser beam was always perpendicular to the artificial joint surface, a novel laser cladding set-up with a robot was designed, of which the joint part clamped by a six-axis robot moved while the laser head was fixed on the workbench. The proposed methodology was validated with the planned path on the surface of an artificial acetabular cup using simulation and experimentation via an industrial NACHI robot. The results indicated that the path planning method based on topological reconstruction was feasible and more efficient than the traditional robot teaching method.

Generalised vertical projection histograms using multi‐plane homology

© The Institution of Engineering and Technology 2019 Vertical projection histograms are an efficient shape representation for 2D binary silhouettes and have been widely used in pedestrian localisation for video surveillance. The weakness of this method is that it is not invariant to rotation. In this Letter, a generalised vertical projection histogram is proposed to solve this problem, in which the homology transformations of the foreground silhouettes, for a set of parallel planes, are warped to, and accumulated, in the original foreground map. Then a method, similar to the vertical projection histogram, is carried out to localise the pedestrians in the foreground silhouettes. The algorithm applies an integrated approach using both image projection and geometric projection. Its value is demonstrated in a case study on pedestrian localisation with cast shadows.

High Pressure Structural Investigation of Benzoic Acid: Raman Spectroscopy and X-ray Diffraction

The structural stability of benzoic acid (C6H5COOH, BA), a hydrogen-bonded molecular crystal, has been investigated by Raman spectroscopy and angle-dispersive X-ray diffraction (ADXRD) up to ∼18 GPa at room temperature. Under ambient conditions, benzoic acid molecules are arranged in two sets of parallel planes and held together by hydrogen bonding and van der Waals interactions. Small changes (e.g., emergence of new peaks, splitting of original peaks) can be observed in the Raman spectra at high pressures. However, no obvious changes can be observed in the X-ray diffraction measurements, which rules out any symmetry/structure changes within this pressure range. The pressure dependence of lattice parameters is presented, which shows monotonously decrease without any anomalies. The experimental isothermal pressure–volume data are well fitted by the third-order Birch–Murnaghan equation of state, yielding bulk modulus B0 = 41.7(6) GPa and a first pressure derivative B0′ = 4.5(4). Axial compressibility shows ...

Construction and investigation of 3D vessels net of the brain according to MRI data using the method of variation of scanning plane

The blood realizes the transport of substances, which are necessary for livelihoods, throughout the body. The assumption about the relationship genotype and structure of vasculature (in particular of brain) is natural. In the paper we consider models of vessel net for two genetic lines of laboratory mice. Vascular net obtained as a result of preprocessing MRI data. MRI scanning is realized using the method of variation of slope of scanning plane, i.e. by several sets of parallel planes specified by different normal vectors. The following special processing allowed to construct models of vessel nets without fragmentation. The purpose of the work is to compare the vascular network models of two different genetic lines of laboratory mice.

Reconstruction of unbroken vasculature of mouse by varying the slope of the scan plane in MRI

Reconstruction of vascular net of small laboratory animals from MRI data is associated with some problems. This paper proposes a method of MRI data processing which allows to eliminate the fragmentation of reconstructed vascular net. Problem of vessels fragmentation occurs in the case when vessels are parallel to the scanning plane. Our approach is based on multiple scanning, object under consideration is probed by several sets of parallel planes. The algorithm is applied to real MRI data of small laboratory animals and shows good results.

Reasons for high-temperature superconductivity in the electron–phonon system of hydrogen sulfide

We have calculated the electron and phonon spectra, as well as the densities of the electron and phonon states, of the stable orthorhombic structure of hydrogen sulfide SH2 in the pressure interval 100–180 GPa. It is found that at a pressure of 175 GPa, a set of parallel planes of hydrogen atoms is formed due to a structural modification of the unit cell under pressure with complete accumulation of all hydrogen atoms in these planes. As a result, the electronic properties of the system become quasi-two-dimensional. We have also analyzed the collective synphase and antiphase vibrations of hydrogen atoms in these planes, leading to the occurrence of two high-energy peaks in the phonon density of states.

Study on complicated solid modeling and Cartesian grid generation method

A Cartesian grid generation method is developed in this study. Two kinds of solid modeling methods, CSG and STL models, are used for complicated solid modeling. The staircase boundary approximation is implemented to handle irregular geometries and the computational domain is discretized using a regular Cartesian grid. Using the edge-based integral slice algorithm, the models are sliced with a set of parallel planes to generate 2D slices information. The scan line filling technique is used to achieve grid generation after slicing. Two grid generation examples with a CSG model and a STL model are given to test the capability of the grid generation method. For grid displaying, a method is proposed to remove the hidden surfaces fasten based on the topology of orthogonal hexahedral grids. The parallelization of grid displaying is achieved by employing multi-threaded parallel technique. Parallel test results show that the parallel algorithm has the absolute advantage on speed compared to the serial algorithm.

The Intersection and its Application for Non-Circular Quadric Curved Surface Based on the Theory of Projective Correspondence

Based on the theory of projective correspondence, the principle of affine correspondence and projective correspondence is proposed to resolve the intersection of non-circular quadric curved surface (NCQCS). According to the theory of projective geometry, the intersection that NCQCS intersect with a set of parallel planes is a group of homothetic curves. Taking the homothetic curves as corresponding element, spatial projective correspondence between any two homothetic curves is constructed. Similarly, the intersection that any NCQCS intersected by a set of planes through it axis is a group of similar curves. Taking the similar curves as associated element, spatial affine correspondence between any two similar curves is constructed. The intersection and drawing theory, method, application and technology for the NCQCS provides the theoretical and practice support for the intersection of the NCQCS.

Single crystal pillar microcompression tests of the MAX phases Ti2InC and Ti4AlN3

The deformation behavior of micron-sized, single crystal specimens of the MAX phases Ti 2 InC and Ti 4 AlN 3 has been investigated under uniaxial compression. Deformation took place by slip on single planes or sets of parallel planes. For highly inclined slip planes, where slip was hindered by the substrate or punch, deformation was accompanied by micro-cracking, layer bending, and the formation of kink bands. This study confirms the importance of obstacles in the deformation behavior and strength of MAX phases.

Affine Reconstruction Based on Parallel Plane and Infinity Point

Affine reconstruction is to restore the affine shape of the object. Generally, there are two ways of achieving, one is to determine the plane at infinity, another is to determine the plane homography. Using the homography which had determined the plane at infinity achieve affine reconstruction. In this paper, firstly give out the homography of infinity plane and the algorithm of affine reconstruction, then proved: if the scene contains a set of parallel planes and a infinity point, the homography of infinity plane can be obtained and affine reconstruction can be linearly got in the scene. Computer simulation and real experiments show that the linear affine reconstruction algorithm is correct, and the approach has a good precision.

NC machining of free-form Kriging surfaces

An algorithm for three-axis NC tool path generation on sculptured surfaces is introduced when the free-form surface is modeled parametrically by free-form surface Kriging. The flexibility of dual Kriging that easily defines the intersection of the surfaces with a set of parallel planes and Cartesian method are combined to generate the tool-paths automatically. The presented algorithm can simultaneously generate the tool path with a predefined machining accuracy and remove gougings along the tool path. The algorithms are validated by three experiments in rough and finish machining and the results prove its reliability. Since Kriging is based on the interpolation of data points, the proposed algorithm can be used for reverse engineering applications. The system was executed on a standard micro-computer and the software was structured to offer a library of machining functions for endusers.

Surface slicing algorithm based on topology transition

Presented in this paper is an algorithm to compute the intersections of a parametric regular surface with a set of parallel planes. Rather than using an ordinary surface-plane intersection algorithm repeatedly, we pre-process a surface to identify points, called topology transition points (TTP's), on the surface where the topologies of intersection curves change. It turns out that such points can be computed efficiently, exactly and robustly employing a normal surface, and they are categorized into seven distinct groups. Analyzing the properties of such characteristic points on the surface, the starting points to trace intersection curves can be found rather efficiently and robustly. Such intersection contours can be used in various applications including rapid prototyping, solid freeform fabrication, process planning, NC tool path generation for surfaces, etc.

1-Tosyl-1H-pyrrolo[2,3-c]pyridine-5-carboxylic acid ethyl ester

The title compound, C 17 H 16 N 2 O 4 S, was synthesized starting from 1H-pyrrole-2-carboxaldehyde under acidic conditions. The X-ray structure determination has proved that the compound was the expected pyrrolo[2,3-c]pyridine derivative and not the pyrrolo[3,2-c]pyridine isomer. The molecules are packed such that the azaindole rings are stacked in one set of parallel planes and the phenyl rings are stacked in another, with interplanar distances of 3.50 (1) and 3.83 (1) A, respectively, giving the molecule a «V» shape

A general class of rearrangeable interconnection networks

A class of rearrangeable interconnection networks which includes the Benes network as a special case is identified. An instance of this class consists of a set of parallel planes each consisting of a Delta network with a suitable number of additional stages. A formal definition is given and a rearrangeability condition is proven which gives a tradeoff between the number of planes and additional stages necessary. >

Pictorial representation of three‐dimensional electron distributions through a perspective view of contour diagrams in a set of parallel planes

AbstractA method of graphically exhibiting detailed information about a three‐dimensional electron distribution function f(x,y,z) is described. Contour lines f = constant are drawn on a set of equidistant parallel planes that intersect the distribution, and a perspective view of all contours on all planes is displayed. Representative examples are given.

Interactions of molecules with nucleic acids. IX. Evaluation and presentation of electrostatic contours on a steric surface with the removal of hidden lines

AbstractA technique to generate electrostatic contours on a steric surface is presented and applied to the presentation of molecules that interact with DNA. A set of electrostatic points at predetermined values along with their derivatives are obtained on the steric contours as they are generated. The steric contours are generated in a set of parallel planes. Points with given electrostatic values are then connected between and within the contours mathematically with a Taylor's expansion and two rules: the first to tentatively line up points that can be connected, and the second to check to insure that the remaining points can be connected. This method insures that contours will not cross by requiring that a possible connection of two points leaves an even number of remaining points for each electrostatic value in isolated regions of unused points bounded by points that have already been connected. The hidden line algorithm used previously to draw molecules in a space‐filling model within the context of steric contours is applied to the complete problem of the presentation of a molecule bound to DNA with steric contours in parallel planes, and with electrostatic contours drawn on this steric surface.

Utilization of Cross-Plane Rays for Three-Dimensional Reconstruction by Filtered Back-Projection

Present popular computed tomography (CT) algorithms reconstruct an object from the ray measurements lying on a set of parallel planes. This paper presents an algorithm that can also utilize "cross-plane" rays (i.e., rays that cross through many planes) to reconstruct the object. In this reconstruction algorithm, the ray measurements are grouped into two-dimensional projections, filtered, and stored. The filtered projections can then be back-projected onto a three-dimensional matrix or any plane through the three-dimensional volume. General theoretical aspects are presented and then applied to the special case in which ray measurements have been made in all directions. The algorithm is tested using computer-generated data. Expressions for the noise power spectrum and the variance in the reconstruction are derived. It is shown that the noise-to-signal ratio per detected photon for this reconstruction method is close to a theoretical limit, as it also is for normal CT. The ability to use ray measurements that cross many planes is especially useful in emission CT, where order-of-magnitude improvements in image quality per unit dose can be achieved.

Contouring Method by Parallel Light Moiré Holography

Moiré contouring method by parallel light is realized using holography. In Fourier-transform holography, the object placed at the focus of a collimating lens is equivalent to the one placed at infinity. Regular fringes are projected onto the object by tilting the illuminating parallel light slightly between the exposures of double exposure holography. These fringes are deformed by the relief of the object. Imaginary hyperboloids of interference fringes are formed by fine lateral displacement between the two exposures. As the plate is located at the focus of the lens, it is considered that the hyperboloids can be approximated by a set of parallel planes after passing through the lens. These parallel fringes are observed at infinity as a regular grid. The combination of this regular grid with the deformed fringes produces contouring fringes on the object at infinity.

Application of Aerial Photographic Interpretation to the Study of Reservoir Natural Fracture Systems

Aerial photography, through skillful interpretation, can be a potential source of information on natural fracture orientation in a reservoir. The feasibility of the approach is discussed here on the basis of an investigation conducted in the Midland basin of West Texas. Introduction Well developed natural fracture systems, forming intersecting sets of parallel planes, are extremely common within the rocks of the earth's crust. Extensive and systematic fracturing, generated by large stress fields of natural origin, is widespread in all geomorphological divisions of the earth, including those that are tectonically stable where most of the world's known oil producing basins are located. Over the years, considerable scientific inquiry has been directed toward natural fracture systems found in surface formations. Yet little emphasis has been placed on the fact that natural fractures, far from placed on the fact that natural fractures, far from being restricted to the surface of the earth, are equally prevalent in subsurface rocks at all depths. Thus until prevalent in subsurface rocks at all depths. Thus until recently, the petroleum industry has been less than enthusiastic about acknowledging natural fracture systems as routine structural components of producing formations. Indeed, engineering experience in producing formations. Indeed, engineering experience in the field reveals increasingly that the incidence of natural fracturing in reservoirs is much more common than is generally thought, extending well beyond the classic examples cited in the literature. As is universally recognized, the presence of fractures can enhance productivity in dissolved gas drive reservoirs. If it were not for naturally formed fractures, or for the practice of hydraulically inducing "parting" in formations to increase their productivity, many low-permeability reservoirs would perhaps never be commercial. On the other hand, in a reservoir where a frontal displacement mechanism is in effect, fractures can be highly undesirable. In various papers dealing with this subject, analytical studies papers dealing with this subject, analytical studies supported by field evidence have shown that in a reservoir with a rising water table the presence of fractures will result in lower recovery. Perhaps the most significant aspect of natural fracture systems is that they invariably create troublesome channeling problems in reservoirs undergoing recovery by fluid injection. Many investigations have shown that when fractures are present, volumetric sweep efficiency in a reservoir is adversely affected by, among other controlling factors, the degree of fracturing and the orientation of the fracture sets with respect to the alignment of injection-production well pairs. Consequently, in planning fluid injection programs or in dealing with reservoirs that produce by programs or in dealing with reservoirs that produce by frontal displacement, it is important to establish the spatial attitude of the reservoir fracture planes so that their adverse effects can be avoided or at least minimized. Unfortunately, the investigation of fracture conditions in the subsurface remains a technological frontier. No current engineering or logging method, when used alone, is entirely effective in determining conclusively either the presence or the systematic attitude of fractures in a reservoir. JPT P. 37