Intersection Of Plane Research Articles

Variational shape approximation of point set surfaces

In this work, we present a translation of the complete pipeline for variational shape approximation (VSA) to the setting of point sets. First, we describe an explicit example for the theoretically known non-convergence of the currently available VSA approaches. The example motivates us to introduce an alternate version of VSA based on a switch operation for which we prove convergence. Second, we discuss how two operations—split and merge—can be included in a fully automatic pipeline that is in turn independent of the placement and number of initial seeds. Third and finally, we present two approaches how to obtain a simplified mesh from the output of the VSA procedure. This simplification is either based on simple plane intersection or based on a variational optimization problem. Several qualitative and quantitative results prove the relevance of our approach.

Crack formation in strained SiGe grown on Ge-on-Si (111) and its suppression by patterning substrates

We study surface morphologies, defect structures and strain states in tensile-strained SiGe layers grown on Ge-on-Si(111) or Ge(111) substrates. It is found that at the initial stage of partial strain relaxation, cracks are generated on the equivalent (111) slip planes and followed by formation of surface ridge roughness along the intersections of the slip planes and the surface. These cracks and resultant ridge roughness can be avoided by the patterning of the Ge-on-Si(111) substrate presumably owing to stress relief at the edges of the patterns, indicating that this method is promising for strained SiGe-based spintronics and high mobility device applications.

Complete calibration of a structured light stripe vision sensor through a single cylindrical target

In a complex industrial environment, it is not appropriate to use the traditional Zhang's calibration method to shoot multiple checkerboard images in different positions, and due to the contour characteristics of the cylindrical target, camera calibration and line-structured calibration can be simultaneously performed. Therefore, a complete calibration method for a line-structured light system based on a single cylindrical target is proposed. The calibration process is as follows: Placing the cylindrical target at least once and illuminate it with the light strip of the laser projector. The vision sensor captures the target image and then extracts the laser stripes and contour images of the cylindrical target. According to the contour characteristics of the cylindrical target and the definition of the collinear vector, the extracted contour image is used to solve the internal parameters of the camera. Because the line-structured light plane and cylindrical target intersection line in the axial of cylindrical is a standard circle, the equation of the light plane is established on the camera coordinate system. The effectiveness of the method is verified by simulation and physical experiments. The experimental results show that the RMS errors of the 30 distance is 0.07 mm. The proposed method does not need to rely on the constraints of multiple images and is simple to operate, meeting the requirements of industrial 3D measurement technology.

Development’s Features of Industrial Production in the Region

The work is devoted to the analysis of the regional industry level development in the Orenburg region. The state of the oil and gas industry, power industry, metallurgy, mechanical engineering and light industry has been considered. The analysis showed that since 2012, the region is characterized by multidirectional dynamics of the sectoral structure industry, in the face of fluctuations — either growth or production decline in individual sectors. There are positive moments. Orenburg region has successfully implemented its solar potential over the past 5 years. During this period, the region has earned 7 solar power plants with a total capacity of 200 MW. Further, the paper proposes a method for multidimensional assessment of the industry state. It consists in building a beam of coordinated development of industries and determining in the plane called theequal contributions plane of two parameters: distance and angle of rotation. The distance is estimated as the distance between the point representing the given moment and the point of intersection of the beam of coordinated development with the plane of equal contributions. The angle of rotation is determined between the line of intersection of the constant plane on the main type of production (oil production) with the plane of equal contributions and the line passing through the point of intersection of the beam of coordinated development with the plane of equal contributions and representing the point

Implementation of annihilation and junction reactions in vector density-based continuum dislocation dynamics

In a continuum dislocation dynamics (CDD) formulation by Xia and El-Azab (2015 Modelling Simul. Mater. Sci. Eng. 23 055009), dislocations are represented by a set of vector density fields, one per crystallographic slip systems. The space-time evolution of these densities is obtained by solving a set of dislocation transport equations coupled with crystal mechanics. Here, we present an approach for incorporating dislocation annihilation and junction reactions into the dislocation transport equations. These reactions consume dislocations and result in nothing as in the annihilation reactions, or produce new dislocations of different types as in the case of junction reactions. Collinear annihilation, glissile junctions, and sessile junctions are particularly emphasized here. A generalized energy-based criterion for junction reactions is established in terms of the dislocation density and Burgers vectors of the reacting species, and the reaction rate terms for junction reactions are formulated in terms of the dislocation densities. In order to illustrate how the dislocation network changes as a result of junction formation and annihilation in a CDD setting, we present some numerical examples focusing on the reactions processes themselves. The results show that our modeling approach is able to capture the respective dislocation network changes associated with dislocation reactions in FCC crystals: dislocations of opposite line directions encountering each other on collinear slip systems annihilate to connect the dislocations on the two slip systems, glissile junctions form on new slip system behave like Frank–Read sources, and sessile junctions form and expand along the intersection of the slip planes of the reacting dislocation species. A collective-dynamics test showing the frequency of occurrence of junctions of different types relative to each other is also presented.

Extrinsic Calibration of Multiple Two-Dimensional Laser Rangefinders Based on a Trihedron.

Multiple two-dimensional laser rangefinders (LRFs) are applied in many applications like mobile robotics, autonomous vehicles, and three-dimensional reconstruction. The extrinsic calibration between LRFs is the first step to perform data fusion and practical application. In this paper, we proposed a simple method to calibrate LRFs based on a corner composed of three mutually perpendicular planes. In contrast to other methods that require a special pattern or assistance from other sensors, the trihedron corner needed in this method is common in daily environments. In practice, we can adjust the position of the LRFs to observe the corner until the laser scanning plane intersects with three planes of the corner. Then, we formed a Perspective-Three-Point problem to solve the position and orientation of each LRF at the common corner coordinate system. The method was validated with synthetic and real experiments, showing better performance than existing methods.

Motion robust 4D-MRI sorting based on anatomic feature matching: A digital phantom simulation study

PurposeMotion artifacts induced by breathing variations are common in 4D-MRI images. This study aims to reduce the motion artifacts by developing a novel, robust 4D-MRI sorting method based on anatomic feature matching and applicable in both cine and sequential acquisition. MethodThe proposed method uses the diaphragm as the anatomic feature to guide the sorting of 4D-MRI images. Initially, both abdominal 2D sagittal cine MRI images and axial MRI images were acquired. The sagittal cine MRI images were divided into 10 phases as ground truth. Next, the phase of each axial MRI image is determined by matching its diaphragm position in the intersection plane to the ground truth cine MRI. Then, those matched phases axial images were sorted into 10-phase bins which were identical to the ground truth cine images. Finally, 10-phase 4D-MRI were reconstructed from these sorted axial images. The accuracy of reconstructed 4D-MRI data was evaluated by comparing with the ground truth using the 4D eXtended Cardiac Torso (XCAT) digital phantom. The effects of breathing signal, including both regular (cosine function) and irregular (patient data) in both axial cine and sequential scanning modes, on reconstruction accuracy were investigated by calculating total relative error (TRE) of the 4D volumes, Volume-Percent-Difference (VPD) and Center-of-Mass-Shift (COMS) of the estimated tumor volume, compared with the ground truth XCAT images. ResultsIn both scanning modes, reconstructed 4D-MRI images matched well with ground truth with minimal motion artifacts. The averaged TRE of the 4D volume, VPD and COMS of the EOE phase in both scanning modes are 0.32%/1.20%/±0.05 ​mm for regular breathing, and 1.13%/4.26%/±0.21 ​mm for patient irregular breathing. ConclusionThe preliminary evaluation results illustrated the feasibility of the robust 4D-MRI sorting method based on anatomic feature matching. This method provides improved image quality with reduced motion artifacts for both cine and sequential scanning modes.

High accuracy linear method for axis measurement

The attitude parameter is an important state parameter for a long axisymmetric target. The plane intersection (PI) method is a commonly used method for attitude estimation. However, this method only uses planes’ information in the object space under a multiple camera system (more than two cameras simultaneously observing a target). We propose two methods to address the aforementioned issue. One method involves minimizing the square of the object-space angle residual (OAR) and the other method involves minimizing the square of the image-space angle residual (IAR). The linear optimization method is used for the above minimizing problems. The simulation results demonstrate that the IAR method has higher accuracy than the PI and OAR methods under multiple and dual camera systems because it incorporates information of a pair of corresponding image points. Furthermore, our experiments have shown that the linear method is generally faster, and it has an equivalent accuracy compared to the iterative method.

Comparison of Bilateral Mandibular Angle Ostectomy Between East Asian Males and Females: A Study Based on Three-Dimensional Computed Tomography Reconstruction.

Mandibular angle ostectomy is a common plastic surgery for facial contouring in East Asians. However, rarely we could find reports on differences between East Asian males and females undergoing this surgery. To describe the differences between East Asian males and females before and after mandibular angle ostectomy. A total of 22 Asian males and 52 Asian females who underwent mandibular angle ostectomy from April 2015 to November 2018 were enrolled. Three-dimensional computed tomography was used to evaluate the preoperative and postoperative data of the mandible. Thirteen clinical data were measured on reconstructed mandibular models. The differences in data between males and females were analyzed to identify the causes of the differences before and after surgery. The follow-up was 6-12months, and patient satisfaction was also evaluated. The ostectomy volumewas positively correlated with the distance from the intersection of the occlusal plane and the anterior margin of the mandibular ramus to gonion (MR-Go; female, p < 0.01; male, p = 0.02). There was a positive correlation between the ostectomyvolume and the postoperative drainage fluid (The drainage fluid is mainly blood)volumeafter surgery in females (p < 0.05), while there is no significant correlation between these two data in males (p = 0.19). Patients with a long distance from the second molar to the lower edge of the mandibular body (SM-MB) tended to have a higher risk of postoperative bleeding (female, r = 0.56, p < 0.01; male, r = 0.73, p = 0.01). Because of the difference in the anatomical size of the mandible and different aesthetic requirements for facial contouring between males and females, surgeons encounter different intraoperative conditions resulting in difficulties during surgery. Understanding differences in mandibular angles predicts differences in ostectomyvolume and postoperative bleeding risk, thus aiding surgeons and leading to better operative outcomes. This journal requires that authors assign a level of evidence to each article. For a full description of these Evidence-Based Medicine ratings, please refer to the Table of Contents or the online Instructions to Authors www.springer.com/00266.

Quaternary environmental evolution in the South Carpathians reconstructed from glaciokarst geomorphology and sedimentary archives

The Carpathian island-type glaciokarst has a great potential of preserving signals of past environments, archived in cave deposits like speleothems and clastic infills. We present here the geomorphology and structural control of several relict alpine caves and the surrounding glaciated marble karst in the Făgăraș Mountains. Four truncated and partially unroofed caves remained on the ridge-top of Mușeteica Mountain, above the glacial cirque, while a ponor cave that developed on the cirque bottom could be related to the Last Glacial Period. Structural measurements and cave morphology showed that the conduits formed at the intersection of foliation planes and tectonic fractures on the NE-SW and NW-SE directions. Cave development reflects three speleogenetic stages: 1) texture- and fabric-controlled dissolution and distension; 2) structurally-controlled breakdown; and 3) truncation, unroofing, and cave infilling with sediments. Slow diffuse dissolution was typical for the ridge-top caves, whereas M1 Cave developed by pressure flow.Further, we report the first UTh speleothem ages, related to the evolution of alpine caves and island glaciokarst in the South Carpathians during the Middle and Late Pleistocene. Dating results show a minimum estimated age of ~560 ka for the ridge-top caves, and that speleothem deposition met optimal conditions only during warmer periods, largely corresponding to interglacials. Stable carbon isotope values in speleothems range between −9.96‰ and −4.11‰, indicating the presence of plant and soil organic activity at the time of deposition. In total, five speleothem growth phases were distinguished during the last ~560 ka.We excavated the sediment infill of a ridge-top doline down to a 2-m depth. Radiocarbon dating revealed that it was deposited during the Late Holocene, and preliminary pollen analysis identified a plant assemblage dominated by grasses.Using the relationships between karst development, glaciation, and cave sedimentary archives, we present a time slice chronology of alpine landscape evolution at >560 ka, ~400 ka, ~330 ka, the Last Glacial Period (70–12 ka), and the Late Holocene. Our geomorphological, isotopic, and geochronological results also support the existing hypothesis that the South Carpathians may have experienced at least two glacial phases during the Pleistocene. Glacial erosion rate during the Last Glacial Period, and most likely during the penultimate glaciation, averages around 0.6 mm yr−1.

Образование нанометровых трещин и фрактолюминесценция при разрушении углеродной керамики

Raman spectrum of the surface layer with a thickness of approximately 80 nm of a porous carbon ceramic was obtained (the porosity was used equal to 5%). Spectrum analysis showed that the ceramics contains crystals of silicon carbide - 6H-SiC and silicon. The destruction of ceramics by diamond microcrystals resulted in fractoluminescence (FL). Spectrum of FL contains two bands at 1.6 and 1.9 eV. The first band is formed by breaking down the silicon crystals, and the second band is formed by breaking down the 6H-SiC crystals. The time dependence of the intensity of FL signals with a time resolution of 2 ns is obtained. Three types of signals were observed: one type of signal is formed when the 6H-SiC crystals break down, the second type of signal is formed when the silicon crystals break down, and the third type of signal is formed when these crystals break down simultaneously. The appearance of signals is associated with the formation of cracks arising from the breaking down of the barriers formed at the intersection of slip planes of dislocations in silicon carbide and silicon crystals. The size of cracks in 6H-SiC is estimated: the smallest ones is 5.5 nm, and the largest is approximately 18 nm.

Digital Objects in Rhombic Dodecahedron Grid

Abstract Rhombic dodecahedron is a space filling polyhedron which represents the close packing of spheres in 3D space and the Voronoi structures of the face centered cubic (FCC) lattice. In this paper, we describe a new coordinate system where every 3-integer coordinates grid point corresponds to a rhombic dodecahedron centroid. In order to illustrate the interest of the new coordinate system, we propose the characterization of 3D digital plane with its topological features, such as the interrelation between the thickness of the digital plane and the separability constraint we aim to obtain. We also present the characterization of 3D digital lines and study it as the intersection of multiple digital planes. Characterization of 3D digital sphere with relevant topological features is proposed as well along with the 48-symmetry appearing in the new coordinate system.

Toolpath algorithm for free form irregular contoured walls / surfaces with internal deflecting connections

This paper presents a toolpath generation method to efficiently machine free form irregular contoured walls / surfaces (FIWS) containing internal deflecting connections (IDC’s). The toolpath generation method is based on a series of identifications and calculations, where initially a ‘Main Computable Zone (MCZ)’ in the Machinable Areas (Ma’s) of FIWS is identified based on the Tool track dimensions (Td). Then the MCZ’s are divided into Split Computable Zones (SCZ’s) and Split Computable Zones for Internal Connections (SCZI’s) which are subsequently sub divided as ‘Categorized Computable Zones’ (CCZ) with simple-medium-high complexity. The identification of CCZ’s is based on the 10 different types of FIWS representations developed for this study. From the CCZ’s categorization of complexity, they are further split into smaller ‘Machinable Zones (MZ’s)’ using a 4-step algorithm. In the algorithm, the first step calculates a common plane (CP) to cut the steep areas in the CCZ’s where the tool cannot have full access for machining. Once the CP is identified, the second step is to extend it by moving them along the CCZ’s and calculate the necessary ‘Machinable Zones (MZ’s)’ in the next stage. This is done by finding the intersection of CP with the FIWS through a point to point / line plane intersection concept. After this step, the MZ’s are re-iterated by including the open and closed surface criteria and is analyzed for the IDC’s to be combined in the fourth stage. This is achieved by adding up the IDC’s with the existing MZ’s computed by the algorithm. At every stage, the algorithm considers tool collision avoidance and tool rubbing in the CCZ’s and MZ’s . This is by an automatic computation based on the height to fixture clearance for safer neck length which avoids collision and rubbings in the final toolpaths. Finally, a combined tool path is generated for all the MZ’s and has been verified / tested for a sample part and impeller containing similar shapes using UG NX / STEP –NC software.

Evaluating Angularity of Coarse Aggregates Using the Virtual Cutting Method Based on 3D Point Cloud Images

In this paper, a new method called the Virtual Cutting Method is proposed to evaluate the angularity index (AI) values of 3D point cloud coarse aggregate images with the aim of characterizing the angularity of aggregates on conveyor belts. The 3D point cloud images of coarse aggregates were first captured, preprocessed, and segmented into single 3D aggregate objects. Based on the processed 3D aggregate images, intersection contours were extracted using a series of intersection planes with an equivalent angle between two adjacent planes. The AI was evaluated by averaging the angularity of the contours using the gradient method, which was used in the AIMS2 system. Statistical analysis was then performed to select the optimum angle between two adjacent planes. It was found that an angle of five degrees was the ideal angle, as it can balance the execution time and effectiveness of the method. Finally, the AI results of the Virtual Cutting Method were compared with those of 2D and 3D Projection Methods. It was found that the AI rankings of the three methods for different aggregate textures are generally consistent. The findings of this study conclude that the Virtual Cutting Method can be employed to quantify the angularity of a single aggregate or aggregates in piles on conveyor belts based on 3D point cloud images.

Modeling of geometry and insertion force of a new lancet medical needle.

Lancet needle is a typical medical treatment device. Its tip consists of two lancet planes and one bevel plane. When the lancet needle is inserted into soft organ tissue, the insertion force may influence the needle cutting direction and treatment effect and increase the pain. One of the main factors affecting this insertion force is the geometry of the needle tip. Based on the research on the shape and processing method of the conventional lancet needle, a new lancet needle tip geometry was obtained by adjusting the relative position of the grinding wheel to the needle. A mathematical model of this new lancet needle was established. The relationship between processing parameters and needle shape was analyzed, and the needle insertion force was predicted. Compared with the conventional lancet needle, the new lancet needle is sharper, and the insertion force on the cutting edge is smaller. However, this change in the grinding position of the needle lancet plane has a great influence on the shape of needle tip near the intersection of the bevel plane and the lancet plane. Some special second bevel angle and rotated angle will cause a large change in the specific force at the intersection place, which is not conducive to reducing the insertion force.

Research on Reasonable Spacing of Adjacent Highway Plane Intersections

In China’s relevant specifications, the minimum spacing of plane intersections is simply defined according to the grade of highway, and the design speed of intersections and the influence of intersection geometry are not considered. In this paper, the traffic flow characteristics of road sections, the influencing factors of the intersection of road intersections and the sections between plane intersections are divided into entry points. The intersection functional zone and the length of smooth running zone are theoretically analysed. According to the influence of factors, the length of each segment is calculated separately, and the reasonable spacing index of the intersection is proposed.

Traffic Safety Analysis of Highway Plane Intersection

As a meeting point of motor vehicles, non-motor vehicles, pedestrians, etc., road intersections are prone to traffic safety accidents, which in turn seriously affect traffic order. This paper studies the causes of frequent occurrences of road intersections from the aspects of people, vehicles, road traffic environment and management, analyses the existing road junction accident prevention measures, and bases on the intersection accidents and existing accident prevention measures, proposes several measures for the government and related enterprises. The effective prevention and control of traffic accidents at highway intersections is a complex system project, which requires the participation and efforts of all parties. This study can also provide reference for this.

Synthesis, growth, linear and nonlinear optical, electrical and surface studies of a hybrid nonlinear optical material: [Hg3CdCl2(SCN)6

The hybrid non-linear optical (NLO) material of mercury cadmium chloride thiocyanate [Hg3CdCl2(SCN)6] (MCCTC) single crystal with a dimension of 10 × 5 × 5 mm3 was grown by the slow evaporation method. Further, the crystal structure and lattice constants were calculated and confirmed by a single crystal x-ray diffraction measurement. The powder x-ray diffraction (PXRD) study was used to calculate the periodic intersection of lattice planes (h k l). Further, high-resolution x-ray diffraction (HXRD) study indicated the presence of two-dimensional (2D) defects in MCCTC single crystal. The surface morphology and present of the various chemical compositions of MCCTC single crystal were analyzed by FESEM and EDAX analyzer. The reverse growth rate of the grown crystal was estimated by etching studies. The existence of well-designed various functional groups and the coordination of C-N stretching vibrations in a grown MCCTC were identified through FT-IR and further confirmed by FT-Raman spectroscopy. The single crystal of MCCTC has the optical band gap of ∼4.33 eV and ∼58% of optical transmittance, which was calculated from UV–vis-NIR spectroscopy by Tauc’s relation. The third and second harmonic generation was calculated by the Z- scan and Kurtz powder technique. The measured value of higher (third harmonic) harmonic generation of real and imaginary parts of non-linear susceptibility χ(3) is found to be 2.44 × 10–9 esu. The NLO efficiency of MCCTC was 17 times superior to potassium dihydrogen phosphate (KDP), 3 times superior to urea and other organometallic thiocyanate families. Additionally, electrical and dielectric properties (dielectric constant and loss) of MCCTC were measured using impedance spectrometer.

Aircraft Pose Estimation Based on Geometry Structure Features and Line Correspondences.

A robust and accurate aircraft pose estimation method is proposed in this paper. The aircraft pose reflects the flight status of the aircraft and accurate pose measurement is of great importance in many aerospace applications. This work aims to establish a universal framework to estimate the aircraft pose based on generic geometry structure features. In our method, line features are extracted to describe the structure of an aircraft in single images and the generic geometry features are exploited to form line groups for aircraft structure recognition. Parallel line clustering is utilized to detect the fuselage reference line and bilateral symmetry property of aircraft provides an important constraint for the extraction of wing edge lines under weak perspective projection. After identifying the main structure of the aircraft, a planes intersection method is used to obtain the 3D pose parameters based on the established line correspondences. Our proposed method can increase the measuring range of binocular vision sensors and has the advantage of not relying on 3D models, cooperative marks or other feature datasets. Experimental results show that our method can obtain reliable and accurate pose information of different types of aircraft.

The trajectory intersection: An approach for nonlinear down-sampling

Abstract Poincare section is a method for representing the trajectory of dynamical systems in terms of a set of discrete points in a lower dimension. Herein, inspired by the idea of the Poincare section, we proposed a method for drastically reducing the size of a data set that describes a dynamical system, principally a dynamical system operating in the chaotic regime, while retaining its essential information. The main idea of the proposed method is finding an optimal plane intersecting the trajectory of the system based on information entropy. First, a novel formulation of the trajectory intersection as a differentiable closed form transformation is proposed. Then, optimal parameters of the intersection plane are found through numerical optimization. Finally, the resulting points are arranged in unique coordination by use of principal component analysis (PCA). Our findings indicate that this method is able to preserve the behavior of dynamical systems in both of the state space and time domain. Moreover, transitions of the system among dynamical regimes are detectable. Therefore, our methodology characterizes the dynamical system adequately while the number of samples is noticeably reduced.