Point Grids Research Articles

Optimizing algorithm for high-precision imaging stitching systems based on spline surfaces

As optical systems continue to advance, non-uniform rational B-spline (NURBS) surfaces increasingly being considered in asymmetric optical systems due to their localized control characteristics. However, the representation of NURBS surfaces has complicated the analysis of these systems, leading to a significant computational burden. To address this challenge, we propose an optimizing algorithm for imaging optical systems based on high-precision ray tracing of NURBS surfaces. This method initiates with getting a knot grid as prior information, in conjunction with the Newton-Raphson algorithm, to obtain high-precision numerical solutions for the intersection of rays with a NURBS surface. Building upon this methodology, we introduce an optimization technique that includes shape evaluation to generate an evaluation function specific to NURBS surfaces. This approach is then applied within a rapid optimization process that accounted for the region of ray influence. Under consistent control point grids and sampling ray conditions, we present an off-axis four-mirror system to showcase that our algorithm has achieved a computational efficiency improvement of approximately 14 times compared to the previous method. This high-precision imaging design based on spline surfaces fulfills the need for efficient and accurate algorithms for NURBS surface applications in various imaging systems, providing guidance for practical applications.

Study on the Characteristics of Trackside Acoustic Flow Field of High-Speed Train under the Influence of Crosswind.

During the on-track acoustic detection process, a potential flow model and an acoustic finite element mathematical model based on synthetic wind are utilized, taking into account the combined effects of vehicle speed, wind direction angle, and crosswind speed. Simulation and modeling are achieved using Automatic Matching of Acoustic Radiation Boundary Conditions (AML) technology, enabling obtaining a distribution map and sound pressure frequency response curve of the trackside acoustic field under crosswind conditions by setting up field point grids. It is found that sound pressure values at the same location gradually increase as the vehicle speed increases in the frequency range of 10 Hz to 70 Hz, at different vehicle speeds. The sound pressure values and distribution area of the trackside acoustic field are the largest when the crosswind speed is 10 m/s (wind force at level five), allowing for easier location of the sound source when a fault occurs. The study also reveals that under different wind direction angles, the same location's sound pressure value on the trackside gradually decreases as the wind direction angle increases, to lower than that of the non-crosswind condition, severely hindering the reception and diagnosis of acoustic signals.

Enhancing extraction of two-dimensional engineering drawings from three-dimensional data of existing buildings

Accurately extracting two-dimensional (2D) engineering drawings from existing buildings' three-dimensional (3D) data is crucial for building renovation, protection, and research. This research aims to optimize existing algorithms and propose new ones to achieve fast, automatic, accurate, and rich-information extraction of 2D engineering drawings. The study focuses on 2D orthographic drawings, the curvature analysis of 3D models, the conversion from point grids to polylines, and the automated dimensioning of drawings. Novel methods are utilized to analyze 3D data based on obtained point cloud and mesh models. In our experiments, each model required four days of fieldwork and ten days of data processing. The automated approach generated accurate 2D curve drawings, significantly more efficient than manual drawing in Autocad software. The dimensioning work, typically taking hours, was completed in just 2 min using a computer algorithm. The critical contribution of this study lies in providing essential theoretical and practical guidance for promoting the development of digital building technology and engineering practice. This research introduces optimized algorithms and novel methods for extracting 2D engineering drawings from 3D data, addressing the challenges of accuracy, efficiency, and information richness. The efficiency gains achieved and the integration of automation highlight the novelty of this research.

The behavior mapping of masonry arches subjected to lumped deformations

This work presents the proof-of-concept for a fast and cheap non-destructive monitoring system called “Behavior Mapping BP” for the analysis up to collapse of masonry. It belongs to a vision-based measurement similar to DIC but much more straightforward and inexpensive. It identifies and quantifies mechanical deformations between rigid blocks solely through a 4x4 point grid and works by extracting data from videos. First, the possible motions between two rigid blocks are described and followed by how the point grids can identify and quantify their motions through repeated calculations of lengths, dot products, and right triangles. Two benchmark tests were performed to validate the approach. The first was through images of defined deformations and the second was video recordings of an in-scale arch subjected to horizontal springing settlement. 2D homography provided the key to transform the recorded point grids to the cartesian plane for measurement. Finally, the procedure is successfully applied to a case study of a video recorded failure of a 27-block arch: with only the knowledge of the point grid template and extracting images from the video, the mechanical joints motions are identified and quantified. The procedure can be easily applied to any masonry wall in-plane loaded and -using more than one camera- to out-of-plane loaded panels.

Atomic growing for grid alignment

Detecting and aligning structured signals such as point grids plays a fundamental role in many signal processing applications. Joint determination of non-grid points and estimation of non-linear spatial distortions applied to the grid is a key challenge for grid alignment. This paper proposes a candidate solution. The method described herein starts from a small nearly regular region found in the point set and then expands the list of candidate points included in the grid. The proposed method was tested on geometrically transformed point sets and sets of locations derived from imagery of 3D prints. It is shown that a low-complexity grid alignment method can nonetheless achieve high grid alignment accuracy.

Estimation in Partially Observed Functional Linear Quantile Regression

Currently, working with partially observed functional data has attracted a greatly increasing attention, since there are many applications in which each functional curve may be observed only on a subset of a common domain, and the incompleteness makes most existing methods for functional data analysis ineffective. In this paper, motivated by the appealing characteristics of conditional quantile regression, the authors consider the functional linear quantile regression, assuming the explanatory functions are observed partially on dense but discrete point grids of some random subintervals of the domain. A functional principal component analysis (FPCA) based estimator is proposed for the slope function, and the convergence rate of the estimator is investigated. In addition, the finite sample performance of the proposed estimator is evaluated through simulation studies and a real data application.

Efficient lattice dynamics calculations for correlated materials with DFT+DMFT

Phonons are fundamentally important for many materials properties, including thermal and electronic transport, superconductivity, and structural stability. Here, we describe a method to compute phonons in correlated materials using state-of-the-art DFT+DMFT calculations. Our approach combines a robust DFT+DMFT implementation to calculate forces with the direct method for lattice dynamics using nondiagonal supercells. The use of nondiagonal instead of diagonal supercells drastically reduces the computational expense associated with the DFT+DMFT calculations. We benchmark the method for typical correlated materials (Fe, NiO, MnO, SrVO$_3$), testing for $\mathbf{q}$-point grid convergence and different computational parameters of the DFT+DMFT calculations. The efficiency of the nondiagonal supercell method allows us to access $\mathbf{q}$-point grids of up to $6\times6\times6$. In addition, we discover that for the small displacements that atoms are subject to in the lattice dynamics calculation, fixing the self-energy to that of the equilibrium configuration is in many cases an excellent approximation that further reduces the cost of the DFT+DMFT calculations. This fixed self-energy approximation is expected to hold for materials that are not close to a phase transition. Overall, our work provides an efficient and general method for the calculation of phonons using DFT+DMFT, opening many possibilities for the study of lattice dynamics and associated phenomena in correlated materials.

Generalized regular k-point grid generation on the fly

In the DFT community, it is common practice to use regular k -point grids (Monkhorst-Pack, MP) for Brillioun zone integration. Recently Wisesa et al. (2016) and Morgan et al. (2018) demonstrated that generalized regular (GR) grids offer an advantage over traditional MP grids. The difference is simple but effective. At the same k -point density, GR grids have greater symmetry and 60% fewer irreducible k -points. GR grids have not been widely adopted because one must search through a large number of candidate grids; in many cases, a brute force search could take hours. This work describes an algorithm that can quickly search over GR grids for those that have the most uniform distribution of points and the best symmetry reduction. The grids are ∼ 60% more efficient, on average, than MP grids and can now be generated on the fly in seconds.

Theory of generalized discrepancies on a ball of arbitrary finite dimensions and algorithms for finding low-discrepancy point sets

One of the objectives of this paper is to extend the idea of the generalized discrepancy to the ball of arbitrary finite dimensions and to study its properties. We first construct orthonormal systems in higher dimensions, Sobolev spaces as well as particular differential operators. The discrepancy is then derived from an error estimate for numerical integration on a ball. We also present some new statistical and numerical properties of the generalized discrepancy which have also been unknown in three dimensions before. In addition, this paper focuses on constructing and implementing novel algorithms in order to obtain low-discrepancy point grids on the ball. Such low-discrepancy grids are uniformly distributed and are appropriate for quadrature rules (sometimes also called cubature rules) and as centres of localized trial functions in tomographic inverse problems on the ball. For this purpose, we also consider the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm and examine different BFGS updates and line search methods.

Combination of Isogeometric analysis and level-set method in topology optimization of heat-conduction systems

In this paper, an isogeometrical approach for topology optimization in two-dimensional heat-transfer problems, including a concentrated heat flow and uniformly distributed heat generation has been developed using the level-set method and reaction–diffusion equation for the evolution of the design variables. The NURBS surface illustrates the exact geometry representation and the level sets lead to the identification of topological variation in the NURBS surface. The level-set surface is extended based on the value of the design variables at the control points of the NURBS surface as an implicit dynamic hyper-surface in higher dimension. The same basis functions are employed to approximate the unknown temperatures and geometry modeling. Since the coordinates of the level-set grids are similar to the coordinates of the control point grids, the sensitivity analysis of the control point grids is obtained and used as a velocity field, to evolution the reaction–diffusion equation. Then, any change in the coordinates of the level-set grids is mapped over the physical domain which is parameterized using NURBS. In the optimization formulation, the heat transfer potential capacity is considered as the objective function. Also, the constraint is the maximum volume fraction of the material. Finally, several numerical examples are presented to demonstrate the optimal topology described in CAD systems and its sensitivity to various loading.

A robust algorithm for k-point grid generation and symmetry reduction

We develop an algorithm for i) computing generalized regular -point grids, ii) reducing the grids to their symmetrically distinct points, and iii) mapping the reduced grid points into the Brillouin zone. The algorithm exploits the connection between integer matrices and finite groups to achieve a computational complexity that is linear with the number of -points. The favorable scaling means that, at a given -point density, all possible commensurate grids can be generated (as suggested by Moreno and Soler) and quickly reduced to identify the grid with the fewest symmetrically unique -points. These optimal grids provide significant speed-up compared to Monkhorst–Pack -point grids; they have better symmetry reduction resulting in fewer irreducible -points at a given grid density. The integer nature of this new reduction algorithm also simplifies issues with finite precision in current implementations. The algorithm is available as open source software.

Validation of three-dimensional echocardiographic principal strain analysis for assessing left ventricular contractility: An animal study.

The three-dimensional (3D) principal strain represents the major direction and magnitude of the deformation by its definition and can be measured using 3D echocardiography. We aimed to validate 3D echocardiographic left ventricular (LV) global principal strains as an assessment of LV contractility by comparison with gold standard invasive measurements. In 14 beagles, the LV pressure-volume loop was recorded to invasively measure the end-systolic pressure-volume relationship (ESPVR) and dP/dt as reference indicators representing LV contractility. The echocardiographic image was obtained simultaneously, and endocardial motions and volume changes were extracted in the form of speckle-tracking point grids to calculate strains. High or low inotropic states were induced pharmacologically by using an intravenous infusion of dobutamine and esmolol, respectively. The direction of 3D endocardial global principal strain (GP1S) appeared to be circumferential. The dP/dt showed the highest Pearson's correlation coefficients with GP1S (r = -0.845, P < 0.001), whereas ESPVR showed the best correlation with global secondary strain (GP2S; r = -0.819, P < 0.001). In comparison with GP1S and GP2S, global circumferential (GCS) and longitudinal strains (GLS) tended to correlate less with invasive measurements, respectively. LV ejection fraction showed excellent correlations with GP1S or GCS, but the correlation with GLS was relatively weak. The correlations between invasive measurements and GP2S or GLS were strengthened when strains were corrected by the LV residual volume ratio, whereas those of GP1S or GCS were weakened after correction. The principal direction of the LV endocardial contraction presents circumferential behavior reflecting LV volume change. The 3D principal strains derived from 3D echocardiography are reliable indicators for LV contractility and seem better than conventional strains.

Pressure overload induced right ventricular remodeling is not attenuated by the anti-fibrotic agent pirfenidone.

Cardiac fibrosis contributes to the development of heart failure in pulmonary hypertension. We aimed to assess the development of fibrosis and the effects of treatment with the anti-fibrotic agent pirfenidone in pressure overload induced right ventricular (RV) failure. Wistar rat weanlings were randomized to pulmonary trunk banding (PTB) or sham surgery. One week after the procedure, PTB rats were randomized into two groups with either six weeks on standard chow or treatment with pirfenidone mixed in chow (700 mg/kg/day). RV hemodynamic effects were evaluated by echocardiography, cardiac magnetic resonance imaging (MRI), and pressure-volume measurements. Sections from the isolated RV, left ventricle, and septum were sampled systematically; stereological point grids and the nucleator were used to estimate volume of fibrosis and cardiac hypertrophy, respectively. PTB caused RV failure in all rats subjected to the procedure. The volume fraction of fibrosis in the RV increased threefold in PTB rats corresponding to a sixfold increase in total volume of RV fibrosis. Volume fraction of fibrosis and total volume of fibrosis also increased in the septum and in the left ventricle. Pirfenidone reduced body weight but did not improve RV hemodynamics or reduce cardiac fibrosis. RV cardiomyocyte profile area was increased twofold in PTB rats without any effect of pirfenidone. RV pressure overload after PTB induced not only RV but also septal and left ventricular fibrosis assessed by stereology. Treatment with pirfenidone reduced body weight but did not reduce the development of cardiac fibrosis or delay the progression of RV failure.

EFFECT OF LONG-TERM VAGOTONIA ON STRUCTURAL CHANGES IN THE WALL OF ABDOMINAL AORTA DURING IMMOBILIZATION STRESS IN EXPERIMENTAL STUDY

This work covers current questions on studying structural changes in the wall of the abdominal aorta during the modelled long-term immobilization stress against vagotonia. The purpose of this study was to reveal the effect of prolonged vagotonia on the structure of the wall of the abdominal aorta in rats in the experiment. The studies were performed on three comparable groups of hundred-day Wistar rats, which were exposed to immobilization stress and vagotonia for a period of 10 days. Immobilization was chosen as a method to induce stress model. The rats were placed into a special plastic box, in this way limiting their movements for four hours at room temperature. Vagotonia was modelled by the administration of pyridostigmine bromide, reversible anticholinesterase. Histological preparations of the abdominal aorta were studied by x40, x100, x400 magnification using the Primo Star 5 microscope (Carl Zeiss, FRG) followed by photography of microscopic images. Computer morphometry was performed with x100 and x400 magnification and then the image were displayed on the computer monitor using the DVR and AxioVision image analysis software (Rel.4.8.2) in μm. We assessed the thickness of the subendothelial layer, and namely an internal elastic membrane and media. The ratio of the extent of the abdominal aorta lumen to the vascular wall was calculated in the Adobe Photoshop program by the A. A. Glagoliev method through overlaying of point grids on sections, the results were converted into percentages. The studies were carried out in five fields of five different sections in each rat. The results of the variation analysis of the morphological data obtained have revealed some features of restructuring the vascular wall of the abdominal aorta due to prolonged immobilization stress accompanied by vagotonia. It has been found out that prolonged exposure of hundred-day Wistar rats to immobilization stress leads to a decrease in thickness and certain morphological changes in all layers of the abdominal aorta wall and a decrease in the percentage of the component of the vessel wall. When accompanied by prolonged immobilization and vagotonia, preservation of the endothelial layer of the abdominal aorta was observed against the background of a decrease in intimal thickness and degenerative cell changes, as well as media thickening and focal changes in adventitia.

Efficiency of Generalized Regular [formula omitted]-point grids

Most DFT practitioners use regular grids (Monkhorst-Pack, MP) for integrations in the Brillouin zone. Although regular grids are the natural choice and easy to generate, more general grids whose generating vectors are not merely integer divisions of the reciprocal lattice vectors, are usually more efficient (Wisesa et al., 2016). We demonstrate the efficiency of generalized regular (GR) grids compared to Monkhorst-Pack (MP) and simultaneously commensurate (SC) grids. In the case of metals, for total energy accuracies of one meV/atom, GR grids are 60% faster on average than MP grids and 20% faster than SC grids. GR grids also have greater freedom in choosing the k-point density, enabling the practitioner to achieve a target accuracy with the minimum computational cost.

Distribution of Connective Tissue in the Male and Female Porcine Liver: Histological Mapping and Recommendations for Sampling

The pig is a large animal model that is often used in experimental medicine. The aim of this study was to assess, in normal pig livers, sexual dimorphism in the normal fraction of hepatic interlobular and intralobular connective tissue (CT) in six hepatic lobes and in three macroscopical regions of interest (ROIs) with different positions relative to the liver vasculature. Using stereological point grids, the fractions of CT were quantified in histological sections stained with aniline blue and nuclear fast red. Samples (415 tissue blocks) were collected from healthy piglets, representing paracaval, paraportal and peripheral ROIs. There was considerable variability in the CT fraction at all sampling levels. In males the mean fraction of interlobular CT was 4.7±2.4% (mean±SD) and ranged from 0% to 11.4%. In females the mean fraction of the interlobular CT was 3.6±2.2% and ranged from 0% to 12.3%. The mean fraction of intralobular (perisinusoidal summed with pericentral) CT was <0.2% in both sexes. The interlobular CT represented >99.8% of the total hepatic CT and the fractions were highly correlated (Spearman r=0.998, P <0.05). The smallest CT fraction was observed in the left medial lobe and in the paracaval ROI and the largest CT fraction was detected in the quadrate lobe and in the peripheral ROI. For planning experiments involving the histological quantification of liver fibrosis and requiring comparison between the liver lobes, these data facilitate the power analysis for sample size needed to detect the expected relative increase or decrease in the fraction of CT.

Measurement point density and measurement methods in determining the geometric imperfections of shell surfaces

Abstract In geodetic measurements of deformations in shell cooling towers, an important factor is to optimize the number of points representing the exterior surface of the shell. The conducted analyses of damage to such structures proved that cooling towers exhibited shell deformation consisting of irregular vertical waves (three concavities and two convexities), as well as seven horizontal waves. On this basis, it is claimed that, in accordance with the Shannon theorem, the correct representation of the generated waves requires the measurement of the cooling tower shell in a minimum of 12 vertical and 14 horizontal sections. Such density of the points may not be sufficient to represent local imperfections of the shell. The article presents the results of test measurements and their analysis, which were conducted to verify the assumptions as to the optimal number of measurement points for the shell of a cooling tower. The evaluation was based on a comparative analysis of the data obtained by the Terrestrial Laser Scanning (TLS) method, creating a very detailed model of geometric imperfections in an actual cooling tower with a height of 100 m. Based on the data obtained by the TLS method, point grids of various density were generated. An additional measurement of the cooling tower shell deformation was performed using a precise electronic total station with reflectorless measurement option. Therefore, it was possible to assess the accuracy of measurements by laser scanning in relation to measurements obtained by reflectorless total stations.

Numerical Simulation for Shale Gas Flow in Complex Fracture System of Fractured Horizontal Well

Abstract Complex fracture systems including natural fractures and hydraulic fractures exist in shale gas reservoir with fractured horizontal well development. The flow of shale gas is a multi-scale flow process from microscopic nanometer pores to macroscopic large fractures. Due to the complexity of seepage mechanism and fracture parameters, it is difficult to realize fine numerical simulation for fractured horizontal wells in shale gas reservoirs. Mechanisms of adsorption–desorption on the surface of shale pores, slippage and Knudsen diffusion in the nanometer pores, Darcy and non-Darcy seepage in the matrix block and fractures are considered comprehensively in this paper. Through fine description of the complex fracture systems after horizontal well fracturing in shale gas reservoir, the problems of conventional corner point grids which are inflexible, directional, difficult to geometrically discretize arbitrarily oriented fractures are overcome. Discrete fracture network model based on unstructured perpendicular bisection grids is built in the numerical simulation. The results indicate that the discrete fracture network model can accurately describe fracture parameters including length, azimuth and density, and that the influences of fracture parameters on development effect of fractured horizontal well can be finely simulated. Cumulative production rate of shale gas is positively related to fracture half-length, fracture segments and fracture conductivity. When total fracture length is constant, fracturing effect is better if single fracture half-length or penetration ratio is relatively large and fracturing segments are moderate. Research results provide theoretical support for optimal design of fractured horizontal well in shale gas reservoir.

Pseudo-differential Operators, Cubature and Equidistribution on the 3D ball: An Approach Based on Orthonormal Basis Systems

ABSTRACTIn this paper, the distribution of points on a unit ball in ℝ3 is investigated. The ansatz is motivated by an approach for point grids on the unit sphere by Cui and Freeden. A formula for a generalized discrepancy is developed, which is then used to check the uniformity of point grids on a ball. The generalized discrepancy originates from an error bound for a quadrature (cubature) rule on the ball with uniform weights. In particular, we discuss the integration of functions from particular Sobolev spaces based on known orthonormal systems on the ball. This includes the introduction of a concept of pseudo-differential operators on the ball. Finally, different point grids are constructed on the ball and are compared by the discrepancy. Furthermore, numerical and graphical comparisons of the grids are presented.

Converting heterogeneous complex geological models to consistent finite element models: methods, development, and application to deep geothermal reservoir operation

Static geological models representing complex geological systems are the prerequisite of dynamic model simulations applied for assessing subsurface processes. The corner point grid approach has been applied to represent the complexity in geometry, hydraulic connectivity, and heterogeneity found in these static geological models. Due to the occurrence of faults, pinch-outs, and eroded geological layers, corner point grids easily degenerate, which leads to model inconsistencies. This study introduces a workflow for converting heterogeneous geological models to consistent finite element models, accounting for regular and irregular hexahedral blocks of the corner point grid by converting to a set of hexahedra, prism, pyramid, and tetrahedral elements, based on the individual degeneration situation. Heterogeneous geological data such as permeability or porosity can be transferred layer-wise or on a block-wise basis. Additionally, well trajectories can be accurately mapped to the converted finite element mesh, to place the corresponding source terms. The developed workflow is tested on dedicated test cases and applied to convert a real complex field site from the North German Basin for use in a deep geothermal reservoir operation. The field application demonstrates the robustness and applicability of the newly developed conversion workflow and the suitability of the converted mesh for dynamic finite element reservoir model simulations.