Geometric Partitioning Research Articles

Non-uniform inlet flow definition for highly skewed model propeller by geometric partitioning

Ship design involves many calculations to provide a propulsion system with the appropriate speed. Prioritizing speed-resistance calculations affects main engine, gearbox, propeller, and other auxiliary system selection. Here, the propeller is most intriguing. Since the propeller operates in a fluid domain, internal and external factors affect it. Despite being designed for service speed, water flow can affect the efficiency of a propeller at the ship's stern. Under open-water circumstances, a ship's hull affects a propeller's hydrodynamic performance. The effect usually decreases propeller efficiency, so it's important to know how ship hull and propeller design interact before production. To overcome this issue, researchers test towing tanks extensively. Computational Fluid Dynamics, which is efficient and cost-effective, is also commonly used. This study examines the hydrodynamics of a fishing vessel's highly skewed model propeller. The objective of this study was to assess the propeller's efficiency under uniform and non-uniform flow conditions and investigate an alternative method for dividing the inlet area, which has not been studied in the literature. The study has effectively met its goals, producing satisfactory error margins for both operating conditions. This research significantly contributes to understanding the relationship between hull configuration and propeller design, particularly in non-uniform flow scenarios.

Three-dimensional motion vector translation for geometric partitioning mode in panoramic video coding using H.266/VVC

Three-dimensional motion vector translation for geometric partitioning mode in panoramic video coding using H.266/VVC

An efficient parameterized simulation framework for 3D scarf-repaired composite laminates

This paper proposes a parameterized simulation framework for predicting the load-bearing capacity of 3D scarf-repaired composite laminates which remarkably reduces the modeling time from several hours to just a few seconds. The specific implementation is demonstrated through a detailed step-by-step explanation. The main contribution lies in: (1) By introducing a reusable geometric partitioning method for composite layers and implementing a partitioning method-based numbering scheme for element and node, the effective management of element and node IDs of elements and nodes in such complex 3D models is greatly facilitated; (2) By ingeniously combining open-source meshing tools and text rewriting techniques, a highly efficient approach has been developed to construct complete models for such structures, showcasing the remarkable potential of these existing techniques in this field. The reliability of the efficient parameterized simulation framework proposed in this study is verified through the comparison between strength values acquired from progressive damage analysis (PDA) and experiment data reported in the existing literature.

Adaptive Merge Candidate Selection based on Geometric Partitioning Mode beyond Versatile Video Coding

Adaptive Merge Candidate Selection based on Geometric Partitioning Mode beyond Versatile Video Coding

Boltzmann-Shannon interaction entropy: A normalized measure for continuous variables with an application as a subsample quality metric.

The recent introduction of geometric partition entropy offered an alternative to differential Shannon entropy for the quantification of uncertainty as estimated from a sample drawn from a one-dimensional bounded continuous probability distribution. In addition to being a fresh perspective for the basis of continuous information theory, this new approach provided several improvements over traditional entropy estimators including its effectiveness on sparse samples and a proper incorporation of the impact from extreme outliers. However, a complimentary relationship exists between the new geometric approach and the basic form of its frequency-based predecessor that is leveraged here to define an entropy measure with no bias toward the sample size. This stable normalized measure is named the Boltzmann-Shannon interaction entropy (BSIE)) as it is defined in terms of a standard divergence between the measure-based and frequency-based distributions that can be associated with the two historical figures. This parameter-free measure can be accurately estimated in a computationally efficient manner, and we illustrate its utility as a quality metric for subsampling in the context of nonlinear polynomial regression.

An efficient geometric partitioning mode by adaptive blending method for screen content coding

AbstractGeometric partitioning mode (GPM) was newly adopted in Versatile Video Coding (VVC) to increase the partitioning precision of the arbitrary boundaries of actual objects. Note that the blending process of the GPM is not suitable for screen content with various sharp and strong edges. To alleviate this drawback, three new GPM matrices are introduced, and an efficient GPM is proposed to utilize four different GPM matrices and implicitly determine one of them depending on the discontinuity and gradients of the two predictors. The proposed method achieves an average BD‐rate reduction of 1.2% and 1.6% without additional computational complexity for random access and low‐delay B configurations, respectively, over the VVC test model (VTM18.0).

Analytical Evaluation of Time-Differentiated Retarded-Time Vector Potentials on SWG Bases

It is shown in this letter that the term of the time domain-radiated electromagnetic fields from a non-conductive object in a loss-free medium consisting of the time convolutions of the retarded-time vector potentials sampled on a Schaubert-Wilton-Glisson (SWG) spatial basis and a piecewise-polynomial temporal basis pair can be computed using only analytically-evaluated closed-form expressions. The corresponding impulsively-excited potentials are related to the mean vector and the solid angle measured from the intersection of the tetrahedron and the hyper-cone centered at the observation point. The closed-form expressions that appear after the convolution operations with the temporal-basis result in a novel volumetric integration scheme with a novel geometric partitioning of the above-mentioned intersection. The validity of the obtained formulae is demonstrated through the comparison of the results to those obtained in the frequency domain using numerical quadrature and transformed into the time domain.

Analysis of displacement evolution characteristics of reverse-dip layered rock slope based on geological geometric partition

To investigate the toppling displacement evolution characteristics of anti-dip rock slopes, the Xiaodongcao-Zhengjiadagou bank slope is taken as an engineering case, and firstly, the geological geometric distribution characteristics of the slope are obtained by superimposing the lithology, slope, and elevation raster layers of the slope through ArcGIS, and the geological partition with the largest area is the Lower Triassic Daye Formation, bottom elevation, and medium slope; based on the actual surface displacement monitoring data, the spatio-temporal evolution nephogram of toppling displacement of bank slope every half year is interpolated by Inverse Distance Weight method, and then the last displacement nephogram is assigned to the thousandth and superimposed with the geological geometric partition to obtain the displacement superposition characteristics. The results show that: the obvious zone of horizontal displacement deformation mainly occurs in the front and middle of the bank slope, mainly shear deformation, vertical displacement is primarily in the front and the back edge of the bank slope and the total displacement deformation is more similar to the horizontal displacement; the horizontal displacement value is larger than the vertical displacement value, the horizontal displacement deformation controls the overall deformation of the bank slope; through the analysis of the geometric superposition evolution of the anti-dip rock slope, the displacement superposition strong deformation zone is located at the boundary between the Triassic Jialingjiang Formation (T1j) and the Triassic Daye Formation (T1d).

Geometric Partition Entropy: Coarse-Graining a Continuous State Space

Entropy is re-examined as a quantification of ignorance in the predictability of a one dimensional continuous phenomenon. Although traditional estimators for entropy have been widely utilized in this context, we show that both the thermodynamic and Shannon’s theory of entropy are fundamentally discrete, and that the limiting process used to define differential entropy suffers from similar problems to those encountered in thermodynamics. In contrast, we consider a sampled data set to be observations of microstates (unmeasurable in thermodynamics and nonexistent in Shannon’s discrete theory), meaning, in this context, it is the macrostates of the underlying phenomenon that are unknown. To obtain a particular coarse-grained model we define macrostates using quantiles of the sample and define an ignorance density distribution based on the distances between quantiles. The geometric partition entropy is then just the Shannon entropy of this finite distribution. Our measure is more consistent and informative than histogram-binning, especially when applied to complex distributions and those with extreme outliers or under limited sampling. Its computational efficiency and avoidance of negative values can also make it preferable to geometric estimators such as k-nearest neighbors. We suggest applications that are unique to this estimator and illustrate its general utility through an application to time series in the approximation of an ergodic symbolic dynamics from limited observations.

Geometric Partitioning Mode with Inter and Intra Prediction for Beyond Versatile Video Coding

Geometric Partitioning Mode with Inter and Intra Prediction for Beyond Versatile Video Coding

Assessment of Mechanical Properties for Three-Dimensional Needled Composites: A Geometric Partitioning Strategy Dealing with Mesoscopic Needling Damage.

A geometric partitioning strategy was proposed to evaluate the mechanical properties of three-dimensional needled composites. The microstructure of the composite was divided to accurately characterize the mesoscopic damage in the needling regions and the macroscopic damage in the un-needling regions, to balance the computational accuracy and efficiency. The general method of cells (GMC) models along with the damage criteria were established for different material phases in the needling regions, while the continuum damage mechanics (CDM) model was adopted to portray the damage evolution in the un-needling regions. Through conducting the multi-scale simulation, the mechanical properties of the needled composites were predicted, based upon which the effect of repeated needling on the mesoscale damage process was further investigated. Results showed that the predictions are in good agreement with the experiments, with a relative error of 2.6% for strength and 4.4% for failure strain. The proposed approach can provide guidance for the process optimization and design of needled composites.

Bisecting envelopes of convex polygons

We introduce a new subject – bisecting deltoids – by giving status to two curves, the area-bisecting deltoid and the perimeter-bisecting deltoid of a convex polygon, of which the second is a new curve. These are the envelopes of all lines that bisect either the area or the perimeter of the polygon. The subject is located between the Euclidean and convex geometries in the same way as the elliptic and hyperbolic geometries are located between the Euclidean and differential geometries. We show that these curves have numerous geometric, differential, analytic, topological and combinatorial properties.From the direction of the Euclidean, differential and analytic geometries, we describe the two curves both as geometric and analytic loci. Particular emphasis is given to deltoids of quadrilaterals, which are classified, and those of regular polygons. Our results here extend the known results of [5], [15] and [51] on bisecting deltoids of triangles and those of [58] and [66] on area-bisecting deltoids of convex polygons.From the direction of convex geometry and combinatorial topology, we describe the area- or perimeter-bisecting partitions, or the incidence partitions – two partitions of the plane that are common to these curves. The area (perimeter) bisecting partition is the partition of the plane given by labeling each point by the number lines through it that bisect the area (perimeter) of the polygon. The same label is achieved by counting the number of tangents to the area (perimeter) bisecting deltoid that pass through the point. The bisecting partition is different from the geometric partition, which is common to any closed curve in the plane. Our description of the bisecting partition extends the known results of [45] and [66]. This is made possible by a new counting technique, the total sweep count.

Geometric partitioning schemes to reduce modeling bias in statistical volume elements smaller than the scale of isotropic and homogeneous size limits

In predicting failure of a material, small scale material properties are critical, and yet small scale random heterogeneities are difficult to characterize accurately and efficiently. In building fracture models, work has focused on statistical characterization of local random microstructure at small to intermediate scales (termed micro- or mesoscale). Many materials can be characterized as effectively isotropic and homogeneous at a large scale. In contrast, at a micro- or mesoscale, Statistical Volume Elements (SVE) often show significant anisotropy and heterogeneity. Characterizing the properties of SVE presents challenges because modeling choices, such as the length scale, boundary conditions applied, and boundary shape chosen, may introduce modeling bias.Modeling bias must be separated from the actual prediction of anisotropic and heterogeneous characteristics at the SVE level, in order to provide an accurate basis for fracture simulation. Much literature has been devoted to characterizing the size of an RVE in order to effectively homogenize a material, however, there is less study of the effective isotropic limit. The representative size may be different when approaching the homogeneous limit or the isotropic limit.In this work, elastic and strength properties will be evaluated at multiple scales using SVE with square and circular (so-called “regular”) geometry. A Voronoi tessellation based geometry, where aggregation of Voronoi cells is achieved using square or circular grids, is studied and compared with regular partitioning methods. Models will be tested on two types of microstructures, one that is isotropic at the macroscale, and one which contains a slight directional bias. Results for different SVE geometries will be compared to demonstrate how SVE modeling choices affect the characterization of anisotropy and heterogeneity at the micro- and mesoscale.

Toward informed partitioning for load balancing: A proof-of-concept

Most parallel applications suffer from load imbalance, a crucial performance degradation factor. In particle simulations, this is mainly due to the migration of particles between processing elements, which eventually gather unevenly and create workload imbalance. Dynamic load balancing is used at various iterations to mitigate load imbalance, employing a partitioning method to divide the computational space evenly while minimizing communications. In this paper, we propose a novel partitioning methodology called “informed partitioning”. It uses information based on the evolution of the computation to reduce the load balancing growth and the number of load balancing calls. In this paper, we illustrate informed partitioning by proposing a new geometric partitioning technique for particles simulations. This technique is derived from the well-known recursive coordinate bisection and employs the velocity of the particles to guide the bisection axis. To properly compare the performance of our new method with existing partitioning techniques during application execution, we introduce an effort metric based on a theoretical model of load balanced parallel application time. We propose a proof-of-concept of informed partitioning, through a numerical study, on three N-Body simulations with various particle dynamics, and we discuss its performance against popular geometric partitioning techniques. Moreover, we show that our effort metric can be used to rank partitioning techniques by their efficiency at any time point during the simulation. Eventually, this could be used to choose the best partitioning on the fly. In the numerical study, we report that our novel concept increases the performance of two experiments out of three by up to 76% and 15%, while being marginally slower by only 3% in one experiment. Also, we discuss the limitations of our implementation of informed partitioning and our effort metric.

SAR image segmentation with combined Bayes’ rule, GMTRJ, and EM algorithms

ABSTRACT This study analyses the roles of all the classes in the segmentation procedure, and aims to improve the segmentation accuracy of synthetic aperture radar (SAR) images. Accordingly, weight variables of all classes for SAR images are defined and incorporated into the segmentation model by Bayes’ rule and geometric partition tessellation. In addition, the Generalized Multiple-Try Reversible Jump (GMTRJ) and expectation maximization (EM) algorithms are designed to obtain the values of weight variables and the optimal segmentation by simulating the segmentation model. The greater the value of the weight variable, the more important the role of its class. The proposed approach can automatically determine the classes’ roles in the segmentation procedure and segment SAR images accurately and quickly. Finally, the proposed and comparison approaches are tested on SAR images, and the results fully demonstrate the effectiveness of the proposed approach.

Spatio-Temporal Correlation Guided Geometric Partitioning for Versatile Video Coding.

Geometric partitioning has attracted increasing attention by its remarkable motion field description capability in the hybrid video coding framework. However, the existing geometric partitioning (GEO) scheme in Versatile Video Coding (VVC) causes a non-negligible burden for signaling the side information. Consequently, the coding efficiency is limited. In view of this, we propose a spatio-temporal correlation guided geometric partitioning (STGEO) scheme to efficiently describe the object information in the motion field of video coding. The proposed method can economize the bits consumed for side information signaling, including the partitioning mode and motion information. We firstly analyze the characteristics of partitioning mode decision and motion vector selection in a statistically-sound way. Based on the observed spatio-temporal correlation, we design a mode prediction and coding method to reduce the overhead for representing the above mentioned side information. The main idea is to predict the STGEO modes and motion candidates that have higher selection possibilities, which can guide the entropy coding, i.e., representing the predicted high-probability modes and motion candidates with fewer bits. In particular, the high-probability STGEO modes are predicted based on the edge information and history modes of adjacent STGEO-coded blocks. The corresponding motion information is represented by the index in a merge candidate list, which is adaptively inferred based on the off-line trained merge candidate selection probability. Simulation results show that the proposed approach achieves 0.95% and 1.98% bit-rate savings on average compared to VTM-8.0 without GEO for Random Access and Low-Delay B configurations, respectively.

Marina el-Alamein as an Example of Painting Decoration of Main Spaces of Hellenistic-Roman Houses in Egypt

The article is based on the research conducted by the authors. The houses from the ancient town discovered in 1985 on the Mediterranean coast at the location of today’s Marina el-Alamein, are among the rare remains of Egyptian residential buildings from Hellenistic and Roman times. There are few remains of houses from this period in major cities, including the capital of Alexandria. The ancient town, which functioned under the influence of nearby Alexandria, developed from the second century BC to the sixth century AD. Various types of buildings, relatively well preserved here, provide information on a reduced scale about the architecture of Alexandria, as well as the lives of its inhabitants. This also applies in particular to residential houses, their décor and colours. The ancient town of Marina el-Alamein can be seen as demonstrating solutions that are more common. The present article aims to analyse the preserved remains of painting decoration in the main spaces of houses and attempts to reconstruct forms and the principles of their creation on the background of better-known solutions from other regions. Houses in Marina generally implemented layouts defined by flagstone-paved portico courtyards, sporadically taking the form of an incomplete peristyle, and reception halls oikos, which could be accompanied by smaller adjoining rooms. Both the columns and entablature with the cornices of the porticoes as well as the walls of the main rooms were painted. Wall decoration was organised by geometric partitions, filled in variously. The aedicula that served religious purposes, placed centrally in the rear walls of the main reception rooms, was also polychrome. The painted decoration can be reconstructed from the preserved remains, as rich and intensely colourful, similar to Hellenistic and Roman layouts from other regions, but differing in details.

Displacement evolution of reverse-dip rock slope considering the change of the reservoir level

The fluctuation and periodic change of reservoir level are the important incentives that affect the stability of the reverse-dip rock slope. Based on the field monitoring data, this paper investigates the topping deformation evolution characteristics of a typical reverse-dip slope containing different geological partitions considering the fluctuation of reservoir level. A typical reverse-dip rock slope was taken as an engineering case, whose geological factors including elevation, slope angle, and aspect were first obtained by a field survey. Subsequently, the factors were superimposed through ArcGIS to obtain the geological partitions. Afterwards, a spatiotemporal evolution nephogram of the topping displacement was obtained by discrete monitoring data of surface displacement of the slope. Finally, the deformation characteristic of the prone zone was analyzed by superposing the nephogram of the displacement and the geometrical partition, considering the change of the reservoir level. The results show that the largest geological and geometric characteristic zone is at the bottom elevation, medium slope, and north aspect. The zone with significant horizontal displacement is distributed in the front and middle edges of the slope, which increases with the increase of the reservoir level and vice versa. The vertical displacement mainly occurs in the trailing of the slope. The area of superimposed displacement in strong deformation zones increases as either the reservoir level rises or falls. After the superposition, zones with strong deformation increase with the variation of the reservoir level, and the area with the largest displacement is distributed at the medium gradient, low elevation, and north aspect zones.

Motion Vector Coding and Block Merging in the Versatile Video Coding Standard

This paper overviews the motion vector coding and block merging techniques in the Versatile Video Coding (VVC) standard developed by the Joint Video Experts Team (JVET). In general, inter-prediction techniques in VVC can be classified into two major groups: “whole block-based inter prediction” and “subblock-based inter prediction”. In this paper, we focus on techniques for whole block-based inter prediction. As in its predecessor, High Efficiency Video Coding (HEVC), whole block-based inter prediction in VVC is represented by adaptive motion vector prediction (AMVP) mode or merge mode. Newly introduced features purely for AMVP mode include symmetric motion vector difference and adaptive motion vector resolution. The features purely for merge mode include pairwise average merge, merge with motion vector difference, combined inter-intra prediction and geometric partitioning mode. Coding tools such as history-based motion vector prediction and bidirectional prediction with coding unit weights can be applied on both AMVP mode and merge mode. This paper discusses the design principles and the implementation of the new inter-prediction methods. Using objective metrics, simulation results show that the methods overviewed in the paper can jointly achieve 6.2% and 4.7% BD-rate savings on average with the random access and low-delay configurations, respectively. Significant subjective picture quality improvements of some tools are also reported when comparing the resulting pictures at same bitrates.

Exponential convergence of the hp-version of the composite Gauss-Legendre quadrature for integrals with endpoint singularities

In this paper we propose and analyze an hp-version of the composite Gauss-Legendre quadrature rule which includes local subdivision of the integration domain and local variation of the number of quadrature nodes employed on each subinterval. We derive an a priori error estimate that is fully explicit in the local length of each subinterval, in the local number of quadrature nodes employed on each subinterval, and in the local regularity of the integrand. In particular, for integrands with singularities at one or both endpoints, we prove that exponential convergence can be achieved by using geometric partition of the integration domain and linearly increasing of the number of quadrature nodes in successive subintervals. Numerical experiments are provided to illustrate the theoretical results.