Elliptical Arcs Research Articles

LSTM-based Prediction of Excavating Resistive Force Using Bucket Trajectory Shape

Unmanned construction machine has become a promising technology in the civil engineering field. The machine is still less efficient, especially in excavating soil, than the manned construction because the unmanned machine works carefully to avoid potential hazards due to unpredicted soil deformation as well as excavation force. This research aims to predict time-series resistive force of bucket during soil excavation based on the Recurrent Neural Network. First, we experimentally obtain excavating resistive force for various excavation trajectories. In the experiment, a bucket follows pre-determined trajectories with four different elliptical arcs, and the resistive force acting on the bucket is measured. The prediction model of the resistive force is then elaborated by indexing the bucket trajectories. The model validation confirms that the aspect ratio of the ellipse of the trajectories is an effective index for accurately predicting the excavating resistive force.

Analysis of Wear Characteristics of Elliptic Arc Finger Seal Based on Fractal Theory

Analysis of Wear Characteristics of Elliptic Arc Finger Seal Based on Fractal Theory

Temporal residual network based multi-head attention model for Arabic handwriting recognition

In this study, we developed a new system for online Arabic handwriting recognition based on temporal residual networks with multi-head attention model. The main idea behind the application of attention mechanism was to focus on the most relevant parts of the data by a weighted combination of all input sequences. Moreover, we applied beta elliptic approach to represent both kinematic and geometric aspects of the handwriting motion. This approach consists of representing the neuromuscular impulses involving during the writing act. In the dynamic profile, the curvilinear velocity can be fitted by an algebraic sum of overlapped beta functions, while the original trajectory can be rebuilt by elliptic arcs delimited between successive extremum velocity instants. The experiments were conducted on LMCA database containing the trajectory coordinates of 23141 Arabic handwriting letters, and showed very promising results that achieved the recognition rate of 97,12%

Characteristic Mapping for Ellipse Detection Acceleration

It is challenging to characterize the intrinsic geometry of high-degree algebraic curves with lower-degree algebraic curves. The reduction in the curve's degree implies lower computation costs, which is crucial for various practical computer vision systems. In this paper, we develop a characteristic mapping (CM) to recursively degenerate 3n points on a planar curve of n th order to 3(n-1) points on a curve of (n-1) th order. The proposed characteristic mapping enables curve grouping on a line, a curve of the lowest order, that preserves the intrinsic geometric properties of a higher-order curve (ellipse). We prove a necessary condition and derive an efficient arc grouping module that finds valid elliptical arc segments by determining whether the mapped three points are colinear, invoking minimal computation. We embed the module into two latest arc-based ellipse detection methods, which reduces their running time by 25% and 50% on average over five widely used data sets. This yields faster detection than the state-of-the-art algorithms while keeping their precision comparable or even higher. Two CM embedded methods also significantly surpass a deep learning method on all evaluation metrics.

Cubic Trigonometric Hermite Interpolation Curve: Construction, Properties, and Shape Optimization

Cubic Hermite interpolation curve plays a very important role in interpolation curves modeling, but it has three shortcomings including low continuity, difficult shape adjustment, and the inability to accurately represent some common engineering curves. We construct a cubic trigonometric Hermite interpolation curve to make up the three shortcomings of cubic Hermite interpolation curve once and for all. The cubic trigonometric Hermite interpolation curve not only inherits the features of cubic Hermite interpolation curve but also achieves C2 continuity, has local and global adjustability, and can accurately represent elliptical arc, circular arc, quadratic parabolic arc, cubic parabolic arc, and astroid arc that often appear in engineering. In addition, we give the schemes for optimizing the shape of the cubic trigonometric Hermite interpolation curve based on internal energy minimization. The schemes include optimizing the shape of planar curve and spatial curve. Some modeling examples show that the proposed schemes are effective and the cubic trigonometric Hermite interpolation curve is more practical than cubic Hermite interpolation curve.

Optimization Exploration on Impact Resistance of Bionic Sandwich Panel Inspired by the Appendage Structure

Sandwich panel is a widely used protective component, this paper designs Bidirectionally Arranged Bionic sandwich Panel (BABP) and Unidirectionally Arranged Bionic sandwich Panel (UABP) according to the appendage of Odontodactylus scyllarus. Meanwhile, Triangular sandwich Panel (TP), Corrugated sandwich Panel (CP) and Elliptical arc sandwich Panel (EP) are accordingly designed as a comparison. Hyperworks and LS-DYNA are used to simulate the impact conditions, and the drop-weight test shows that the finite element simulation is reliable. Bionic sandwich panels have excellent protective effect at the impact velocity of 6–14[Formula: see text]m/s. UABP has the best comprehensive impact resistance by comparing the deformation, specific energy absorption (SEA) and peak force (PF) of the five kinds of sandwich panels under five impact velocities. Parameter analysis and response surface optimization work based on orthogonal experiments are carried out for UABP, the results are that the wall thickness [Formula: see text] and the triangle-width ratio [Formula: see text] have extremely significant influences on the SEA, and the order of influence is [Formula: see text]; the wall thickness [Formula: see text] and the arc-width ratio [Formula: see text] have extremely influences on PF, and the triangle-width ratio [Formula: see text] has a significant influence on PF, and the order of influence is [Formula: see text]. Both the errors about SEA and PF of the optimal solutions are less than 5%. The comprehensive evaluation index of the optimal UABP is larger than that of sandwich panels by 29.15%, 52.61%, 65.64%, 40.5%. This research is expected to provide new perspectives on the design of sandwich panels.

Image Edge Analysis and Application Based on Least Squares Fitting Model

This paper presents an effective method to automatically segment and fit the edge contour curve data of a picture into straight line segments, circular arc segments or elliptical arc segments. Firstly, the curvature of each point is calculated, and the curvature change breakpoints are found to distinguish between straight lines, circular arcs and elliptical arcs; then, circular arc segments and elliptical arcs are distinguished by the change degree of curvature of adjacent points, and the automatic segmentation of contour edges is realized. Finally, the circular arc segment and elliptic arc segment are fitted by least squares method, based on which the length of the straight line, the direction angle of the circular arc, the rotation angle of the elliptic arc and other related information are calculated. The results show that our model can better identify the feature texture information of image edges.

Shape approximation of sessile droplet by the equivalence between vertical capillary force and hydrostatic pressure

Liquids are widely employed in the investigations of wetting in the form of droplets, especially for superhydrophobic surfaces. An accurate approximation for the shape of sessile droplets is of significance for facilitating the studies of surface wetting. Inspired by the principle of the drop weight method, we derived the equivalent relationship between the vertical capillary force at the contact line and the hydrostatic pressure of a sessile droplet on horizontal substrates. On the basis of the force equivalence, a new model using elliptical arcs to approximate the profile of actual droplets is developed. In addition to predicting the droplet shape, the proposed model enables the inverse estimation of the physical parameters according to the characteristic sizes of the droplet profile. The estimation results accord well with the measurements within a wide range of droplet volumes, which fully demonstrates the validity and application potential of our model. Moreover, the force equivalence has been utilized to explain the volume difference of evaporative droplets falling through the superhydrophobic holes present on different grades of mesh substrates. It is anticipated that the newly proposed force-based model will contribute to the deep understanding of sessile droplet-related phenomena, such as the Cassie-Wenzel transition and nondestructive transfer.

Application of elliptic integrals in marine navigation

AbstractIf the Earth's oblateness is neglected in marine navigation, then the sphere gives a relatively simple solution for course and distance between any two points. The navigation sphere where a span of one minute of arc is equal to nautical mile is used. The primary deficiency of this approach is the lack of a closed-form formula that takes the Earth's eccentricity into account. Considering the Earth as an oblate spheroid, i.e., a rotational ellipsoid with a small flattening, the problem of computing the length of the meridian arc leads to the understanding of elliptic integrals. In this paper, incomplete elliptic integrals of the first, second and third kind are used to find an arbitrary elliptical arc. The results prove an advantage of using geocentric latitude compared to geodetic and reduced latitude.

Rational Bézier Guarding

AbstractWe present a reliable method to generate planar meshes of nonlinear rational triangular elements. The elements are guaranteed to be valid, i.e. defined by injective rational functions. The mesh is guaranteed to conform exactly, without geometric error, to arbitrary rational domain boundary and feature curves. The method generalizes the recent Bézier Guarding technique, which is applicable only to polynomial curves and elements. This generalization enables the accurate handling of practically important cases involving, for instance, circular or elliptic arcs and NURBS curves, which cannot be matched by polynomial elements. Furthermore, although many practical scenarios are concerned with rational functions of quadratic and cubic degree only, our method is fully general and supports arbitrary degree. We demonstrate the method on a variety of test cases.

The interacting pair of galaxies Arp 82: integral field spectroscopy and numerical simulations

ABSTRACT Spectral data cubes of the interacting pair of galaxies NGC 2535 and NGC 2536 (the Arp 82 system) targeting bright emission lines in the visible band, obtained with the imaging Fourier transform spectrometer (iFTS) SITELLE attached to the Canada–France–Hawaii Telescope (CFHT), are presented. Analysis of H$\alpha $ velocity maps reveals a bar in $\rm NGC\, 2536$. In $\rm NGC\, 2535$, we find strong non-circular motions outside the ocular ring, in the elliptical arc and tidal tails of $\rm NGC\, 2535$, and a misalignment between the kinematic and photometric position angles. We detect 155 H ii region complexes in the interacting pair of galaxies and determine oxygen abundances for 66 of them using different calibrators. We find, regardless of the indicator used, that the oxygen abundance distribution in $\rm NGC\, 2536$ is shallow, whereas in $\rm NGC\, 2535$, it is best fitted by two slopes, the break occurring beyond the ocular ring. The inner slope is comparable to the one observed in isolated normal star-forming galaxies, but the outer slope is shallow. We present a numerical simulation of the interaction that reproduces the observed tidal features, kinematics, and metallicity distribution, to investigate the effect of the interaction on the galaxies. The model indicates that the galaxies have undergone a close encounter, strongly prograde for the primary, and are halfway in their course to a second close encounter.

Morphological and topographic evaluation of the mandibular canal and its relationship with the facial profile, skeletal class, and sex.

The aim of this study was to evaluate the morphology and topography of the mandibular canal in patients with different facial profiles, skeletal classes, and sexes. Cone-beam computed tomography volumes of 103 patients were classified according to facial profile and skeletal class. Two examiners classified the mandibular canal into a linear, spoon-shaped, elliptical arc, or turning curvature and measured four related linear distances. The most frequent mandibular canal curvature was identified and multi-way ANOVA with Tukey's test compared the linear measurements between facial types, skeletal class, and sexes (α = 0.05). Kappa and intraclass correlation coefficients were used to assess the reproducibility of qualitative and quantitative variables, respectively. The examiners showed excellent reproducibility. The four curvatures of the mandibular canal were found, but the spoon-shaped and elliptical arch were the most frequent. No significant differences were observed for most of the linear measurements between the different facial profiles, skeletal classes, and sexes (p > 0.05). Spoon-shaped and elliptical arch are the most frequent curvatures of the mandibular canal; furthermore, its morphology and topography seem to be little influenced by the facial profile, skeletal class, and sex.

Speed Planning and Interpolation Algorithm of High-Speed Nurbs Curve Based on an Elliptical Arc Fitting

Speed Planning and Interpolation Algorithm of High-Speed Nurbs Curve Based on an Elliptical Arc Fitting

Bézier Curves and Surfaces with three Parameters and Extensions in the Triangular Domain

To define a new basis function to obtain a basis that can inherit the excellent properties of the traditional B-spline method and Bézier method, global and locality of shape adjustment, and can accurately represent the elliptical arc and circle. Firstly, an optimal standard full positive base, the cut angle algorithm, the 1 C and 2 C continuous proof of the base under the quasi-extended Chebyshev space in this paper. Secondly, the base on the rectangular field to the triangular field to obtain the quasi-cubic triangular Bernstein-Bézier base on the triangular field. Thirdly, this base can accurately represent the elliptic arc and circle, and then gives the base cutting algorithm on the triangular domain, and reverse introduce two conditions under which the quasi-cubic triangular Bernstein-Bézier surfaces are 1 G continuous in surface splicing. After a lot of analysis and examples, the new basis function has excellent properties of traditional methods, and can also flexibly adjust the shape parameters to obtain the required curve surface, which meets the actual industrial design requirements.

New distributed beamforming techniques based on optimized elliptical arc geometry for back lobe cancellation of linear antenna arrays

The presence of array back lobe is a major source of interference, power loss, and degrades the signal-to-interference ratio (SIR) in wireless communication systems. In this paper, new distributed beamforming techniques based on an optimized elliptical arc geometry (EAG) are proposed for back lobe cancellation of linear antenna arrays (LAA). The optimized EAG allows for flexible control of the elements' locations and initial transmission phases of their radiations, allowing them to add constructively towards the main beam direction and add destructively towards the back lobe direction. Firstly, two EAG based beamforming techniques are introduced using either a single ellipse-EAG (SE-EAG) or double ellipses-EAGs (DE-EAG). In these techniques, the back lobes are minimized by optimizing both the minor axes of the elliptical arcs and the elements' angular distributions using the particle swarm optimization (PSO) technique. While the elements' transmission energies are kept the same as that of the original LAA. For further back lobe minimization, the double ellipses-EAG with optimized energies (DE-EAG-WOE) beamforming technique is introduced, where both elements' transmission energies and positions are optimized. To verify the superiority and the possibility of practical validation of the proposed techniques, the proposed distributed array configurations based on the DE-EAG-WOE are realized using the CST Microwave Studio software package using dipole elements.

Improved mechanical properties and energy absorption of Ti6Al4V laser powder bed fusion lattice structures using curving lattice struts

A porous lattice structure with highly controllable mechanical properties, low weight, and high strength is the most promising option for many fields, such as the aerospace, automobile, and biomedical industries. However, the most common and critical issue is the excessively high stress concentration at the struts’ nodes when the lattice structure is loaded. Thus, a curving lattice design strategy is proposed, maintaining a light structure, through which either a circular or elliptical arc is used in the lattice struts to obtain new forms of curving lattice structures. By establishing theoretical models and preparing samples by laser powder bed fusion (L-PBF), combined with scanning electron microscopy (SEM), quasi-static uniaxial compressive experiments, finite element analysis (FEA), and Gibson-Ashby models, excellent results were obtained. The stress distribution of the original under the loads was altered in the curving lattice structure and the stress concentration at the nodes of the struts was effectively relieved, dramatically improving its mechanical properties. Compared with the original structure, the specific elastic modulus and specific compressive strength of curving lattice structures were maximally increased by 213.7% and 126.2%, respectively. Meanwhile, the curving lattice structure had a superior energy absorption capacity, with a significant increase of 92.9%.

Structures based on elliptical arcs in the problems of designing trajectories and creating mechanical systems

Abstract. An experimental study of the strain of a rectilinear segment of a pipeline Du 200 made of steel 20 under cyclic loading by internal pressure was carry out. The tests were performed on a pneumohydraulic stand under conditions of flat stress, normal temperatures, and load cycle asymmetry with registration of circular and axial elastic-plastic strain. The aim of the work was to test an experimental technique for studying the effect of ratcheting (unilateral accumulation of plastic deformations) on real structural elements when changing the modes of cyclic loading. According to the results of the study, curves of cyclic deformation (ratcheting) of the pipe in the circular and axial direction on the basis 100 cycles were obtained.

Do individual characteristics influence the beta-elliptic modeling errors during ellipse drawing movements?

This paper investigates whether age, gender, and degree of familiarity with writing have an influence on the Beta-elliptic model errors during hand-drawing on a graphical tablet. A database of elliptical hand drawing movements was built within a sample of 99 participants aged between 19 and 85 years. Using the Beta-elliptic model, the velocity profile was modeled by overlapped Beta functions and the drawing trajectory was segmented between velocity extrema and each segment geometry was modeled by elliptic arcs. Average absolute and relative geometric, curvature and curvilinear velocity errors were 0.27 mm, 0.68%, 4.54 mm, 0.48%, 4.68 mm/s, and 8.79% respectively. Statistical analyses revealed not significant or low correlation between modeling errors and age and movement velocity, and no significant or low error differences according to gender or degree of familiarity with writing.

Numerical Studies on the Stiffness of Arc Elliptical Cross-section Helical Spring Subjected to Circumference Force

Due to its excellent properties, elliptical cross-section helical spring has been widely used in automobile industry, such as valve spring, arc spring used in Dual Mass Flywheel and so on. Existing stiffness formulae of helical spring remain to be tested, and stiffness property of elliptical cross-section arc spring has been little studied. Hence, study on the stiffness of elliptical cross-section helical spring is significant in the development of elliptical cross-section helical spring. This paper proposes a method to study the stiffness property of elliptical cross-section helical spring that the experiment design method is adopted with finite element analysis. Firstly, the finite element analysis method was used to verify the cylindrical (circular cross-section and elliptical cross-section) springs. Then, the regression formula was designed and derived compared with the reference springs’ stiffness formulae by experimental design. Last, regression formula was verified with existing experiment data. The novelty in this paper is that simulation technology of arc spring was investigated and a stiffness regression equation of arc elliptical cross-section spring was obtained using orthogonal regression design, with significance in wide use of the arc elliptical cross-section helical spring promotion.

Elastostatic problems of crack lying along the interface of an elliptical inclusion embedded in elastic media

The problems of an elliptical arc crack lying along the interface of an anisotropic inclusion are considered in this article. By means of the complex series expansion of the stress functions, the related coefficients in the stress functions are obtained using the continuity condition for the stresses at the imperfect interface and using equilibrium condition based on relationships of stresses and displacements at the imperfect interface between matrix and inclusion. The displacements and stresses at the interface in the matrix and in the inclusion can be calculated. The imperfection at the interface between matrix and inclusion is expressed by the Fourier series, which can be used to represent the crack lying along the interface and the perfect interface. The method presented in this article can be used to analyze the problems of crack, inclusion, and hole in the anisotropic materials due to separate or combined effect of eigenstrains and far-field tension.