Elliptical Arcs Research Articles

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

Efficient Analysis of Unlined Elliptic Tunnels: An Approximate Method for Dynamic Response to Incident Plane SH Waves

ABSTRACT Dynamic analysis of underground structures, such as tunnels, is crucial to ensure their safety and stability during seismic loading. This paper proposes a more general method of large elliptic arc assumption-based wave function expansion, which is attributed to the important role of the large circular arc assumption-based wave function expansion method in the elastic wave scattering problem. The study is conducted within elliptic coordinate systems, employing the Mathieu function and Mathieu function addition theorem. The applicability and limitations of this method are analysed by comparing it with the existing exact analytical solutions obtained through the mirror-based wave function expansion method.

Measuring mislocalization of angle vertices.

Localisation of simple stimuli such as angle vertices may contribute to a plethora of illusory effects. We focus on the Müller-Lyer illusion in an attempt to measure and characterise a more elementary effect that may contribute to the magnitude of said illusion. Perceived location error of angle vertices (a single set of Müller-Lyer fins) and arcs in a 2D plane was measured with the aim to provide clarification of ambiguous results from studies of angle localisation and expand the results to other types of stimuli. In three experiments, we utilised the method of constant stimuli in order to determine perceived locations of angle vertices (Experiments 1 and 2) as well as circular and elliptical arcs (Experiment 3). The results show significant distortions of perceived compared to objective vertex locations (all effect sizes d > 1.01, p < .001). Experiment 2 revealed strong effects of angle size and fin length on localisation error. Mislocalization was larger for more acute angles and longer angle fins (both ηp² = .43, p < .001). In Experiment 3, localisation errors were larger for longer arcs (ηp² = .19, p = .001) irrespective of shape (circular or elliptical). We discuss the effect in the context of modern trends in research of the Müller-Lyer illusion as well as the widely popular centroid theory. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

A high-precision ellipse detection method based on quadrant representation and top-down fitting

Ellipse detection is a basic task in many computer-vision related problems. While widely studied in recent years, accurate and efficient detection in real-world images is still a challenge. In this paper, a novel ellipse detector, with high accuracy and efficiency, is proposed. The detector models edge by block sequences, and extracts a set of elliptical arcs, which are classified into four sets. Then top-down ellipse fitting strategy that also makes the method able to detect small and flat ellipses is designed. A two-level validation process is used to select highly probable potential ellipses, especially for fragmented ellipses. Experiments on four synthetic datasets show that the proposed method performs far better than existing methods. In images with severe cluttering and occlusion, the F-measure can still be around 0.9. On four real image datasets the proposed method achieves better F-measure scores with competitive speed than state-of-the-art techniques.

Synthesis of Elliptically Shaped Aperiodic Antenna Arrays Subject to Complex Design Constraints

AbstractState‐of‐the‐art conformal array pattern synthesis techniques typically suffer from a significant computational burden. This article builds upon the auxiliary array pattern synthesis technique, allowing the technique to work on elliptical contours. This deterministic method is both computationally efficient and capable of handling complex design cases with additional design constraints. In order to highlight the versatility and applicability, the method has been applied to an elliptical arc array comprised of Rampart antennas and an elliptical ring array using dipole elements. The results have been validated through full‐wave electromagnetic simulations, as well as physical measurements. Both arrays presented show good agreement with the proposed synthesis technique. Highlighting the ability to satisfy additional design constraints, such as enforcing a minimal element spacing or having a controlled beamformer‐network complexity.

High precision 3 × 3 coupler demodulation algorithm with an additional phase shift judgment module

Ellipse fitting algorithms (EFAs) have been widely used in 3×3 coupler demodulation systems to reduce the requirement for symmetry of the 3×3 couplers. Based on the relative stability of the splitting ratio and phase difference after the establishment of the 3×3 coupler demodulation system, we solve the problem that EFA fails to work when the stimulating signal is small. Depending on the existence of a symmetry point about the origin, an additional phase shift judgment module is used to determine whether the Lissajous figure is larger than π rad. If the elliptical arc exceeds π rad, the EFA is executed. Otherwise, the previous parameters are used to correct the ellipse. Parameters are updated in real time to ensure high precision. The experimental results show that the total harmonic distortion (THD) of the ameliorated algorithm is improved by 1.28% compared to the EFA without the judgment module with a stimulus amplitude of 30 mV. The proposed scheme can effectively improve the dynamic range of the 3×3 coupler demodulation to reach 125.64 dB @ 1 kHz and 1% THD. The algorithm ensures the effective operation of the EFA under small phase shift conditions and improves the accuracy of phase demodulation.

Algorithm Research Based on an Elliptical Arc Fitting Curve

Algorithm Research Based on an Elliptical Arc Fitting Curve

A sub-millinewton resolution biaxial force sensor with temperature self-compensation for vascular intervention

This article presents a fiber Bragg grating (FBG)-based highly sensitive micro-biaxial force sensor for vascular intervention surgery. It features a 3D-printed integrated structure incorporating an FBG- embedded cavity at its front end for temperature decoupling and an elliptical arc ball hinge to improve lateral sensitivity. Four FBG-embedded fibers are suspended in a circular array within the flexible hinge to minimize lateral strain crosstalk and increase measurement accuracy. Finite-element analysis has been implemented to validate the flexure performance, while both static and dynamic loading experiments have been performed to validate the sensor performance. The experiments revealed resolutions of 0.761 and 0.765 mN, respectively for the two lateral forces within a range of −1 to 1 N, and dynamic measurement error lower than 0.67 % of full scale. Temperature compensation experiments are conducted under loaded conditions for both axes, showing errors of lower than 1.6 % and 1.2 %. The ability to decouple force and temperature will benefit its broad application for vascular intervention surgery.

Processable Hydroxide Ink with Oriented Microstructure.

Hydroxides are recognized as promising candidates for industrially relevant processes, including catalysis, energy conversion/storage, gas separation, etc. However, the intrinsic poor processability originating from their structural property greatly hinders their development in practical applications. Here, we report a unique yet processable highly-concentrated nickel/cobalt double hydroxide ink to meet the practical demand. The inner nanoflakes in ink possess a high width/thickness ratio (> 100), which endows the highly-concentrated ink (60mg mL-1 ) with liquid-like rheology properties. Further, the elliptical diffusive arc in small-angle X-ray scattering (SAXS) pattern and porous and ordered alignment morphology in cryogenic temperature scanning electron microscopy (Cryo-SEM) confirm the locally oriented arrangement of nanoflakes in the ink. Benefiting from this interior-ordered structure, the ink can be processed into meter-level film, continuous yarn, and rigid and free-standing aerogel, respectively. In particular, the films can be used as electrodes directly in aqueous zinc ion batteries and deliver a favorable capacity (382 mAh g-1 @ 200mA g-1 ) as well as long cycle stability (capacity retention rate of 88% @ 1000mA g-1 after 400 cycles). Moreover, the enlarged-batched fabrication with introduction of efficient thermal conduction in a 10 L reactor is also carried out successfully. Our results clarify the inner relationship between microstructure-rheology and mechanical engineering, thus paving the way to develop hydroxide-based products for future practical applications at the industrial level. This article is protected by copyright. All rights reserved.

Calculation of mutual inductance between circular and arbitrarily shaped filaments via segmentation method

In this article, two analytical formulas for the calculation of mutual inductance between a circular filament and line segment arbitrarily positioning in the space are derived by using Mutual Inductance Method (MIM) and Babic’s Method (BM), respectively. Using the fact that any curve can be interpolated by a set of line segments, a method for calculation of mutual inductance between a circular filament and filament having an arbitrary shape in the space is proposed based on the derived analytical formulas. The derived two formulas and the proposed method (Segmentation Method) were numerically validated by using FastHenry software and reference examples from the literature. In particular, the proposed method was successfully applied to the calculation of mutual inductance between the circular filament and the following special curves such as circle, circular arc, elliptic arc, ellipse, spiral, helices and conical helices. All results of the calculation are in good agreement with the reference examples.

Coherent chord computation and cross ratio for accurate ellipse detection

This paper presents a new method for detecting ellipses in images, which has many applications in pattern recognition and robotic tasks. Previous approaches typically use sophisticated arc grouping strategies or calculate differential such as tangents, and thereby they are less efficient or more sensitive to noise. In this work, we present a novel ellipse detector, based on the simple yet effective chord computation, and on the projective invariant cross ratio, which achieves promising performance in both accuracy and efficiency. First, elliptical arcs are extracted by fast vector computations along with the removal of straight segments to speed up detection. Then, arcs from the same ellipse are grouped together according to the relative location and the intersecting chord constraints, both are on coherent chord computation without differential. Additionally, an efficient additive principle is applied to further accelerate the grouping process. Finally, a novel and robust verification by area-deduced cross ratio is introduced to pick out salient ellipses. Compared with predecessor methods, cross ratio is not only simple for computation, but also has invariant properties (used to discriminate ellipses). Extensive experiments on seven public datasets (including synthetic and real-world images) are implemented. The results highlight the salient advantages of the proposed method compared to state-of-the-art detectors: Easier to implementation, more robust against occlusion and noise, as well as attaining higher F-measure.

Low-Loss Nodeless Conjoined-Tube Anti-Resonant Hollow-Core Fiber

We propose a novel nodeless conjoined-tube hollow-core fiber (CT-HCF) with elliptical arcs as negative curvature boundaries to limit the leakage of transmitted light. The cladding nodes are effectively eliminated by the attachment of arcs to the outermost dielectric tube. Numerical simulations performed using the full-vector finite element method show that a significant reduction in fiber loss over a wide bandwidth can be obtained. The confinement losses for the proposed fiber are two orders of magnitude lower than those obtained for a typical CT-HCF. The total loss, including confinement loss and surface scattering loss, is also investigated. The proposed fiber shows a loss of less than 0.1 dB/km for a bandwidth of 450 nm, with a minimum loss of 6.58·10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> dB/m at 1.45 μm. Moreover, the proposed fiber exhibits good single-mode performance, with the higher-order mode extinction ratio reaching a maximum value of 39341 at 1.7 μm.

Study on magnetic pulse spot welding process for AA5052 aluminium alloy

Magnetic pulse spot welding (MPSW) is a safe, efficient and environmentally friendly process, which is very suitable for joining aluminium alloys. AA5052 aluminium alloy sheets were joined by MPSW. Specifically, the bump on the flyer plate was driven to impact the parent plate at high velocity to achieve metallurgical bonding. The formation process, mechanical properties and micro-morphology of the joint were studied. The results showed that the bump of the flyer plate impacted the parent plate at high velocity caused by Lorentz force to form welding seam. The shape of the welding seam was two incompletely continuous symmetrical elliptical arcs due to the different welding velocities and welding angles in each zone. The strength of the joint was higher than that of the base metal at appropriate process parameters. Specifically, the relatively better process parameters were welding gap of 1.4 mm, welding diameter of 16 mm and discharge energy of 36 kJ. The maximum loads of tensile shear and cross-tension were 4887 N, 1744 N. There were a large amount of dimples at the fracture of welding seam, and the toughness of joint was good.

Research on Assembly Method of Threaded Fasteners Based on Visual and Force Information

Threaded fastening operations are widely used in assembly and are typically time-consuming and costly. In low-volume, high-value manufacturing, fastening operations are carried out manually by skilled workers. The existing approaches are found to be less flexible and robust for performing assembly in a less structured industrial environment. This paper introduces a novel algorithm for detecting the position and orientation of threaded holes and a new method for tightening bolts. First, the elliptic arc fitting method and the three-point method are used to estimate the initial position and orientation of the threaded hole, and the force impact caused by switching from the free space to the constrained space during bolt tightening is solved. Second, by monitoring the deformation of passive compliance, the position information is introduced into the control process to better control the radial force between the bolt and the threaded hole in the tightening process. The constant force controller and orientation compliance controller are designed according to the adaptive control theory. A series of experiments are carried out. The results show that the proposed method can estimate the initial position and orientation of an M24 bolt with an average position error of 0.36 mm, 0.43 mm and 0.46 mm and an orientation error of 0.65°, 0.46° and 0.59°, and it can tighten the bolt with a success rate of 98.5%.

Highly Birefringent and Low-Loss Hollow-Core Anti-Resonant Fiber Based on a Hybrid Guidance Mechanism

A highly birefringent and low-loss hollow-core anti-resonant fiber (HC-ARF) based on a hybrid guidance mechanism is proposed and investigated by using a finite element method. The hybrid guidance mechanism is caused by the anti-resonance effect and the total internal reflection effect. The proposed HC-ARF is obtained by employing twin symmetrical and mutually tangential elliptical arc anti-resonance layers (EA-ARLs) in a conventional 8-tube HC-ARF. Because of the anti-resonance mechanism and the total internal reflection mechanism in the EA-ARL, mode coupling appears between the core mode and the cladding mode. Simulation results indicate that the proposed HC-ARF can achieve birefringence as high as 10−2 in a near-infrared range of 1400 nm to 1600 nm and a low confinement loss (CL) of 7.74 × 10−4 dB/m (9.26 × 10−4 dB/m) for x- and y-polarization components of the fundamental mode (FM) at 1550 nm. In addition, the existence of the 8-tube anti-resonance structure in the cladding significantly suppresses the CL of the x-polarization component of the FM significantly, but the impact on the CL of the y-polarization FM can be ignored, which is determined mainly by the twin EA-ARLs. Furthermore, the performance of the birefringence and CL are also investigated by changing the values of other fiber structure parameters. Our proposed structure successfully shows the ability of the hybrid guidance mechanism in the application of CL manipulation of orthogonal polarization components.

Research on Optimization of Profile Parameters in Screw Compressor Based on BP Neural Network and Genetic Algorithm

In order to accurately calculate the geometric characteristics of the twin-screw compressor and obtain the optimal profile parameters, a calculation method for the geometric characteristics of twin-screw compressors was proposed to simplify the profile parameter design in this paper. In this method, the database of geometric characteristics is established by back-propagation (BP) neural network, and the genetic algorithm is used to find the optimal profile design parameters. The effects of training methods and hidden layers on the calculation accuracy of neural network are discussed. The effects of profile parameters, including inner radius of the male rotor, protection angle, radius of the elliptic arc, outer radius of the female rotor on the comprehensive evaluation value composed of length of the contact line, blow hole area and area utilization rate, are analyzed. The results show that the time consumed for the database established by BP neural network is 92.8% shorter than that of the traditional method and the error is within 1.5% of the traditional method. Based on the genetic algorithm, compared with the original profile, the blow hole area of the screw compressor profile optimized by genetic algorithm is reduced by 54.8%, the length of contact line is increased by 1.57% and the area utilization rate is increased by 0.32%. The CFD numerical model is used to verify the optimization method, and it can be observed that the leakage through the blow hole of the optimized model is reduced, which makes the average mass flow rate increase by 5.2%, indicating the effectiveness of the rotor profile parameter optimization method.

Theoretical model and simulation of a twin-Screw multiphase pump with novel smooth screw rotors for gas-Oil mixed transportation

A pair of screw rotors, the core components of twin-screw multiphase pumps, primarily determine the pump performance. The conventional screw rotor contains unsmooth edges caused by unsmooth points in the cross-sectional profiles, which will lead to the abrasion, wear and fatigue near the unsmooth edges of the screw rotors during operation. For solving this problem, a novel pair of fully smooth screw rotors without unsmooth edges were proposed, and their cross-sectional profiles composed of the elliptical arcs and their conjugate curves were put forward. Parametric equations of the proposed screw rotor profiles were also derived, and then the effects of geometric parameters on the pump performance of the proposed screw rotors were discussed. Furthermore, the transient flow of the twin-screw multiphase pump with the proposed screw rotors were carried out by numerical simulations. The distributions of pressure and velocity in the proposed pump were obtained. The gap leakage and backflow velocity at each gap varying with time and location in the working process were also analyzed. The results indicate that the carryover of the proposed screw rotors is reduced by 90.49%, while its area utilization ratio is increased by 0.8%, and the length of the spatial contact curve is reduced by 25.71% in comparison with the conventional screw rotors. Thus, the superiority and feasibility of the proposed screw rotors are validated.

Restoration of motion-blurred star images with elliptical star streaks

The restoration of motion-blurred star images under high dynamic conditions is important for the high-precision attitude measurement of star sensors. Through motion modelling analysis, it is found that the streak of the imaged star point (star streak) is an elliptical arc. However, existing star image restoration methods are only suitable for the case where the star streak is a straight line. For this reason, a star image restoration algorithm for elliptical star streaks is proposed in this paper. First, the elliptical star streak is transformed into a circular star streak by projective transformation. Then, the circular star streak is transformed into a straight star streak by polar coordinate transformation. Finally, the restored original star image is obtained by restoration methods for straight star streaks and coordinate inverse transformation. At the same time, the algorithm is further optimized by subdividing the polar coordinates. The experiment shows that the proposed algorithm is effective and the restoration accuracy is at the same level as that of existing star image restoration methods for straight star streaks.

Cows Grazing in Elliptagons

Summary If a string is looped around three or more pins placed at the vertices of a regular polygon, then the resulting curve traced by a pencil pulling the string taut is an amalgam of elliptic arcs, which we call an elliptagon. An elliptagon may be viewed as the boundary of the grazing area of a cow tethered to a loop of rope around a barn whose base is a regular polygon. We determine the grazing area for a cow, inside the elliptagon but outside the barn, as a function of the number of edges n of the polygon and the length L of the rope, and we show that elliptagons are smooth curves. We investigate the length of rope for which the grazing area is equal to the area of the base of the barn, and compute the limit of the ratio of this length to the perimeter of the barn as n approaches infinity.

An Improved Method and the Theoretical Equations for River Regulation Lines

The regulation of wandering rivers is a universal problem that attracts significant attention. To effectively control the dynamic state of river course, it is necessary to adjust and construct river training works, which can be regarded as inseparable parts of the planning of river regulation lines. In this study, by comprehensively analyzing the water and sediment discharge in the wandering river of the Yellow River over the period 1952–2020, the large change in water and sediment conditions will inevitably affect the change in river regimes. By analyzing the river regime evolution process from 1990 to 2020 and calculating the river change index, it is found that the wandering channel of the Yellow River has gradually been stabilized, and there is no longer a large channel change, but a small amplitude swing still occurs frequently since 2010. Therefore, these phenomena highlight an urgent need for improving the planning of river regulation lines. According to the properties of parabola, circular arcs, elliptical arcs and curvature arcs, these curves are used to describe the flow path of the river. The theoretical equations of river regulation line with four curve forms are developed based on the latest river regimes and the location of the existing training works as the basis. Four groups of theoretical equations were verified by selecting typical river bends or reaches. The innovative practices from this study may assist in providing technical references, which control the frequent changes that occurred in river regime, as well as guaranteeing the healthy and sustainable development of rivers.