Bessel Curve Research Articles

Study on Three-Dimensional Digital Expression and Robot Bending Method of Orthodontic Archwire.

Malocclusion is the third largest oral disease in the world. At present, the most effective treatment method for malocclusion is the fixed orthodontic technique based on orthodontic archwires. Robotic archwire bending can overcome the shortcomings of manual bending such as low efficiency and low precision. The three-dimensional digital expression and robot bending method of orthodontic archwire are studied to realize the orthodontic archwire bending using a robot. Tooth is identified by the doctors' common method. The shape, position, and constraint relationship of orthodontic archwire in three-dimensional space are expressed by the Bessel curve. The bending of the archwire curve is realized by transmitting the archwire curve into the alternative lines. The planning method of forming points and the spatial angle planning method are proposed. The archwire bending experiment is carried out with the maxillary information of a patient. The error rate of the experimental and ideal values is between 2.94% and 6.74%. It can meet the physician's basic requirements after simple modification. Therefore, it can be considered that the method of using discrete Bessel curve to carry out the control point planning and angle planning is suitable for the orthodontic archwire-bending robot system, which has certain feasibility and practicability in clinical treatment.

Optimal condition for employing an axicon-generated Bessel beam to fabricate cylindrical microlens arrays

A numerical algorithm, modelling the transformation from a Gaussian beam to a Bessel beam, is presented for the purpose to study the optimal condition for employing an axicon-generated Bessel beam to fabricate cylindrical microlens arrays (CMLAs). By applying the numerical algorithm to simulate the spatial intensity distribution behind the axicon under different defects of a rotund-apex and different diameter ratios of an incident beam to the axicon, we find that the diffraction effects formed by the axicon edge can be almost eliminated when the diameter ratio is less than 1:2, but the spatial intensity distribution is disturbed dramatically even a few tens of microns deviation of the apex, especially for the front part of the axicon-generated Bessel beam. Fortunately, the lateral intensity profile in the rear part still maintains a desirable Bessel curve. Therefore, the rear part of the Bessel area and the less than 1:2 diameter ratio are the optimal choice for employing an axicon-generated Bessel beam to implement surface microstructures fabrication. Furthermore, by applying the optimal conditions to direct writing microstructures on fused silica with a femtosecond (fs) laser, a large area close-packed CMLA is fabricated. The CMLA presents high quality and uniformity and its optical performance is also demonstrated.

Topological recursion on the Bessel curve

The Witten-Kontsevich theorem states that a certain generating function for intersection numbers on the moduli space of stable curves is a tau-function for the KdV integrable hierarchy. This generating function can be recovered via the topological recursion applied to the Airy curve $x=\frac{1}{2}y^2$. In this paper, we consider the topological recursion applied to the irregular spectral curve $xy^2=\frac{1}{2}$, which we call the Bessel curve. We prove that the associated partition function is also a KdV tau-function, which satisfies Virasoro constraints, a cut-and-join type recursion, and a quantum curve equation. Together, the Airy and Bessel curves govern the local behaviour of all spectral curves with simple branch points.

Roaming Path Generation Algorithm and Optimization Based On Bezier Curve

Camera roaming plays an extremely important role in constructing various roaming scenarios for virtual systems. However, the existing path (camera) roaming algorithm has the disadvantages of excessive human participation in the roaming path generation process, unpredictable roaming effect, unsmart camera conversion, and mismatched roaming camera and commentary. Therefore, a convenient and automatic path roaming algorithm is proposed. At the same time, the intelligent conversion of the camera is implemented. Based on this, optimization is performed to enable smart matching between the camera and the commentary audio and narration text. First, the key model in the roaming scene is marked to obtain its spatial position; Then the Bessel curve generation principle is studied, and Bessel splines are fitted to the key points according to the mathematical model of the Bezier curve； And then the camera movement is invoked，and the function implements roaming. Finally, the algorithm is optimized to achieve intelligent matching of voice subtitles and pictures. In this way, the automation and intelligence of the roaming path are realized.

Painlevé 2 Equation with Arbitrary Monodromy Parameter, Topological Recursion and Determinantal Formulas

The goal of this article is to prove that the determinantal formulas of the Painlev'e 2 system identify with the correlation functions computed from the topological recursion on their spectral curve for an arbitrary non-zero monodromy parameter. The result is established for two different Lax pairs associated to the Painlev'e 2 system, namely the Jimbo-Miwa Lax pair and the Harnad-Tracy-Widom Lax pair, whose spectral curves are not connected by any symplectic transformation. We provide a new method to prove the topological type property without using the insertion operators. In the process, taking the time parameter t to infinity gives that the symplectic invariants F(g) computed from the Hermite-Weber curve and the Bessel curve are equal to respectively. This result generalizes similar results obtained from random matrix theory in the special case where {\theta} = 0. We believe that this approach should apply for all 6 Painlev'e equations with arbitrary monodromy parameters. Explicit computations up to g = 3 are provided along the paper as an illustration of the results.

Evaluation of Surface Clutter for Future Geostationary Spaceborne Weather Radar

Surface clutter interference will be one of the important problems for the future of geostationary spaceborne weather radar (GSWR). The aim of this work is to provide some numerical analyses on surface clutter interference and part of the performance evaluation for the future implementation of GSWR. The received powers of rain echoes, land and sea surfaces from a radar scattering volume are calculated numerically based on the derived radar equations, assuming a uniform rain layer and appropriate land and sea surface scattering models. An antenna pattern function based on a Bessel curve and Taylor weighting is considered to approximate the realistic spherical antenna of a GSWR. The power ratio of the rain echo signal to clutter (SCR) is then used to evaluate the extension of surface clutter interference. The study demonstrates that the entire region of surface clutter interference in GSWR will be wider than those in tropical rainfall measuring mission precipitation radar (TRMM PR). Most strong surface clutter comes from the antenna mainlobe, and the decrease of clutter contamination through reducing the level of the antenna sidelobe and range sidelobe are not obvious. In addition, the clutter interference is easily affected by rain attenuation in the Ka-band. When rain intensity is greater than 10 mm/h, most of rain echoes at off-nadir scanning angles will not be interfered by surface clutter.

Integration of scanning and image processing algorithms for lane detection based on fuzzy method

In order to detect lane rapidly and accurately, the integration of scanning and image processing algorithms (SIP) based on the fuzzy method is proposed. Further, combination of the proposed algorithm with an adaptive threshold value for image binarization, the least-square method and Bessel curve algorithm are proposed for detection and to fit the lane. The proposed SIP algorithm was evaluated by various tests. The experimental results indicate that the average time consumed for the detection of lane in each frame is 16.7639 ms, and the accuracy of lane detection is 95%. The proposed algorithm demonstrates good robustness, and can be used as the core algorithm for further application in lane departure warning systems.

Design Study of Two-Dimensional Anti-Counterfeiting Code Based on Moirés Mechanism

Two dimensional code security system can be used to encrypt the user is decoded product, inspection by anti fake system or mobile phone software, can be genuine security information products. The Fourier transform of the amendment in the two-dimensional code patterns on the basis, transforming it into the function value is input to the server system. After a raster image processor (RIP) to draw the value of Bessel curve fitting, and tend to image in a plurality of sine function description, at the same time using the Visual Basic to draw a sinusoidal function diagram, the output image information two-dimensional code generation. Finally, through the internal matching storage printing output pattern and server security code information, you can verify the authenticity of products. It provides a simple and convenient method, and accurate for the commodity information traceability and product anti-counterfeiting identification.

Real-Time Trajectory Control of Robots Omnidirectional Mobile Obstacle Avoidance

On the basis of Dick Stella algorithm and Bessel Curve, this paper proposes an improved algorithm for real-time obstacle avoidance control of mobile robots. With strong robustness, this algorithm can effectively solve the problem of robot path planning and tracking while meeting the dynamic constraint conditions. The simulation results show that the improved algorithm shortens the robot moving period and remarkably improves the motion planning in robot obstacle avoidance.

Fourier analysis of blurred images for the measurement of the in-plane dynamics of MEMS

The goal of this paper is to use FFT imaging techniques to measure in-plane resonances of MEMS devices from blurred microphotographs where the presence of resonance is not visually discernable. A method is presented for measuring the high-frequency (in the 10s–100s of kHz range) response characteristics of MEMS devices using only standard optical microscope cameras (15–30 Hz frame rate) and applying Fourier analysis of camera images of periodic patterns on the oscillating devices. In the frequency domain, in-plane blurring acts as a low pass filter, attenuating all frequency components, but preferentially attenuating the higher order harmonics. A theoretical formula for the blur-induced attenuation of the harmonics of Fourier series components is derived and it is shown that it follows a Bessel curve. The theoretical predictions were verified experimentally using a series of camera microphotographs of three different variations of an electro-thermally driven pad suspended on springs. The predicted attenuations of harmonics were observed and verified. The analysis of the measured attenuation was able to (1) determine in-plane resonant frequencies, (2) measure submicron motions and (3) characterize the nonlinear dynamics (modeled by the Duffing equation). The amplitude uncertainty of the FFT method for detecting in-plane resonant peaks at 75 kHz and 3.5 V was found to be ±0.027 µm using a single image and ±0.011 µm using an average of 10 images.

Study on Bezier Curve Variable Step-length Algorithm

Abstract Bessel Curve also known as Bezier Curve, through which the general vector graphics software accurately draws curves, as the Bezier curve is relatively easy to calculate and its stable characteristic, in many areas it has been widely applied. However, for the deficiency of less efficiency exists in the common Bezier Curve Generation Algorithm, the selection of the parameter step-length significantly affects the accuracy and efficiency of the generated curve. This paper aims at the efficiency available in the existing Bezier Curve Generation Algorithm to propose the Variable Step-length Algorithm; by changing the parameter step-length of the curve generation algorithm, it can significantly reduce the calculations of a large number of duplicate points in the point-by-point generation algorithm; the algorithm not only maintains a higher accuracy, but also significantly improves the efficiency generated in the curve, with better application.

Detection of Cosmic-Ray Hits for Single Spectroscopic CCD Images

ABSTRACTA new method of detecting cosmic-ray hits from single spectroscopic CCD images is proposed in this paper. First, one-order difference operations in two directions respectively are calculated to detect the candidate points of the cosmic-ray hits by using two thresholds. Second, Bessel curve fitting is adopted to calculate the deviations of the candidate points so as to find the confirmation points of cosmic-ray hits. At the end of this paper, five groups of simulation data and one group of observation data from SDSS are used to demonstrate the effectiveness of the proposed method.