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This research addresses the limitations of existing autonomous vehicle path planning algorithms, notably their slow processing speeds and suboptimal route efficiency. We introduce an innovative path planning algorithm that synergizes the A* algorithm with the Rapidly-exploring Random Tree (RRT) approach. This hybrid model significantly enhances route timeliness and reliability, particularly in obstacle avoidance scenarios for driverless vehicles. Our methodology employs a 'two-level map' approach, where a lower-resolution grid map is derived from a high-resolution map. Utilizing the A* algorithm on this framework, we ascertain a preliminary 'coarse path' for the navigation target. The RRT algorithm, modified to reduce the traditional redundancy associated with random uniform sampling, is then applied for probabilistic sampling within this defined area. ovel aspect of our approach is the simultaneous generation of two trees, originating from both the start and end points, guided by a target-biased strategy and dual-direction theory. This method probabilistically expands towards the node of the opposite tree, thereby enhancing both the generation speed and trajectory viability. Further refinements are made through a pruning process, optimizing the path, and employing Bezier curves for smoothing, ensuring compliance with the dynamic constraints of Ackerman chassis vehicles. Comparative analysis in complex environments demonstrates the superiority of our proposed algorithm. It outperforms traditional methods with a 400 % increase in planning speed relative to the RRT-Connect algorithm, and a 30 % reduction in average path length. Additionally, the mean curvature of routes generated by our algorithm is 19 % lower than traditional routes, underscoring significant advancements in both the timeliness and viability of the planned routes. [ABSTRACT FROM AUTHOR]

In recent years, numerous images are engaged over various unprotected broad networks, causing safety and privacy threats to users. This is where image encryption plays a role in ensuring the secrecy of multimedia data. This article suggests a cryptosystem that employs Elliptic Curve Cryptosystem (ECC) on Hill Cipher matrix known as ECCHC and cubic Bezier coefficient matrix. The cubic Bezier coefficient matrix is utilized as an extra layer of security over ECCHC for image encryption and decryption. The proposed technique is designed to produce an efficient cryptosystem algorithm that provides a high level of security with no discernible difference in the decrypted image. The suggested approach will be subjected to a series of security tests to ensure its performance and efficiency. According to simulation outcomes, the suggested technique has a decent encryption and decryption impact. The proposed scheme includes more than 2 100 key search, making it extremely difficult for unauthorized third parties to predict the keys in order to breach the proposed system. In statistical analysis, the image histograms are regularly distributed, and entropy value of the ciphered images are nearing 8, indicating that the ciphered images are extremely unpredictable. Finally, the PSNR values of the decrypted images of grayscale and RGB with additional noise intensities up to 0.1 are 10.6264 and 10.3707, respectively, demonstrating that the approach is capable of dealing with a certain degree of noise assault. [ABSTRACT FROM AUTHOR]

In recent years, numerous images are engaged over various unprotected broad networks, causing safety and privacy threats to users. This is where image encryption plays a role in ensuring the secrecy of multimedia data. This article suggests a cryptosystem that employs Elliptic Curve Cryptosystem (ECC) on Hill Cipher matrix known as ECCHC and cubic Bezier coefficient matrix. The cubic Bezier coefficient matrix is utilized as an extra layer of security over ECCHC for image encryption and decryption. The proposed technique is designed to produce an efficient cryptosystem algorithm that provides a high level of security with no discernible difference in the decrypted image. The suggested approach will be subjected to a series of security tests to ensure its performance and efficiency. According to simulation outcomes, the suggested technique has a decent encryption and decryption impact. The proposed scheme includes more than 2 100 key search, making it extremely difficult for unauthorized third parties to predict the keys in order to breach the proposed system. In statistical analysis, the image histograms are regularly distributed, and entropy value of the ciphered images are nearing 8, indicating that the ciphered images are extremely unpredictable. Finally, the PSNR values of the decrypted images of grayscale and RGB with additional noise intensities up to 0.1 are 10.6264 and 10.3707, respectively, demonstrating that the approach is capable of dealing with a certain degree of noise assault. [ABSTRACT FROM AUTHOR]

Telemedicine plays an important role in Corona Virus Disease 2019 (COVID-19). The virtual surgery simulation system, as a key component in telemedicine, requires to compute in real-time. Therefore, this paper proposes a realtime cutting model based on finite element and order reduction method, which improves the computational speed and ensure the real-time performance. The proposed model uses the finite element model to construct a deformation model of the virtual lung. Meanwhile, a model order reduction method combining proper orthogonal decomposition and Galerkin projection is employed to reduce the amount of deformation computation. In addition, the cutting path is formed according to the collision intersection position of the surgical instrument and the lesion area of the virtual lung. Then, the Bezier curve is adopted to draw the incision outline after the virtual lung has been cut. Finally, the simulation system is set up on the PHANTOM OMNI force haptic feedback device to realize the cutting simulation of the virtual lung. Experimental results show that the proposed model can enhance the real-time performance of telemedicine, reduce the complexity of the cutting simulation and make the incision smoother and more natural. [ABSTRACT FROM AUTHOR]

In order to improve the aerodynamic performance of the airfoil, the airfoil shape and the angle of attack (AOA) are optimized at the same time by the multi-island genetic algorithm in this paper. The goal of the optimization is to maximize the lift-to-drag ratio which is calculated by the computational fluid dynamics method. The airfoil is parameterized by the Bézier curve. The thickness and the camber of airfoil are no longer restricted to ensure a wide range of airfoil generation. The airfoil is optimized under different Reynolds numbers. The optimized airfoils obtained by the unconstrained AOA method are compared with several standard airfoils. The results show that the maximum lift-to-drag ratio of the optimized airfoil is much greater than the compared airfoils, and the optimized airfoils have good aerodynamic characteristics in a wide range of angle of attack. By comparing with the optimized airfoils obtained by the constrained AOA method, it shows that the constrained AOA method can't guarantee that the preconstrained angle of attack is the optimal angle of attack of the airfoil, nor can obtain the maximum lift-to-drag ratio airfoil of all angles of attack and all airfoils. However, by using the angle of attack as one of the optimization variables, these problems can be solved well. [ABSTRACT FROM AUTHOR]

This work demonstrates in practical terms the evolutionary concepts and computational applications of Parametric Curves. Specific cases were drawn from higher order parametric Bezier curves of degrees 2 and above. Bezier curves find real life applications in diverse areas of Engineering and Computer Science, such as computer graphics, robotics, animations, virtual reality, among others. Some of the evolutionary issues explored in this work are in the areas of parametric equations derivations, proof of related theorems, first and second order calculus related computations, among others. A Practical case is demonstrated using a graphical design, physical hand sketching, and programmatic implementation of two opposite-faced handless cups, all evolved using quadratic Bezier curves. The actual drawing was realized using web graphics canvas programming based on HTML 5 and JavaScript. This work will no doubt find relevance in computational researches in the areas of graphics, web programming, automated theorem proofs, robotic motions, among others. [ABSTRACT FROM AUTHOR]

Medical image processing encompasses the utilization of three dimensionally reconstructed images from CT or MRI scans to diagnose pathologies, surgical planning, and radiation dose calculation. The 3D reconstructed images help the radiologists and surgeons to better understand the complicated internal anatomy. This paper proposes a novel technique of using the curve fitting process through optimization for the three dimensional reconstruction of a brain tumor. The curve fitting process achieves accurate reconstruction by estimating the boundaries as well as the corner points of the model. The process of optimization in the curve fitting process is carried out using the new Levy Walk Trajectory based Seagull Optimization Algorithm which combines the merits of Levy walk with the metaheuristic Seagull Optimization Algorithm to obtain better accuracy. The boundary fitting is precisely done by considering the minimization of root mean square error among original and fitted boundaries. Finally, performance of the adopted method is validated over other existing schemes with respect to curve fit analysis and convergence analysis. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Harbin Institute of Technology. Social Sciences Edition / Haerbin Gongye Daxue Xuebao. Shehui Kexue Ban is the property of Harbin Institute of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Arquivos Brasileiros de Oftalmologia is the property of Arquivos Brasileiros de Oftalmologia and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The growing ageing population in China poses a huge demand for rehabilitation care, which can be satisfied by the latest robot technology. Focusing on the motion system of a six degrees-of-freedom (DOF) robot, this paper explores the relationship between the force, torque, velocity and the postures of the end effector and joint. Drawing on robot control theories, the existing manipulator force/position hybrid controllers were reviewed, and a force/position hybrid controller was designed for path planning of rehabilitation robot. Then, the robot was modelled on the Robot Operating System (ROS), using the Unified Robot Description Format (URDF) file and the MoveIt! Setup Assistant. Finally, our controller was tested in the ROS virtual simulation environment. The results show that our controller can facilitate and optimize the design of the path of rehabilitation robot. [ABSTRACT FROM AUTHOR]

The research related to two parts: the first section of the paper (1) is exclusively related to presenting the practical work, i.e. of the animation made in CSS3 descriptive language. The animation was presented in both its design and code aspects. The code was explained in details and the paper showed the animation (after running the mouse pointer over the rectangle) causing the transformation of the rectangle into self-shaping elements with rounded corners. In terms of the style class, CSS3 descriptive language (animation) was presented within HTML5.1 elements. The classes, boxes and the elements within the code were explained in the first section of the paper. The second section of the research (2) presented proving or rejecting the hypothesis based on a survey. The sample on which the research was conducted was a representative one and it was a non-probability (purposive) sample made up of relevant experts and scientists from the realm of web developing and designing. The second section proved and/ or rejected the hypotheses H1, H2, H3 and H4 constituting the basic hypothesis Ht; the section in turn presented and analyzed the research results via graphs concerning the most frequently used web technologies and tools for designing web pages and animations on web pages. Moreover, the application tool voted as “the best” for rendering animations on web pages was stated as well. [ABSTRACT FROM AUTHOR]

A Bezier curve is significant with its control points. When control points are given, the Bezier curve can be written using De Casteljau's algorithm. An important property of Bezier curve is that every coordinate function is a polynomial. Suppose that a curve α (t) is a curve which coordinate functions are polynomial. Can we find points that make the curve α (t) as Bezier curve? This article presents a method for finding points which present α (t) as a Bezier curve. [ABSTRACT FROM AUTHOR]

A new method for the realistic visualization of virtual cables in a 2D environment, which is representing a 3D virtual reality, is presented in this paper. They are described with two consecutive cubic Bezier curves, whose common point is movable. Experiment was carried out and the optimal proportions for the parameters of the curves were obtained in order to achieve a realistic representation of cables. The suggested method has been developed for and implemented in the Engine for Virtual Electrical Engineering Equipment. The obtained results show that it is easy to manipulate the route of the virtual cables in 2D space and that they look realistic for any position of the control point. [ABSTRACT FROM AUTHOR]

The quadratic Riccati differential equations are a class of nonlinear differential equations of much importance, and play a significant role in many fields of applied science. This paper introduces an efficient method for solving the quadratic Riccati differential equation and the Riccati differential-difference equation. In this technique, the Bezier curves method is considered as an algorithm to find the approximate solution of the nonlinear Riccati equation. Some examples in different cases are given to demonstrate simplicity and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

The paper presents a new general method of modelling route segments curvature using differential equations. The method enables joining of route segments of different curvature. Transitional curves of linear and nonlinear curvatures have been identified in the case of joining two circular arcs by S-shaped and C-oval transitions. The obtained S-shaped curves have been compared to the cubic C-Bezier curves and to the Pythagorean hodograph quantic Bezier curve using the Lateral Change of Acceleration diagram and the dynamic model. The analysis of dynamic properties has showed an advantage of the obtained transition curve of nonlinear curvature over Bezier curves. [ABSTRACT FROM AUTHOR]

In minimally invasive robotic surgery (MIRS), a surgeon teleoperates a robotic arm from a master console. This arm operates inside the patient's body through a small orifice which constrains the end-effector's translation along two axes. The workspace of such a robotic arm depends on its design as well as orifice location. Conventionally, the design of such an arm is optimized for large workspace and high dexterity. However, this large workspace might be reachable through only a few orifices, thus making the workspace volume and operation quite sensitive to the orifice location. To overcome this problem, we optimized the design of a 3 degrees of freedom serial robotic arm to attain multiple adjacent (desired number of) possible orifice locations, through which a planar workspace of pre-specified geometry can be traced. To achieve this goal, an algorithm was developed to relate the design of such an MIRS arm to the possible orifice positions. The optimization problem was solved using several metaheuristics such as simulated annealing, Tabu search, artificial bee colonization and genetic algorithm, and their performance was compared. [ABSTRACT FROM AUTHOR]

This paper presents a simple and explicit method for G2-constrained merging of a pair of Bézier curves by minimizing the l2 distance defined in terms of control points. After expressing the l2 distance as a quadratic function of two parameters, the optimally merged curve can be explicitly obtained, which is achieved by control point optimization such that the l2 distance is minimized. The existence of the unique solution is shown by proving that the l2 distance is convex. The proposed method is explicit and efficient since it is non-iterative and expressed by known control points. Numerical examples demonstrate the effectiveness of the new method. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we compare four nonparametric quantile function estimators for randomly right censored data: the Kaplan–Meier estimator, the linearly interpolated Kaplan–Meier estimator, the kernel-type survival function estimator, and the Bézier curve smoothing estimator. Also, we compare several kinds of confidence intervals of quantiles for four nonparametric quantile function estimators. [Copyright &y& Elsevier]

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. [Copyright &y& Elsevier]

Simulation of aquatic plants has always been a difficulty and central issue. For simulation of long and curl leaf of water plants, the method of Bezier curve can be used to generate the major veins (median line) and the edge of curve of the leaf. By moving the control points on the central line or boundary curve, curve interpolation can be applied to generate the side central line. The gird of the leaf framework is generated by the method of triangulation and the dark spot on the leaf is generated by using multitexturing. The result shows that the method can draw the water plants quite well and is very efficient. [ABSTRACT FROM AUTHOR]

The purpose of this study was to establish a geometric design method for the occiusal outlines of complex inlay cavities as a continuation study of a previous design method for simple class I inlay cavity. A method for extending the occiusal outline to the buccal or lingual groove and to three preparation types of the proximal portions of class II inlay cavities -namely, straight line preparation, sweeping curve preparation, and reverse curve preparation- was investigated. To ensure the smoothness of the occlusal outline, a Bézier curve was introduced in the design. A minimal number of control points for the curve was applied to define each preparation type. The design method was experimentally applied to mandibular and maxillary first molars. Smooth outlines of the complex inlay cavities in the molars with tool accessibility throughout the cavities were achievable by using the present method. [ABSTRACT FROM AUTHOR]

In a recent article published in this journal, Baydas and Karakas show how to compute the Bézier representation of a curve given in power form. We note that this straightforward exercise, including a closed-form expression for the transformation matrix, can be found in the existing literature on CAGD. [ABSTRACT FROM AUTHOR]

The kranok pattern is a classical Thai pattern, often seen in the ornamentation of Thai religious artifacts such as Tripiṭaka cabinets, temple doors and coffins. All Thai trainee artists must practice drawing the kranok pattern because it is a fundamental motif in Thai traditional decorative art. Individual skilled artists and instructors have their own preferred ways of drawing the pattern, and their styles differ in ornamental details. Nevertheless, all make use of similar basic structures. Most trainees learn a range of styles by observing experienced artists. After exploring the methods of drawing used by experts and published in textbooks, we designed an algorithm for automatically generating kranok patterns. We used an interactive evolutionary algorithm (IEA) to improve the aesthetic appeal of the generated patterns in response to users' feedback. The aim of our work was not to replace artists with machines, but to enhance human artistic expression. Specifically, the work aimed to help users without artistic skills to create kranok patterns in their own style. The algorithm facilitated the creation of a variety of personalized kranok patterns – diverse in their expressive curvature, refinement and proportions – that were satisfying to the varying preferences of a range of users. We also analyzed the proposed algorithm's behavior in terms of its convergence to generate specific shapes. The proposed method was examined by 28 respondents (27 Thai and 1 foreign) who were selected to include representatives of both sexes as well as experts in both Thai drawing and evolutionary algorithms. The results from our questionnaires showed that all respondents were satisfied with the generated kranok patterns: one respondent was 'completely satisfied', seventeen 'very satisfied', seven 'moderately satisfied', and three 'slightly satisfied'. • Our IEA enables machines to create a variety of Kranok patterns. • The IEA takes each user' feedback to tailor the patterns specially for her. • We study the IEA's behavior and user satisfaction levels. • The IEA rapidly converges and generates desired patterns without annoying users. • From the surveys, most respondents are overall highly satisfied with the application. [ABSTRACT FROM AUTHOR]