Bezier Curves Research Articles

Emulating the Effective Ankle Stiffness of Commercial Prosthetic Feet Using a Robotic Prosthetic Foot Emulator.

Prosthetic foot selection for individuals with lower limb amputation relies primarily on clinician judgment. The prosthesis user rarely has an opportunity to provide experiential input into the decision by trying different feet. A prosthetic foot emulator (PFE) is a robotic prosthetic foot that could facilitate prosthesis users' ability to trial feet with different mechanical characteristics. Here, we introduce a procedure by which a robotic PFE is configured to emulate the sagittal plane effective ankle stiffness of a range of commercial prosthetic forefeet. Mechanical testing was used to collect data on five types of commercial prosthetic feet across a range of foot sizes and intended user body weights. Emulated forefoot profiles were parameterized using Bezier curve fitting on ankle torque-angle data. Mechanical testing was repeated with the PFE, across a subset of emulated foot conditions, to assess the accuracy of the emulation. Linear mixed-effects regression and Bland-Altman Limits of Agreement analyses were used to compare emulated and commercial ankle torque-angle data. Effective ankle stiffness of the emulated feet was significantly associated with the corresponding commercial prosthetic feet (p <0.001). On average, the emulated forefeet reproduced the effective ankle stiffness of corresponding commercial feet within 1%. Furthermore, differences were independent of prosthetic foot type, foot size, or user body weight. These findings suggest that commercial prosthetic foot properties can be effectively mimicked by a PFE, which is the important first step toward enabling prosthesis users to quickly trial different feet using a PFE as part of prosthetic foot prescription.

ALGORITHMS AND ARCHITECTURE OF THE SOFTWARE SYSTEM OF AUTOMATED NATURAL AND ANTHROPOGENIC LANDSCAPE GENERATION

Context. The problem of automation of the generation of natural and anthropogenic landscapes is considered. The subject of the research is methods of procedural generation of landscapes that quickly and realistically visualize natural and anthropogenic objects taking into account different levels of detail. &#x0D; Objective. The goal of the work is to improve the rendering quality and efficiency of the procedural generation process of landscape surfaces at any level of detail based on the implementation of the developed method.&#x0D; Method. The proposed method of visualization involves the construction of a natural landscape using Bezier curves and surfaces and manual editing of individual segments; use of software agents that are responsible for individual steps of generating anthropogenic objects; adaptation of anthropogenic objects to the characteristics of natural landscapes; containerization of three-dimensional objects, which is used in various steps to organize the storage and loading of objects efficiently. A generated heightmap based on the Perlin noise algorithm is used to construct surfaces on individual segments of the natural landscape. Landscape processing software agents are used to unify the design of algorithms for creating and processing information about anthropogenic objects. Correct application operation and error resistance is guaranteed due to the inheritance of a specific interface by all implementations of agents. Containerization with two-level caching ensures the efficiency of display detailing. &#x0D; Results. The developed method is implemented programmatically, and its efficiency is investigated for different variants of input data, which to the greatest extent determine the complexity of visualization objects. &#x0D; Conclusions. The conducted experiments confirmed the efficiency of the proposed algorithmic software and its viability in practice in solving problems of automated landscape generation. Prospects for further research include improvement and expansion of the algorithms for procedural landscape generation, functionality complication of manual visualized object processing, and division of individual objects into separate hierarchies of containers.

Implementing a visual representation of analytic data using a radar chart

This article considers the implementation of one of the ways to visually display analytical data using a radar chart. The implementation of scaling and displaying inscriptions and images by sectors using Bezier curves is described in detail.

GEOMETRIC MODELING OF THE CONTOUR ARCS PASSING THROUGH THE PREDEFINED POINTS

Multidimensional interpolation is an important scientific task in demand of various science fields and technology. The geometrical theory of multidimensional interpolation has been further developed in terms of extending the shaping tools of geometrical modeling at the expense of the contour arcs passing through the predefined points. The proposed method is based on modification of Bezier’s curve with preservation of tangents in its initial and/or final points. Then the Bezier curve retains its geometrical properties of the arc, but additionally has the possibility to pass through several points set in advance. Examples are given of modifying a 5th-order Bezier curve arc into a curve arc passing through four predefined points and a 3rd-order Bezier curve arc passing through three predefined points and having a tangent in the initial point, which is proposed to be used as the onion dome surface forming arc. Such a method helps to reduce the piecewise character of composite curves when building curves. The introduction of such research results into computeraided design and solid-state modeling (CAD/CAM) systems will allow to expand their toolbox in terms of shaping surfaces and solids of technical shapes of various purposes.

Anti-jamming trajectory design for UAV-enabled wireless sensor networks using communication flight corridor

This paper investigates the anti-jamming trajectory design to safeguard the effective data collection, where a unmanned aerial vehicle (UAV) is dispatched to collect data over multiple sensor nodes(SNs) in jamming environment. Under the limited power and transmission range of SNs, we aim to minimize the UAV's flight energy consumption in a finite task period, by jointly optimizing SNs collection sequence and UAV flight trajectory. Firstly, we propose a general optimization framework which consists of path planning and trajectory optimization for the formulated non-convex problem. In the path planning phase, a dynamic programming (DP) algorithm is used to provide the initial path of the UAV, which is the shortest path to visit each SN. In the trajectory optimization phase, we introduce the concept of Communication Flight Corridor (CFC) to meet the non-convex constraints and apply a piecewise Bezier curve, based on Bernoulli polynomial, to represent the flight trajectory of the UAV, which can transform the optimization variables from infinite time variables to polynomial coefficients of finite order. Finally, we simulate the flight trajectory of UAV in hovering mode and continuous flight mode under different parameters, and the simulation results demonstrate the effectiveness of the proposed method.

Computer simulation of the physical neutralization of drones in a Smart City

We present a simple computer simulation model for the interaction of automatic guns with unarmed drones. Each drone is represented as a rigid body that consists of several simple bodies such as parallelepipeds, ellipsoids, etc. The simplified spatial trajectory of the drone is constructed using third-order Bezier curves. A relatively large group of unconnected drones may be simulated in a computationally fast way using this method. Automatic guns are agents that are shooting at drones with a single of burst fire relative to the ideal aiming point. We performed a simulation of the flight of several drones against several automatic guns for different conditions. As a result of this simulation, the spatial distribution of the drone hit probabilities, the special distribution of the fraction of defeated drones depending on the number of guns, and the influence of urban obstacles on the fraction of drones defeated are presented.

Reinforcement learning reward function in unmanned aerial vehicle control tasks

This paper presents a new reward function that can be used for deep reinforcement learning in unmanned aerial vehicle (UAV) control and navigation problems. The reward function is based on the construction and estimation of the time of simplified trajectories to the target, which are third-order Bezier curves. This reward function can be applied unchanged to solve problems in both two-dimensional and three-dimensional virtual environments. The effectiveness of the reward function was tested in a newly developed virtual environment, namely, a simplified two-dimensional environment describing the dynamics of UAV control and flight, taking into account the forces of thrust, inertia, gravity, and aerodynamic drag. In this formulation, three tasks of UAV control and navigation were successfully solved: UAV flight to a given point in space, avoidance of interception by another UAV, and organization of interception of one UAV by another. The three most relevant modern deep reinforcement learning algorithms, Soft actor-critic, Deep Deterministic Policy Gradient, and Twin Delayed Deep Deterministic Policy Gradient were used. All three algorithms performed well, indicating the effectiveness of the selected reward function.

Generalized Bezier components and successive component refinement using moving morphable components

This paper demonstrates developments that introduce generalized Bezier components in the Moving Morphable Components (MMC) optimization framework. Methods of enhancing the parameterization of the components to provide the opportunity for a better optimum, than can be achieved using existing approaches, are also described. The use of control points and Bezier curves for representing structural components provides both additional flexibility in the shape and a parameterization that complies with extrude and swept feature-based templates available in commercial computer-aided design (CAD) packages. Methods of representing these structural components, calculating analytical derivatives, and numerical examples demonstrating their integration in the MMC framework, are presented for a series of author-derived and literature problems. A successive refinement technique demonstrates how the additional flexibility in the structural components enables progressive improvement in the objective function. For the examined problems, increasing the design variables per component (from 5 to 15) resulted in solutions with 6% to 36% reduction in compliance. This improvement was achieved without increasing the number of components in the design space.

Two-dimensional reciprocal cross entropy multi-threshold combined with improved firefly algorithm for lung parenchyma segmentation of COVID-19 CT image

The lesions of COVID-19 CT image show various kinds of ground-glass opacity and consolidation, which are distributed in left lung, right lung or both lungs. The lung lobes are uneven and it have similar gray value to the surrounding arteries, veins, and bronchi. The lesions of COVID-19 have different sizes and shapes in different periods. Accurate segmentation of lung parenchyma in CT image is a key step in COVID-19 detection and diagnosis. Aiming at the unideal effect of traditional image segmentation methods on lung parenchyma segmentation in CT images, a lung parenchyma segmentation method based on two-dimensional reciprocal cross entropy multi-threshold combined with improved firefly algorithm is proposed. Firstly, the optimal threshold method is used to realize the initial segmentation of the lung, so that the segmentation threshold can change adaptively according to the detailed information of lung lobes, trachea, bronchi and ground-glass opacity. Then the lung parenchyma is further processed to obtain the lung parenchyma template, and then the defective template is repaired combined with the improved Freeman chain code and Bezier curve. Finally, the lung parenchyma is extracted by multiplying the template with the lung CT image. The accuracy of lung parenchyma segmentation has been improved in the contrast clarity of CT image and the consistency of lung parenchyma regional features, with an average segmentation accuracy rate of 97.4%. The experimental results show that for COVID-19 and suspected cases, the method has an ideal segmentation effect, and it has good accuracy and robustness.

Visual Scratch Defect Detection System of Aluminum Flat Tube Based on Cubic Bezier Curve Fitting Using Linear Scan Camera

This paper presents a scratch detection system based on a cubic Bezier curve fitting using a linear scan camera. The objective was to detect the scratch defects of an aluminum flat tube stably in real-time under complex uncertain background noise. To that end, according to the features of the input image of the linear scan camera and the scratch defects, the proposed method first segmented the input image to ten equal sections in a longitudinal direction, and for every section, OTSU thresholding and morphological filtering were used to reduce the background noise. After the image preprocessing, every section image was projected along a vertical direction to form a vertical histogram. After that, for each point of every vertical histogram, a novel curve fitting method based on the Monte Carlo method was employed to calculate the best fitted Bezier curve. All the curvatures of the middle point of the best fitted Bezier curves then formed a curvature curve, and the scratches were located by finding the peaks of the curvature curve. Next, the result of the ten sections were fused to find the final positions of the scratches. The experimental results based on the linear scan camera that captured the image of flat tubes on a moving speed of 2m/s showed that the proposed method can detect the scratch defects under complex background noise with a high success rate in real-time.

An effective approach based on Smooth Composite Chebyshev Finite Difference Method and its applications to Bratu-type and higher order Lane–Emden problems

The Smooth Composite Chebyshev Finite Difference method is generalized for higher order initial and boundary value problems. Round-off and truncation error analyses and convergence analysis of the method are also extended to higher order. The proposed method is applied to obtain the highly precise numerical solutions of boundary or initial value problems of the Bratu and higher order Lane Emden types. To visualize the competency of the presented method, the obtained results are compared with nine different methods, namely, Bezier curve method, Adomian decomposition method, Operational matrix collocation method, Direct collocation method, Haar Wavelet Collocation, Bernstein Collocation Method, Improved decomposition method, Quartic B-Spline method and New Cubic B-spline method. The comparisons show that the presented method is highly accurate than the other numerical methods and also gets rid of the singularity of the given problems.

Optimized Bezier Curve Based Intensity Mapping Scheme for Low Light Image Enhancement

Low light enhancement has been very challenging for images acquired under extremely-low light circumstances. In this article, an optimized Bezier curve based intensity mapping scheme for low light image enhancement is proposed. The proposed algorithm is employed to adjust the intensity mapping curve in both dark and bright regions. To enhance the low visibility details and suppress the noise, the control points of the Bezier curve transformation are automatically obtained by the optimal weighting process. The optimal constraints of the weighted probability distribution function are calculated by whale optimization algorithm to solve the problem of under and over enhancement. Tests on different low light images are conducted to expose the efficiency and superiority of the proposed method over other existing methods in terms of improving the visual quality and bringing out the hidden details. The proposed method can preserve some minor details of the brighter portions and significantly reduce the intensive noise hidden in the low light scenes without any color distortion.

FEATURES SIMPLIFICATION USING CUBIC BEZIER PROPERTIES FOR GAIT RECOGNITION ON SMARTPHONE

Smartphone is widely used around the world. It’s user authentication usually used pin code, pattern code, fingerprint and conventional login authentication. This kinds of authentication mechanism is intrusive because those mechanisms requires users to give exclusive interaction for user authentication during the process. One of authentication method which is non-intrusive during data collection is authentication by using gait. This mechanism classified as non-intrusive because this mechanism could gather biometric data without being noticed by the authentication subjects. Since it is non-intrusive, this mechanism allows re-authentications without bothering the authentication subjects. One of the recent gait recognition is using accelerometer on smartphone to measure and capture acceleration data on gait. This method extract step cycles in various length, map and interpolate the data into higher sample count, and then use each of mapped and interpolated data as feature using recognition. Regardless the classification or recognition method, using each mapped and interpolated data as features would result in high processing time during classification or recognition due to high feature count. In this research, we try to simplify the features of gait data with minimum data loss so it might give robust result with less latency by aligning cubic Bezier curve to step cycle data and extracting the Bezier properties.

Redesign Arabic Calligraphy Outline by using Bezier, Wang-Ball and Said-Ball Curves

In the history of the revitalization of traditional art in the modern world, Arabic calligraphy was one of the art phenomena. This research suggests using Bezier curves, Wang Ball curves, and Said-Ball curves to improve Arabic calligraphy. Our goal in calligraphy is to achieve a smooth beautifying contour of a character. The calligraphy outline, which was largely Arabic, was frequently applied in Bezier curve degrees two and three. As a result, the degree elevation for each curve was increased until it reached degree four, allowing for greater Bezier curve study. This paper presents the comparisons between those three curves by using the Arabic calligraphy "Aamin" as the subject. Curve fitting, curve manipulation, mixing, and merging of curves were all examples of how Bezier curves were employed in Computer Aided Design. Ball curves, also known as a generalized ball basis, are a type of curve that has arbitrary even and odd degrees. There were two types of generalized ball curves: Wang-ball curves and Said-ball curves, each with their own special position parameter. The best curves of the Bezier, Wang-Ball, and Said-Ball curves were combined to create "Aamin" calligraphy. All of the results were programmed into the MATLAB software and graphed. For the redesign “Aamin” calligraphy Bezier curve computes the best time compared to Wang-Ball and Said-Ball curve. The computation time in MATLAB software for the degree 2, degree 3 and degree 4 are 1.48 seconds, 1.52 seconds and 2.50 seconds respectively. The higher the degree elevation, the longer the computation time to generate "Aamin" calligraphy, according to these findings. This research provides the fundamental design and empirical findings in the process of improving the production of computerized Arabic calligraphy.

Study on the effect of curvature radius sudden change on mechanism characteristics for the constant-breadth two circular-arc cam mechanism with an inclined flat-faced follower

A two circular-arc cam mechanism is a special kind of constant-breadth cam. At the junction point of each cam contour, a mutation of the curvature radius may be produced, which affects the motion performance of the mechanism, especially its jerk performance at high speed. Based on a proposed motion model, the follower movements of the constant-breadth two circular-arc cam mechanism with an inclined flat-faced follower are analyzed. Bezier Curve is proposed to fit the driving law of the cam mechanism, while variable speed law is adopted to drive the cam mechanism motion, thus reducing motion characteristic value (AV)max (i.e., the maximum value of the velocity multiplied by acceleration for the follower’s motion law of the cam mechanism at the same motion time point) and the jerk of the follower. In this paper, the establishment of the optimization objective functions and constraint conditions, and the control node selections of the cam drive function are researched. The optimization results are obtained by using the primary objective method. The results of a test case calculation and simulation show that, the optimized drive function, according to the variable motor speed, can significantly reduce the value of (AV)max of the follower, while the jerks of the follower system are also reduced considerably. More precisely, the (AV)max value is reduced by 11.63% and the jerks are reduced on average by 15.35%, at the three jerk positions. The proposed methods provide a new approach to improving the kinematic performance of similar cam mechanisms.

Self-motion behaviors of kinematically redundant manipulator for continuous path planning

This paper presents self-motion behaviors of 3-DOF planar robotic arm when it tracks a predefined end-effector path. In this case, the self-motion contributes to geometry of a motion envelope. The Bezier curve degree fifth is utilized as the tracked path. Different geometry of the motion envelope can be used to avoid collision while it also follows the tracked path accurately. A theta global as closed form solution of 3-DOF planar robot is modeled as a polynomial degree sixth. A Genetic Algorithm (GA) as one of meta-heuristic optimizations is used to find optimal solution of the path planning approach. An effect of initial and final joint angles in the robotic arm motion is also investigated. The theta global trajectories are also possible to contain an imaginary number. The imaginary number of the theta global trajectories can be used as a sign that position errors are present and the trajectories need to be repaired using the self-motion analysis.

Design, analysis, and optimization of a strain wave gear with a novel tooth profile

In this study, an optimization process was designed for a strain wave gear (SWG) through finite element analysis (FEA) to improve its performance. Two optimization steps are executed in this process. In the first optimization step, a novel two-dimensional (2D) tooth profile is obtained using a double Bezier curve with a common tangent line profile (DBCCTLP), and the mathematical model of this profile is derived. Subsequently, the obtained tooth profile is optimized through 2D FEA based on the torsional stiffness and number of engaged teeth. A three-dimensional (3D) model of an SWG is subsequently established to explore its 3D meshing performance through FEA and optimize the parameters of its flexible spline (FS). In the second optimization step, 3D FEA is conducted to predict the torsional stiffness, hysteresis loss, and stress of the SWG using the DBCCTLP-based optimum tooth profile. The optimum structural design parameters for a 3D FS cup were determined through 3D FEA and optimization. Finally, the transmission error and cyclic stress for the initial and optimum SWG design were successfully simulated and compared.

RRR-MF: Time-domain feature reconstruction of road roughness in front of anchor machine via multimodal fusion

Road recognition technology extracts roadway roughness information to provide decision information for active control, which is an extremely important issue to be solved in the autonomous operation of anchor machines. However, the reality of road recognition technology in elevation detection of coal machine equipment is far behind earlier expectations. The RRR-MF with SINS as the backbone is proposed to realize the localization and mapping of anchor machines. In addition, The RRR-MF is designed with a feature distribution controller to enhance the roughness features of the floor point cloud and an improved Bezier curve fitting to achieve road roughness reconstruction. Meanwhile, we design an immovable high-precision measurement platform to collect standard values. LeGO-LOAM and LIO-SAM are set as control groups, and the result of RRR-MF is the closest to the standard value with half the error of the other control groups, which meets the needs of active control such as path planning and trajectory tracking.

Well Path Design and Optimization Using Composite Cubic Bezier Curves

Summary Well path design is a primary part of the well plan for well drilling. The main objective of well path design is to generate a continuous and smooth trajectory from a start point to a target point under various design constraints. The conventional approaches usually consist of a number of circular arcs and straight lines, representing build and turn sections and hold sections, respectively. This study presents a new methodology to generate a continuous and smooth well path trajectory with low dogleg severity (DLS) using composite Bezier curves. The trajectory consists of a number of piecewise cubic Bezier curves that satisfy C1 and/or C2 continuity conditions, meaning that the joining curves share the first and second derivatives at the joining points, respectively. The comprehensive methodology for determining the composite curve and the primary properties of the well trajectory is presented. Their advantages regarding feasibility and efficiency are demonstrated in case studies. The proposed method is also applied in a field case, where the automatically generated well path using composite Bezier curves is smoother with a smaller DLS. It can also be quickly updated if a real-time anticollision adjustment is required. The presented work has strong potential to be an efficient and automatic tool for path design and optimization in well planning.

Multi-segment trajectory tracking of the redundant space robot for smooth motion planning based on interpolation of linear polynomials with parabolic blend

This work presents multi-segment trajectory tracking of the redundant space robot for smooth motion planning based on interpolation of linear polynomials with the parabolic blend. First, direct kinematics equation is inhibited with cuckoo search algorithm (CSA) to avoid orientation singularity. Second, the Bezier curve has been used to depict the shape of the joint trajectory by interpolating linear polynomials with the parabolic blend. Third, CSA is used to find the optimal solution of joint trajectories by satisfying the imposed constraints (joint velocity and acceleration).Fourth, various influencing variables, such as joint angles, joint rates, joint accelerations, end-effector attitude quaternion, end-effector position, and base attitude orientation are optimized so that the end-effector smoothly achieves the desired pose by stabilizing the base attitude. At last, the jerk minimized motion planning scheme is executed concerning imposed constraints such as (joint angles, angular velocities, angular accelerations, and torque). The proposed methodology of a redundant 7 Degree of Freedom (DOF) space robot has validated the efficacy of the proposed method. Using this method, a smooth trajectory path is achieved by controlling base attitude orientation while maintaining the end-effector pose during task completion. Additionally, with proposed jerk minimized motion planning, the manipulator vibration is reduced.