Degree reduction of parametric curves and surfaces is an important process in data communication between CAD systems. The degenerate condition of Bezier curves and the constrained optimization method are used to devel...Degree reduction of parametric curves and surfaces is an important process in data communication between CAD systems. The degenerate condition of Bezier curves and the constrained optimization method are used to develop a new degree reduction method for Bezier curves. An error analysis of the degree reduction is also given. The degree reduction scheme is combined with a subdivision algorithm to generate lower degree approximations which are within some preset error tolerance of the prescribed Bezier curve. Geometric continuity between adjacent curve segments is also considered in the subdivision/degree reduction process.展开更多
In this paper, we present two new unified mathematics models of conics and polynomial curves, called algebraic hyperbolic trigonometric （ AHT） Bezier curves and non-uniform algebraic hyperbolic trigonometric （ NUAH...In this paper, we present two new unified mathematics models of conics and polynomial curves, called algebraic hyperbolic trigonometric （ AHT） Bezier curves and non-uniform algebraic hyperbolic trigonometric （ NUAHT） B-spline curves of order n, which are generated over the space span{sin t, cos t, sinh t, cosh t, 1, t,..., t^n-5}, n 7〉 5. The two kinds of curves share most of the properties as those of the Bezier curves and B-spline curves in polynomial space. In particular, they can represent exactly some remarkable transcendental curves such as the helix, the cycloid and the catenary. The subdivision formulae of these new kinds of curves are also given. The generations of the tensor product surfaces are straightforward. Using the new mathematics models, we present the control mesh representations of two classes of minimal surfaces.展开更多
A Particle Image Velocimetry (PIV) method based on the image separation andreconstruction with the median filter and triangular Bezier patch was proposed to measure multiplevelocity fields from single-camera images in...A Particle Image Velocimetry (PIV) method based on the image separation andreconstruction with the median filter and triangular Bezier patch was proposed to measure multiplevelocity fields from single-camera images in the present study. The method was examined on syntheticPIV images with the Green-Taylor two-phase vortex flows and the test results showed high accuracyand highly correct tracking percent compared with the exact solution. An experiment of the bubblyjet flow was also conducted as a practical demonstration of the present method. As a result, it isconfirmed from the simulation image examination and the experimental measurement that the proposedmethod shows a good performance in the measurement of bubble and particle phases.展开更多
An aerodynamic optimization method for axial flow compressor blades available for engineering is developed in this paper. Bezier surface is adopted as parameterization method to control the suction surface of the blad...An aerodynamic optimization method for axial flow compressor blades available for engineering is developed in this paper. Bezier surface is adopted as parameterization method to control the suction surface of the blades, which brings the following advantages:(A) significantly reducing design variables;(B) easy to ensure the mechanical strength of rotating blades;(C) better physical understanding;(D) easy to achieve smooth surface. The Improved Artificial Bee Colony(IABC) algorithm, which significantly increases the convergence speed and global optimization ability, is adopted to find the optimal result. A new engineering optimization tool is constructed by combining the surface parametric control method, the IABC algorithm, with a verified Computational Fluid Dynamics(CFD) simulation method, and it has been successfully applied in the aerodynamic optimization for a single-row transonic rotor(Rotor 37) and a single-stage transonic axialflow compressor(Stage 35). With the constraint that the relative change in the flow rate is less than0.5% and the total pressure ratio does not decrease, within the acceptable time in engineering, the adiabatic efficiency of Rotor 37 at design point increases by 1.02%, while its surge margin 0.84%,and the adiabatic efficiency of Stage 35 0.54%, while its surge margin 1.11% after optimization, to verify the effectiveness and potential in engineering of this new tool for optimization of axial compressor blade.展开更多
Degree reduction of parametric curves and surfaces is an important process in the exchange of product model data between various CAD systems. In this paper the degenerate conditions of triangular Bezier surface patch...Degree reduction of parametric curves and surfaces is an important process in the exchange of product model data between various CAD systems. In this paper the degenerate conditions of triangular Bezier surface patches are derived. The degenerate conditions and constrained optimization methods are used to develop a degree reduction method for triangular Bezier surface patches. The error in the degree reduction of a triangular Bezier surface is also shown to depend on some geometric invariants which decrease exponentially in the subdivision process. Therefore, the degree reduction method can be combined with a subdivision algorithm to generate lower degree approximations which are within some preset error tolerance.展开更多
Aimed at the problems of a traditional ant colony algorithm,such as the path search direction and field of view,an inability to find the shortest path,a propensity toward deadlock and an unsmooth path,an ant colony al...Aimed at the problems of a traditional ant colony algorithm,such as the path search direction and field of view,an inability to find the shortest path,a propensity toward deadlock and an unsmooth path,an ant colony algorithm for use in a new environment is proposed.First,the feature points of an obstacle are extracted to preprocess the grid map environment,which can avoid entering a trap and solve the deadlock problem.Second,these feature points are used as pathfinding access nodes to reduce the node access,with more moving directions to be selected,and the locations of the feature points to be selected determine the range of the pathfinding field of view.Then,based on the feature points,an unequal distribution of pheromones and a two-way parallel path search are used to improve the construction efficiency of the solution,an improved heuristic function is used to enhance the guiding role of the path search,and the pheromone volatilization coefficient is dynamically adjusted to avoid a premature convergence of the algorithm.Third,a Bezier curve is used to smooth the shortest path obtained.Finally,using grid maps with a different complexity and different scales,a simulation comparing the results of the proposed algorithm with those of traditional and other improved ant colony algorithms verifies its feasibility and superiority.展开更多
This paper introduces the algebraic property of bivariate orthonormal Jacobi polynomials into geometric approximation. Based on the latest results on the transformation formulae between bivariate Bernstein polynomials...This paper introduces the algebraic property of bivariate orthonormal Jacobi polynomials into geometric approximation. Based on the latest results on the transformation formulae between bivariate Bernstein polynomials and Jacobi polynomials, we naturally deduce a novel algorithm for multi-degree reduction of triangular B^zier surfaces. This algorithm possesses four characteristics： ability of error forecast, explicit expression, less time consumption, and best precision. That is, firstly, whether there exists a multi-degree reduced surface within a prescribed tolerance is judged beforehand; secondly, all the operations of multi-degree reduction are just to multiply the column vector generated by sorting the series of the control points of the original surface in lexicographic order by a matrix; thirdly, this matrix can be computed at one time and stored in an array before processing degree reduction; fourthly, the multi-degree reduced surface achieves an optimal approximation in the norm L2. Some numerical experiments are presented to validate the effectiveness of this algorithm, and to show that the algorithm is applicable to information processing of products in CAD system.展开更多
A super redundant serpentine manipulator has slender structure and multiple degrees of freedom.It can travel through narrow spaces and move in complex spaces.This manipulator is composed of many modules that can form ...A super redundant serpentine manipulator has slender structure and multiple degrees of freedom.It can travel through narrow spaces and move in complex spaces.This manipulator is composed of many modules that can form different lengths of robot arms for different application sites.The increase in degrees of freedom causes the inverse kinematics of redundant manipulator to be typical and immensely increases the calculation load in the joint space.This paper presents an integrated optimization method to solve the path planning for obstacle avoidance and discrete trajectory tracking of a super redundant manipulator.In this integrated optimization,path planning is established on a Bezier curve,and particle swarm optimization is adopted to adjust the control points of the Bezier curve with the kinematic constraints of manipulator.A feasible obstacle avoidance path is obtained along with a discrete trajectory tracking by using a follow-the-leader strategy.The relative distance between each two discrete path points is limited to reduce the fitting error of the connecting rigid links to the smooth curve.Simulation results show that this integrated optimization method can rapidly search for the appropriate trajectory to guide the manipulator in obtaining the target while achieving obstacle avoidance and meeting joint constraints.The proposed algorithm is suitable for 3D space obstacle avoidance and multitarget path tracking.展开更多
The act of transmitting photos via the Internet has become a routine and significant activity.Enhancing the security measures to safeguard these images from counterfeiting and modifications is a critical domain that c...The act of transmitting photos via the Internet has become a routine and significant activity.Enhancing the security measures to safeguard these images from counterfeiting and modifications is a critical domain that can still be further enhanced.This study presents a system that employs a range of approaches and algorithms to ensure the security of transmitted venous images.The main goal of this work is to create a very effective system for compressing individual biometrics in order to improve the overall accuracy and security of digital photographs by means of image compression.This paper introduces a content-based image authentication mechanism that is suitable for usage across an untrusted network and resistant to data loss during transmission.By employing scale attributes and a key-dependent parametric Long Short-Term Memory(LSTM),it is feasible to improve the resilience of digital signatures against image deterioration and strengthen their security against malicious actions.Furthermore,the successful implementation of transmitting biometric data in a compressed format over a wireless network has been accomplished.For applications involving the transmission and sharing of images across a network.The suggested technique utilizes the scalability of a structural digital signature to attain a satisfactory equilibrium between security and picture transfer.An effective adaptive compression strategy was created to lengthen the overall lifetime of the network by sharing the processing of responsibilities.This scheme ensures a large reduction in computational and energy requirements while minimizing image quality loss.This approach employs multi-scale characteristics to improve the resistance of signatures against image deterioration.The proposed system attained a Gaussian noise value of 98%and a rotation accuracy surpassing 99%.展开更多
Robots driven by batteries are clean, quiet, and can work indoors or in space. However, the battery endurance is a great problem. A new gait parameter design energy saving strategy to extend the working hours of the q...Robots driven by batteries are clean, quiet, and can work indoors or in space. However, the battery endurance is a great problem. A new gait parameter design energy saving strategy to extend the working hours of the quadruped robot is proposed. A dynamic model of the robot is established to estimate and analyze the energy expenditures during trotting. Given a trotting speed, opti- mal stride frequency and stride length can minimize the energy expenditure. However, the relationship between the speed and the optimal gait parameters is nonlinear, which is difficult for practical application. Therefore, a simplified gait parameter design method for energy saving is pro- posed. A critical trotting speed of the quadruped robot is found and can be used to decide the gait parameters. When the robot is travelling lower than this speed, it is better to keep a constant stride length and change the cycle period. When the robot is travelling higher than this speed, it is better to keep a constant cycle period and change the stride length. Simulations and experiments on the quadruped robot show that by using the proposed gait parameter design approach, the energy expenditure can be reduced by about 54% compared with the 100 mm stride length under 500 mm/s speed. In general, an energy expenditure model based on the gait parameter of the quadruped robot is built and the trotting gait parameters design approach for energy saving is proposed.展开更多
We decompose the problem of the optimal multi-degree reduction of Bézier curves with corners constraint into two simpler subproblems, namely making high order interpolations at the two endpoints without degree re...We decompose the problem of the optimal multi-degree reduction of Bézier curves with corners constraint into two simpler subproblems, namely making high order interpolations at the two endpoints without degree reduction, and doing optimal degree reduction without making high order interpolations at the two endpoints. Further, we convert the second subproblem into multi-degree reduction of Jacobi polynomials. Then, we can easily derive the optimal solution using orthonormality of Jacobi polynomials and the least square method of unequally accurate measurement. This method of 'divide and conquer' has several advantages including maintaining high continuity at the two endpoints of the curve, doing multi-degree reduction only once, using explicit approximation expressions, estimating error in advance, low time cost, and high precision. More importantly, it is not only deduced simply and directly, but also can be easily extended to the degree reduction of surfaces. Finally, we present two examples to demonstrate the effectiveness of our algorithm.展开更多
Background Automatic guided vehicles(AGVs)have developed rapidly in recent years and have been used in several fields,including intelligent transportation,cargo assembly,military testing,and others.A key issue in thes...Background Automatic guided vehicles(AGVs)have developed rapidly in recent years and have been used in several fields,including intelligent transportation,cargo assembly,military testing,and others.A key issue in these applications is path planning.Global path planning results based on known environmental information are used as the ideal path for AGVs combined with local path planning to achieve safe and rapid arrival at the destination.Using the global planning method,the ideal path should meet the requirements of as few turns as possible,a short planning time,and continuous path curvature.Methods We propose a global path-planning method based on an improved A^(*)algorithm.The robustness of the algorithm was verified by simulation experiments in typical multiobstacle and indoor scenarios.To improve the efficiency of the path-finding time,we increase the heuristic information weight of the target location and avoid invalid cost calculations of the obstacle areas in the dynamic programming process.Subsequently,the optimality of the number of turns in the path is ensured based on the turning node backtracking optimization method.Because the final global path needs to satisfy the AGV kinematic constraints and curvature continuity condition,we adopt a curve smoothing scheme and select the optimal result that meets the constraints.Conclusions Simulation results show that the improved algorithm proposed in this study outperforms the traditional method and can help AGVs improve the efficiency of task execution by planning a path with low complexity and smoothness.Additionally,this scheme provides a new solution for global path planning of unmanned vehicles.展开更多
文摘Degree reduction of parametric curves and surfaces is an important process in data communication between CAD systems. The degenerate condition of Bezier curves and the constrained optimization method are used to develop a new degree reduction method for Bezier curves. An error analysis of the degree reduction is also given. The degree reduction scheme is combined with a subdivision algorithm to generate lower degree approximations which are within some preset error tolerance of the prescribed Bezier curve. Geometric continuity between adjacent curve segments is also considered in the subdivision/degree reduction process.
基金This work is supported by the National Natural Science Foundation of China under Grant Nos.60473130,10371110the National Grand Fundamental Research 973 Program of China under Grant No.2004CB318000.
文摘In this paper, we present two new unified mathematics models of conics and polynomial curves, called algebraic hyperbolic trigonometric （ AHT） Bezier curves and non-uniform algebraic hyperbolic trigonometric （ NUAHT） B-spline curves of order n, which are generated over the space span{sin t, cos t, sinh t, cosh t, 1, t,..., t^n-5}, n 7〉 5. The two kinds of curves share most of the properties as those of the Bezier curves and B-spline curves in polynomial space. In particular, they can represent exactly some remarkable transcendental curves such as the helix, the cycloid and the catenary. The subdivision formulae of these new kinds of curves are also given. The generations of the tensor product surfaces are straightforward. Using the new mathematics models, we present the control mesh representations of two classes of minimal surfaces.
文摘A Particle Image Velocimetry (PIV) method based on the image separation andreconstruction with the median filter and triangular Bezier patch was proposed to measure multiplevelocity fields from single-camera images in the present study. The method was examined on syntheticPIV images with the Green-Taylor two-phase vortex flows and the test results showed high accuracyand highly correct tracking percent compared with the exact solution. An experiment of the bubblyjet flow was also conducted as a practical demonstration of the present method. As a result, it isconfirmed from the simulation image examination and the experimental measurement that the proposedmethod shows a good performance in the measurement of bubble and particle phases.
基金supported by the National Natural Science Foundation of China(No.51576007)Civil Aircraft Special Research of China(No.MJZ-016-D-30)
文摘An aerodynamic optimization method for axial flow compressor blades available for engineering is developed in this paper. Bezier surface is adopted as parameterization method to control the suction surface of the blades, which brings the following advantages:(A) significantly reducing design variables;(B) easy to ensure the mechanical strength of rotating blades;(C) better physical understanding;(D) easy to achieve smooth surface. The Improved Artificial Bee Colony(IABC) algorithm, which significantly increases the convergence speed and global optimization ability, is adopted to find the optimal result. A new engineering optimization tool is constructed by combining the surface parametric control method, the IABC algorithm, with a verified Computational Fluid Dynamics(CFD) simulation method, and it has been successfully applied in the aerodynamic optimization for a single-row transonic rotor(Rotor 37) and a single-stage transonic axialflow compressor(Stage 35). With the constraint that the relative change in the flow rate is less than0.5% and the total pressure ratio does not decrease, within the acceptable time in engineering, the adiabatic efficiency of Rotor 37 at design point increases by 1.02%, while its surge margin 0.84%,and the adiabatic efficiency of Stage 35 0.54%, while its surge margin 1.11% after optimization, to verify the effectiveness and potential in engineering of this new tool for optimization of axial compressor blade.
文摘Degree reduction of parametric curves and surfaces is an important process in the exchange of product model data between various CAD systems. In this paper the degenerate conditions of triangular Bezier surface patches are derived. The degenerate conditions and constrained optimization methods are used to develop a degree reduction method for triangular Bezier surface patches. The error in the degree reduction of a triangular Bezier surface is also shown to depend on some geometric invariants which decrease exponentially in the subdivision process. Therefore, the degree reduction method can be combined with a subdivision algorithm to generate lower degree approximations which are within some preset error tolerance.
基金the National Natural Science Founda-tion(Nos.62063019 and 61763026)the Gansu Nat-ural Science Foundation Project(No.20JR10RA152)the Gansu Provincial Department of Educa-tion:Excellent Graduate“Innovation Star”Project(No.2021CXZX-507)。
文摘Aimed at the problems of a traditional ant colony algorithm,such as the path search direction and field of view,an inability to find the shortest path,a propensity toward deadlock and an unsmooth path,an ant colony algorithm for use in a new environment is proposed.First,the feature points of an obstacle are extracted to preprocess the grid map environment,which can avoid entering a trap and solve the deadlock problem.Second,these feature points are used as pathfinding access nodes to reduce the node access,with more moving directions to be selected,and the locations of the feature points to be selected determine the range of the pathfinding field of view.Then,based on the feature points,an unequal distribution of pheromones and a two-way parallel path search are used to improve the construction efficiency of the solution,an improved heuristic function is used to enhance the guiding role of the path search,and the pheromone volatilization coefficient is dynamically adjusted to avoid a premature convergence of the algorithm.Third,a Bezier curve is used to smooth the shortest path obtained.Finally,using grid maps with a different complexity and different scales,a simulation comparing the results of the proposed algorithm with those of traditional and other improved ant colony algorithms verifies its feasibility and superiority.
基金Supported by the National Grand Fundamental Research 973 Program of China (Grant No. 2004CB719400)the National Natural Science Foun-dation of China (Grant Nos. 60673031 and 60333010)the National Natural Science Foundation for Innovative Research Groups (Grant No. 60021201)
文摘This paper introduces the algebraic property of bivariate orthonormal Jacobi polynomials into geometric approximation. Based on the latest results on the transformation formulae between bivariate Bernstein polynomials and Jacobi polynomials, we naturally deduce a novel algorithm for multi-degree reduction of triangular B^zier surfaces. This algorithm possesses four characteristics： ability of error forecast, explicit expression, less time consumption, and best precision. That is, firstly, whether there exists a multi-degree reduced surface within a prescribed tolerance is judged beforehand; secondly, all the operations of multi-degree reduction are just to multiply the column vector generated by sorting the series of the control points of the original surface in lexicographic order by a matrix; thirdly, this matrix can be computed at one time and stored in an array before processing degree reduction; fourthly, the multi-degree reduced surface achieves an optimal approximation in the norm L2. Some numerical experiments are presented to validate the effectiveness of this algorithm, and to show that the algorithm is applicable to information processing of products in CAD system.
基金Supported by National Natural Science Foundation of China(Grant No.61733017)Foundation of State Key Laboratory of Robotics of China(Grant No.2018O13)Shanghai Pujiang Program of China(Grant No.18PJD018).
文摘A super redundant serpentine manipulator has slender structure and multiple degrees of freedom.It can travel through narrow spaces and move in complex spaces.This manipulator is composed of many modules that can form different lengths of robot arms for different application sites.The increase in degrees of freedom causes the inverse kinematics of redundant manipulator to be typical and immensely increases the calculation load in the joint space.This paper presents an integrated optimization method to solve the path planning for obstacle avoidance and discrete trajectory tracking of a super redundant manipulator.In this integrated optimization,path planning is established on a Bezier curve,and particle swarm optimization is adopted to adjust the control points of the Bezier curve with the kinematic constraints of manipulator.A feasible obstacle avoidance path is obtained along with a discrete trajectory tracking by using a follow-the-leader strategy.The relative distance between each two discrete path points is limited to reduce the fitting error of the connecting rigid links to the smooth curve.Simulation results show that this integrated optimization method can rapidly search for the appropriate trajectory to guide the manipulator in obtaining the target while achieving obstacle avoidance and meeting joint constraints.The proposed algorithm is suitable for 3D space obstacle avoidance and multitarget path tracking.
文摘The act of transmitting photos via the Internet has become a routine and significant activity.Enhancing the security measures to safeguard these images from counterfeiting and modifications is a critical domain that can still be further enhanced.This study presents a system that employs a range of approaches and algorithms to ensure the security of transmitted venous images.The main goal of this work is to create a very effective system for compressing individual biometrics in order to improve the overall accuracy and security of digital photographs by means of image compression.This paper introduces a content-based image authentication mechanism that is suitable for usage across an untrusted network and resistant to data loss during transmission.By employing scale attributes and a key-dependent parametric Long Short-Term Memory(LSTM),it is feasible to improve the resilience of digital signatures against image deterioration and strengthen their security against malicious actions.Furthermore,the successful implementation of transmitting biometric data in a compressed format over a wireless network has been accomplished.For applications involving the transmission and sharing of images across a network.The suggested technique utilizes the scalability of a structural digital signature to attain a satisfactory equilibrium between security and picture transfer.An effective adaptive compression strategy was created to lengthen the overall lifetime of the network by sharing the processing of responsibilities.This scheme ensures a large reduction in computational and energy requirements while minimizing image quality loss.This approach employs multi-scale characteristics to improve the resistance of signatures against image deterioration.The proposed system attained a Gaussian noise value of 98%and a rotation accuracy surpassing 99%.
基金Supported by National Basic Research Program of China(973Program,Grant No.2013CB035501)
文摘Robots driven by batteries are clean, quiet, and can work indoors or in space. However, the battery endurance is a great problem. A new gait parameter design energy saving strategy to extend the working hours of the quadruped robot is proposed. A dynamic model of the robot is established to estimate and analyze the energy expenditures during trotting. Given a trotting speed, opti- mal stride frequency and stride length can minimize the energy expenditure. However, the relationship between the speed and the optimal gait parameters is nonlinear, which is difficult for practical application. Therefore, a simplified gait parameter design method for energy saving is pro- posed. A critical trotting speed of the quadruped robot is found and can be used to decide the gait parameters. When the robot is travelling lower than this speed, it is better to keep a constant stride length and change the cycle period. When the robot is travelling higher than this speed, it is better to keep a constant cycle period and change the stride length. Simulations and experiments on the quadruped robot show that by using the proposed gait parameter design approach, the energy expenditure can be reduced by about 54% compared with the 100 mm stride length under 500 mm/s speed. In general, an energy expenditure model based on the gait parameter of the quadruped robot is built and the trotting gait parameters design approach for energy saving is proposed.
基金supported by the National Natural Science Foundation of China (No. 60873111)the National Basic Research Program (973) of China (No. 2004CB719400)
文摘We decompose the problem of the optimal multi-degree reduction of Bézier curves with corners constraint into two simpler subproblems, namely making high order interpolations at the two endpoints without degree reduction, and doing optimal degree reduction without making high order interpolations at the two endpoints. Further, we convert the second subproblem into multi-degree reduction of Jacobi polynomials. Then, we can easily derive the optimal solution using orthonormality of Jacobi polynomials and the least square method of unequally accurate measurement. This method of 'divide and conquer' has several advantages including maintaining high continuity at the two endpoints of the curve, doing multi-degree reduction only once, using explicit approximation expressions, estimating error in advance, low time cost, and high precision. More importantly, it is not only deduced simply and directly, but also can be easily extended to the degree reduction of surfaces. Finally, we present two examples to demonstrate the effectiveness of our algorithm.
基金Supported by the Natural Science Foundation of Jiangsu Province (BK20211037)the Science and Technology Development Fund of Wuxi (N20201011)the Nanjing University of Information Science and Technology Wuxi Campus District graduate innovation Project。
文摘Background Automatic guided vehicles(AGVs)have developed rapidly in recent years and have been used in several fields,including intelligent transportation,cargo assembly,military testing,and others.A key issue in these applications is path planning.Global path planning results based on known environmental information are used as the ideal path for AGVs combined with local path planning to achieve safe and rapid arrival at the destination.Using the global planning method,the ideal path should meet the requirements of as few turns as possible,a short planning time,and continuous path curvature.Methods We propose a global path-planning method based on an improved A^(*)algorithm.The robustness of the algorithm was verified by simulation experiments in typical multiobstacle and indoor scenarios.To improve the efficiency of the path-finding time,we increase the heuristic information weight of the target location and avoid invalid cost calculations of the obstacle areas in the dynamic programming process.Subsequently,the optimality of the number of turns in the path is ensured based on the turning node backtracking optimization method.Because the final global path needs to satisfy the AGV kinematic constraints and curvature continuity condition,we adopt a curve smoothing scheme and select the optimal result that meets the constraints.Conclusions Simulation results show that the improved algorithm proposed in this study outperforms the traditional method and can help AGVs improve the efficiency of task execution by planning a path with low complexity and smoothness.Additionally,this scheme provides a new solution for global path planning of unmanned vehicles.
