The quadratic B-spline curve fitting for the shape of log cross sections

This paper describes a new method for simulation of the cross section shape of log. The self-developed MQK3102 log shape recognizing machine was used to acquire the finite discrete sampling points on the cross section of log and those points were fitted with the quadratic B-spline parametric curve. This method can clearly stimulate the real shape of the log cross section and is characterized by limited sampling points and high speed computing. The computed result of the previous curve does not affect the next one, which may avoid the graphic distortion caused by the accumulative error. The method can be used to simulate the whole body shape of log approximately by sampling the cross sections along the length direction of log, thus providing a reference model for optimum saw cutting of log.

Efficient Construction of B-Spline Curves with Minimal Internal Energy

In this paper,we propose an efficient method to construct energy-minimizing B-spline curves by using discrete mask method.The linear relations between control points are firstly derived for different energy-minimization problems,then the construction of B-spline curve with minimal internal energy can be addressed by solving a sparse linear system.The existence and uniqueness of the solution for the linear system are also proved.Experimental results show the efficiency of the proposed approach,and its application in 1 G blending curve construction is also presented.

MODIFIABLE QUARTIC AND QUINTIC CURVES WITH SHAPE-PARAMETERS

This paper presents a method for creating modificable quartic and quintic curves with shape parameters. The curves can achieve C 2 even C 3 continuity and unify both interpolation and approximation to the control points without solving a system of equations or inserting additional control points. They have the local properties like the cubic B spline. Besides, the quintic curve would be able globally to tend the control polygon.

Approximate merging of B-spline curves and surfaces

Applying the distance function between two B-spline curves with respect to the L2 norm as the approximate error, we investigate the problem of approximate merging of two adjacent B-spline curves into one B-spline curve. Then this method can be easily extended to the approximate merging problem of multiple B-spline curves and of two adjacent surfaces. After minimizing the approximate error between curves or surfaces, the approximate merging problem can be transformed into equations solving. We express both the new control points and the precise error of approximation explicitly in matrix form. Based on homogeneous coordinates and quadratic programming, we also introduce a new framework for approximate merging of two adjacent NURBS curves. Finally, several numerical examples demonstrate the effectiveness and validity of the algorithm.

One Fairing Method of Cubic B-spline Curves Based on Weighted Progressive Iterative Approximation

A new method to the problem of fairing planar cubic B-spline curves is introduced in this paper. The method is based on weighted progressive iterative approximation （WPIA for short） and consists of following steps： finding the bad point which needs to fair, deleting the bad point, re-inserting a new data point to keep the structm-e of the curve and applying WPIA method with the new set of the data points to obtain the faired curve. The new set of the data points is formed by the rest of the original data points and the new inserted point. The method can be used for shape design and data processing. Numerical examples are provided to demonstrate the effectiveness of the method.

B-spline curve-based routing in ad hoc networks

Routing algorithms capable of providing quality of service （QoS） will play an important role in future communication networks. For the trajectory-based routing （ TBR）, An effective method of en- coding trajectories into packets is proposed. The method uses a B-spline curve, which provides a lot of flexibility. The simulation results show that the performance of the proposed algorithms is im- proved significantly compared with the existing algorithm.

RECONSTRUCTION OF SYMMETRIC B-SPLINE CURVES AND SURFACES

A method to reconstruct symmetric B-spline curves and surfaces is presented. The symmetry property is realized by using symmetric knot vector and symmetric control points. Firstly, data points are divided into two parts based on the symmetry axis or symmetry plane extracted from data points. Then the divided data points are parameterized and a symmetric knot vector is selected in order to get symmetric B-spline basis functions. Constraint equations regarding the control points are deduced to keep the control points of the B-spline curve or surface to be symmetric with respect to the extracted symmetry axis or symmetry plane. Lastly, the constrained least squares fitting problem is solved with the Lagrange multiplier method. Two examples from industry are given to show that the proposed method is efficient, robust and able to meet the general engineering requirements.

THE RELATIONSHIP BETWEEN PROJECTIVE GEOMETRIC AND RATIONAL QUADRATIC B-SPLINE CURVES

Abstract For two rational quadratic B spline curves with same control vertexes, the cross ratio of four collinear points are represented: which are any one of the vertexes, and the two points that the ray initialing from the vertex intersects with the corresponding segments of the two curves, and the point the ray intersecting with the connecting line between the two neighboring vertexes. Different from rational quadratic Bézier curves, the value is generally related with the location of the ray, and the necessary and sufficient condition of the ratio being independent of the ray's location is showed. Also another cross ratio of the following four collinear points are suggested, i.e. one vertex, the points that the ray from the initial vertex intersects respectively with the curve segment, the line connecting the segments end points, and the line connecting the two neighboring vertexes. This cross ratio is concerned only with the ray's location, but not with the weights of the curve. Furthermore, the cross ratio is projective invariant under the projective transformation between the two segments.

An adaptive generation method for free curve trajectory based on NURBS

To realize the high precision and real-time interpolation of the NURBS （non-uniform rational B-spline） curve, a kinetic model based on the modified sigmoid function is proposed. The constraints of maximum feed rate, chord error, curvature radius and interpolator cycle are discussed. This kinetic model reduces the cubic polynomial S-shape model and the trigonometry function S-shape model from 15 sections into 3 sections under the precondition of jerk, acceleration and feedrate continuity. Then an optimized Adams algorithm using the difference quotient to replace the derivative is presented to calculate the interpolator cycle parameters. The higher-order derivation in the Taylor expansion algorithm can be avoided by this algorithm. Finally, the simplified design is analyzed by reducing the times of computing the low-degree zero-value B-spline basis function and the simplified De Boor-Cox recursive algorithm is proposed. The simulation analysis indicates that by these algorithms, the feed rate is effectively controlled according to tool path. The calculated amount is decreased and the calculated speed is increased while the machining precision is ensured. The experimental results show that the target parameter can be correctly calculated and these algorithms can be applied to actual systems.

Study on Real-time Look-ahead and Adaptive Parametric Curve Interpolator

The principle of real-time look-ahead was introduced and analysed. An adaptive parametric curve interpolator with a real-time look-ahead function was developed for non-uniform rational B-spline (NURBS) curves interpolation, which considering the maximum acceleration/deceleration of the machine tool. In order to deal with the acceleration/deceleration around the feedrate sensitive corners, the look-ahead function was designed and illustrated. It can detect and adjust the feedrate adaptively. With the help of real-time look-ahead, the acceleration/deceleration can be limited to the range of the machine tool capacity. Thus, feedrate fluctuation is reduced. A NURBS curve interpolation experiment was provided to verify the feasibility and advantages of the proposed interpolator with a real-time look-ahead function.

Adaptive B-snake for planar curve approximation

An adaptive B-spline active contour model for planar curve approximation is proposed. Starting with an initial B-spline curve, the finite element method is adopted to make the active B-spline curve converge towards the target curve without the need of data points parameterization. A strategy of automatic control point insertion during the B-spline active contour deformation, adaptive to the shape of the planar curve, is also given. Experimental results show that this method is efficient and accurate in planar curve approximation.

On the Parametric Modeling of Turbine Blade Section Curve

Geometric parameters of the turbine blade are classified according to their destined functions, and the mathematical definition of those parameters in the section curve is introduced in detail. Some parts of the section curve shape can be adjusted freely, offering more flexibility to designers.

A Novel Contour Tracing Algorithm for Object Shape Reconstruction Using Parametric Curves

Parametric curves such as Bézier and B-splines, originally developedfor the design of automobile bodies, are now also used in image processing andcomputer vision. For example, reconstructing an object shape in an image,including different translations, scales, and orientations, can be performedusing these parametric curves. For this, Bézier and B-spline curves can be generatedusing a point set that belongs to the outer boundary of the object. Theresulting object shape can be used in computer vision fields, such as searchingand segmentation methods and training machine learning algorithms. Theprerequisite for reconstructing the shape with parametric curves is to obtainsequentially the points in the point set. In this study, a novel algorithm hasbeen developed that sequentially obtains the pixel locations constituting theouter boundary of the object. The proposed algorithm, unlike the methods inthe literature, is implemented using a filter containing weights and an outercircle surrounding the object. In a binary format image, the starting point ofthe tracing is determined using the outer circle, and the next tracing movementand the pixel to be labeled as the boundary point is found by the filter weights.Then, control points that define the curve shape are selected by reducing thenumber of sequential points. Thus, the Bézier and B-spline curve equationsdescribing the shape are obtained using these points. In addition, differenttranslations, scales, and rotations of the object shape are easily provided bychanging the positions of the control points. It has also been shown that themissing part of the object can be completed thanks to the parametric curves.

Quintic B-Spline Method for Solving Sharma Tasso Oliver Equation

When analysing the thermal conductivity of magnetic fluids, the traditional Sharma-Tasso-Olver (STO) equation is crucial. The Sharma-Tasso-Olive equation’s approximate solution is the primary goal of this work. The quintic B-spline collocation method is used for solving such nonlinear partial differential equations. The developed plan uses the collocation approach and finite difference method to solve the problem under consideration. The given problem is discretized in both time and space directions. Forward difference formula is used for temporal discretization. Collocation method is used for spatial discretization. Additionally, by using Von Neumann stability analysis, it is demonstrated that the devised scheme is stable and convergent with regard to time. Examining two analytical approaches to show the effectiveness and performance of our approximate solution.

Multiresolution for Closed Curves and Surfaces Using Wavelets

Multiresolution modeling is becoming a powerful tool for fast display, and geometric data compression and transmission of complex shapes. Most of the existing literatures investigating the multiresolution for B-spline curves and surfaces are concentrated on open ones. In this paper, we focus on the multiresolution representations and editing of closed B-spline curves and surfaces using wavelets. A repetition approach is adopted for the multiresolution analysis of closed B-spline curves and surfaces. Since the closed curve or surface itself is periodic, it can overcome the drawback brought by the repetition method, i.e. introducing the discontinuities at the boundaries. Based on the models at different multiresolution levels, the multiresolution editing methods of closed curves and surfaces are introduced. Users can edit the overall shape of a closed one while preserving its details, or change its details without affecting its overall shape.

Effects of Dissipative Terms on Dissipative Soliton Resonance Curve

Dissipative soliton resonance (DSR) is a phenomenon where the energy of a soliton in a dissipative system increases without limit at certain values of the system parameters. Using the method of collective variable approach, we have found an approximate relation between the parameters of the normalized complex cubic-quintic Ginzburg-Landau equation where the resonance manifests itself. Comparisons between the results obtained by collective variable approach, and those obtained by the method of moments show good qualitative agreement. This choice also helps to see the influence of the active terms on the resonance curve, so can be very useful in constructing passively mode-locked laser that generate solitons with the highest possible energies.

Ship hull plate processing surface fairing with constraints based on B-spline

The problem of ship hull plate processing surface fairing with constraints based on B-spline is solved in this paper. The algorithm for B-spline curve fairing with constraints is one of the most common methods in plane curve fairing. The algorithm can be applied to global and local curve fairing. It can constrain the perturbation range of the control points and the shape variation of the curve, and get a better fairing result in plane curves. In this paper, a new fairing algorithm with constraints for curves and surfaces in space is presented. Then this method is applied to the experiments of ship hull plate processing surface. Finally numerical results are obtained to show the efficiency of this method.

基于人工免疫-改进粒子群优化算法的机械臂轨迹规划研究

焊接机器人运动轨迹复杂、控制精度要求高。提出了一种满足多目标约束的轨迹规划方法。针对机器人轨迹平滑性要求,以5次非均匀有理B样条(Non-Uniform Rational B-Splines,NURBS)曲线为基础,对笛卡儿空间路径点进行参数化表达;根据工业机器人路径约束及工况需求,选取时间、能耗、跃度3个运动学指标作为目标优化函数,采用人工免疫双态粒子群进行轨迹优化;为了平衡粒子“探索”与“利用”,增加双模态模型,引入人工免疫系统,提升了粒子多样性与后期收敛能力;根据Pareto解集得到满足约束的焊接机器人各关节最优轨迹,通过Matlab仿真证明了方法的有效性;最后,针对空间相贯曲线焊缝进行了焊接试验。结果显示,规划的轨迹符合实际工程需求。

基于五次B样条的工业机器人轨迹优化

为提高工业机器人的工作效率,提出一种以时间最优为目标的轨迹优化方法,在5次B样条曲线轨迹规划原理的基础上,引入遗传算法对轨迹进行优化。针对工作时间建立适应度函数,并通过选择交叉概率和变异概率操作产生新的轨迹解,与未被淘汰的父代组成新的种群,经过迭代求得运行时间最优的期望解。利用MATLAB软件对这一方法进行仿真,结果表明,经分析遗传算法优化后,轨迹运行时间明显减少,且具有良好的轨迹效果。

某埋头弹机枪拨弹杠杆动力学分析及优化

某埋头弹机枪使用了与传统枪弹结构完全不同的埋头弹,为了适应这种弹药,该埋头弹机枪与传统机枪在结构上也有很大的差异。其中,相较于传统机枪,该埋头弹机枪的输弹行程更为靠后,为了减小全枪长度,不得不缩短拨弹杠杆中曲线槽部分的长度。这使得枪机框上的导柱进入拨弹杠杆曲线槽时,对拨弹杠杆的冲击力很大,从而对整个输弹机构的可靠工作造成极为不利的影响,同时也会严重降低枪机框的动能,使得输弹动作难以完成。现以导柱与拨弹杠杆之间的最大冲击力为目标函数,选用5次函数曲线作为拨弹杠杆曲线槽理论轮廓线的形状,运用遗传算法对该理论轮廓线进行优化,使得导柱与拨弹杠杆之间的最大冲击力降为优化前的1/3。试验验证表明,枪机框在进入拨弹杠杆曲线槽的过程中,速度损失由原来的0.94 m/s降低到0.28 m/s,达到了优化目的,该研究结果为该枪的改进提供了可靠的理论依据。