B-Spline曲线聚风装置直线翼垂直轴风力机启动性能数值模拟

为了提升直线翼垂直轴风力机的启动性能,基于B-Spline曲线生成方法,提出一种具有流线型轮廓的聚风装置,将其分别安装在风轮顶端和底端,用以提升风轮附近的来流风速,使风轮汲取更多风能,达到更易启动的特点.选取聚风装置的5个结构参数进行设计:聚风装置与风轮间隙距离ΔL、底圆半径R_(1)、顶圆半径R_(2)、入口角度α_(1)和出口角度α_(2).设计方法采用二次旋转正交组合筛选最优模型,通过三维数值模拟研究聚风装置参数对直线翼垂直轴风力机启动性能的影响,获得了最佳外形参数组合.此外,对有无加装聚风装置的直线翼垂直轴风力机进行了静态三维数值模拟.结果表明,通过添加具有外凸流线型轮廓的聚风装置,直线翼垂直轴风力机的启动性能有显著提升.在风速较低的情况下,性能改善更加明显.聚风装置可使直线翼垂直轴风力机的平均启动力矩系数最大增加38.8%,峰值平均启动力矩系数最大可增加31.2%.

基于B-spline的路径规划与轨迹跟踪研究

为满足局部路径规划换道路径下的特性和提高智能驾驶车辆在多种变曲率条件下的路径跟踪精度和稳定性,采用贝塞尔曲线、B-spline等路径规划换道条件下的方法,分别在圆形轨迹、8字形轨迹、S形轨迹、正弦曲线形轨迹路径下,基于MATLAB对4类路径跟踪算法进行分析,得出最合理的B-spline路径规划和跟踪算法。结果表明,B-spline算法在换道点和并道点曲率为0,满足换道条件的要求;MPC算法在正弦轨迹下比其他算法平均误差小约48.6%,在圆形轨迹下比其他算法平均误差小约84%,说明该算法在多种轨迹下都具有很好的跟踪性,能在一定程度上保证智能驾驶汽车的安全性和稳定性,为今后智能车辆路径规划和轨迹跟踪控制研究提供参考。

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.

Cubic Algebraic Spline Curves Design

In this paper we propose a construction method of the planar cubic algebraic splinecurve with endpoint interpolation conditions and a specific analysis of its properties. Thepiecewise cubic algebraic curve has G2 continuous contact with the control polygon at twoendpoints and is G2 continuous between each segments of itself. The process of this method issimple and clear, and provides a new way of thinking to design implicit curves.

A Finite Element Cable Model and Its Applications Based on the Cubic Spline Curve

For accurate prediction of the deformation of cable in the towed system, a new finite element model is presented that provides a representation of both the bending and torsional effects. In this paper, the cubic spline interpolation function is applied as the trial solution. By using a weighted residual approach, the discretized motion equations for the new finite element model are developed. The model is calculated with the computation program complier by Matlab. Several numerical examples are presented to illustrate the numerical schemes. The results of numerical simulation are stable and valid, and consistent with the mechanical properties of the cable. The model can be applied to kinematics analysis and the design of ocean cable, such as mooring lines, towing, and ROV umbilical cables.

A fast direct point-by-point generating algorithm for B Spline curves and surfaces

Traditional generating algorithms for B Spline curves and surfaces require approximation methods where how to increment the parameter to get the best approximation is problematic; or they take the pixel-based method needing matrix trans- formation from B Spline representation to Bézier form. Here, a fast, direct point-by-point generating algorithm for B Spline curves and surfaces is presented. The algorithm does not need matrix transformation, can be used for uniform or nonuniform B Spline curves and surfaces of any degree, and has high generating speed and good rendering accuracy.

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.

C^n-CONTINUOUS B-TYPE SPLINE CURVES WITH ITSLOCALIZATION INTERPOLATION AND APPROXIMATION

This paper presents a class of Cn- continuous B- type spline curves with some paramet- ric factors.The length of their local support is equal to4.Taking the different values of the parametric factors,the curves can become free- type curves or interpolate a set of given points even mix the both cases.When the parametric factors satisfy the certain conditions,the degrees of the curves can be decreased as low as possible.Besides,when all the parametric factors tend to zero,the curves globally approximate to the control polygon.

PH-spline approximation for Bézier curve and rendering offset

In this paper, a G1, C1, C2 PH-spline is employed as an approximation for a given Bzier curve within error bound and further renders offset which can be regarded as an approximate offset to the Bzier curve. The errors between PH-spline and the Bzier curve, the offset to PH-spline and the offset to the given Bzier curve are also estimated. A new algorithm for constructing offset to the Bzier curve is proposed.

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.

Reconstruction of B-spline surface by interpolating boundary curves and approximating inner points

In this paper, we present an algorithm for reconstruction of B-spline surface such that it interpolates the four given bound- ary curves and simultaneously approximates some given inner points. The main idea of our method is： first, we construct an initial surface which interpolates the four given boundary curves; then, while keeping the boundary control points of the initial surface un- changed, we reposition the inner control points of the surface with energy optimization method. Examples show that our algorithm is practicable and effective.

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.

Estimation of the water–oil–gas relative permeability curve from immiscible WAG coreflood experiments using the cubic B-spline model

Immiscible water-alternating-gas（WAG） flooding is an EOR technique that has proven successful for water drive reservoirs due to its ability to improve displacement and sweep efficiency.Nevertheless,considering the complicated phase behavior and various multiphase flow characteristics,gas tends to break through early in production wells in heterogeneous formations because of overriding,fingering,and channeling,which may result in unfavorable recovery performance.On the basis of phase behavior studies,minimum miscibility pressure measurements,and immiscible WAG coreflood experiments,the cubic B-spline model（CBM） was employed to describe the three-phase relative permeability curve.Using the Levenberg-Marquardt algorithm to adjust the vector of unknown model parameters of the CBM sequentially,optimization of production performance including pressure drop,water cut,and the cumulative gas-oil ratio was performed.A novel numerical inversion method was established for estimation of the water-oil-gas relative permeability curve during the immiscible WAG process.Based on the quantitative characterization of major recovery mechanisms,the proposed method was validated by interpreting coreflood data of the immiscible WAG experiment.The proposed method is reliable and can meet engineering requirements.It provides a basic calculation theory for implicit estimation of oil-water-gas relative permeability curve.

Knot Insertion Algorithms for ECT B-spline Curves

Knot insertion algorithm is one of the most important technologies of B-spline method. By inserting a knot the local prop- erties of B-spline curve and the control flexibility of its shape can be fiu＇ther improved, also the segmentation of the curve can be rea- lized. ECT spline curve is drew by the multi-knots spline curve with associated matrix in ECT spline space; Muehlbach G and Tang Y and many others have deduced the existence and uniqueness of the ECT spline function and developed many of its important properties .This paper mainly focuses on the knot insertion algorithm of ECT B-spline curve.It is the widest popularization of B-spline Behm algorithm and theory. Inspired by the Behm algorithm, in the ECT spline space, structure of generalized P61ya poly- nomials and generalized de Boor Fix dual functional, expressing new control points which are inserted after the knot by linear com- bination of original control vertex the single knot, and there are two cases, one is the single knot, the other is the double knot. Then finally comes the insertion algorithm of ECT spline curve knot. By application of the knot insertion algorithm, this paper also gives out the knot insertion algorithm of four order geometric continuous piecewise polynomial B-spline and algebraic trigonometric spline B-spline, which is consistent with previous results.

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.

基于二维B-splines方法研究强磁场中类氢离子He+的低能能级

采用改进的二维B-spline方法在柱坐标系下研究了强磁场下类氢离子He^(+)的结构和电子空间几率密度,计算包含三种对称性0^(+)、0^(-)和(^(-)1)^(+)共10个本征态1 0^(+)、2 0^(+)、ν 0^(-)(ν=1~4)和ν(-1)^(+)(ν=1~4)的能级,选定磁感应强度分别为0、0.001、0.003、0.005、0.007、0.010、0.030、0.050、0.070、0.100、0.200、0.300、0.500、0.700和1.000 a.u.。计算结果表明,类氢离子He^(+)的能级在强磁场中发生劈裂,简并度消除,得到了各个能级随磁感应强度变化规律,并且发现随着磁感应强度的增加能级高低会改变,甚至会发生能级翻转现象;定量地研究了类氢离子He^(+)的基态1 0^(+)和激发态3 0^(-)几率密度分布随磁感应强度的变化规律,并与氢原子进行比较。本研究部分计算结果与他人研究结果十分吻合,有助于进一步理解其他复杂原子的电子运动行为。

一种基于曲率和B样条的矿区装载车辆连续路径规划方法

矿区装载车辆的任务是从进入点到装载点进行装载,然后离开矿区。在进入装载点前,车辆要在回转点改变行进方向,以便倒车进入装载点。针对装载车辆的任务特点,本文提出了一种基于曲率和B样条的路径规划方法。首先,基于车辆运动模型设计了A*算法的成本函数,获得了与车辆转弯半径相关的离散路径。为了进一步获得装载车辆的连续路径,又提出了改进的B样条插值法,使得连续路径两端切线符合车辆起始点和终点的位姿。随后,基于模拟退火算法,获得了车辆的回转点,使得车辆可以在进入装载点前改变前进方向。仿真结果表明,所提出的连续路径规划方法能够保证生成曲率连续的装载车辆路径,并保证路径两端符合车辆在起始点和终点的位姿,为矿区装载车辆的自动驾驶技术提供了基础。