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%.

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.

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.

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.

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.

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。

基于B样条的螺旋桨桨叶参数化及曲面生成

为了提高螺旋桨优化过程中桨叶的参数化灵活性和建模效率,开展基于B样条方法的螺旋桨桨叶参数化及曲面生成研究。基于B样条曲线方法,采用最小二乘法对不同半径处的叶切面型值点进行拟合,并利用比例、偏移、坐标转换等方法,实现了桨叶叶切面和外形轮廓的参数化;基于B样条曲面方法,高效生成螺旋桨叶面、叶背、叶根和叶顶曲面;基于Python语言完成相关程序编写,并给出程序的UML类图。最终,通过对螺旋桨实例进行对比分析,证明螺旋桨桨叶参数化的灵活性和桨叶曲面生成的高效性。

基于5阶B样条的避障泊车路径规划

[目的]为实现安全泊车,针对自动泊车路径规划方法中泊车环境存在障碍物的情况进行路径规划研究.[方法]提出基于5阶B样条曲线的双步式避障泊车路径规划方法,建立泊车环境避障及障碍物避障约束函数,以B样条路径曲线控制点为主要变量,以泊车完成时车辆在车位内且车身平行于车位为目标,建立含有多个非线性约束的泊车路径函数,并进行求解.[结果]数值仿真结果表明,基于5阶B样条曲线的避障泊车路径规划方法,可得到同时满足环境避障约束、障碍物避障约束及车辆参数约束的泊车轨迹曲线,能够实现当泊车环境存在障碍物时的路径规划.[结论]本文提出的5阶B样条曲线双步式避障泊车路径规划方法适用于平行泊车与垂直泊车,能够有效规划出一条可行的避障泊车路径,且保证行驶过程中车辆转向角速度连续,车辆与障碍物保持一定安全距离.该方法能够应用在较多泊车场景,具有较好的理论意义与工程价值.

基于B样条优化的改进纯追踪农机导航曲线跟踪方法

针对驾驶农机采样路径平滑性对跟踪效果的影响和曲线路径变曲率特性导致跟踪适应性较低的问题,提出了一种基于B样条路径优化的积分补偿模糊纯追踪控制方法。首先采用B样条插值方法平滑优化采样路径信息;再基于行驶规律分析农机曲率与作业速度对跟踪控制的相互作用关系,设计了模糊调整前视距离的纯追踪控制方法,该方法根据前期试验结果采用拖拉机速度和前视路径平均曲率模糊整定纯追踪前视距离,同时采用跟踪横向偏差设计前轮转角积分补偿,减小稳态误差。设计构建了曲线跟踪Simulink仿真模型并进行了仿真试验。仿真结果表明,改进方法的平均绝对横向偏差均值和最大绝对横向偏差均值相较于传统纯追踪控制方法降低4.8%和7.1%。进行了拖拉机田间正弦曲线跟踪试验,插值路径对比试验结果表明,路径插值后跟踪误差较插值前降低75.9%。控制算法对比试验结果表明,拖拉机以速度1.0、1.5、2.5 m/s跟踪不同幅值正弦曲线路径时,采用改进纯追踪方法平均绝对横向偏差均值分别降低36.80%、62.50%和61.03%,标准差均值分别降低27.8%、24.0%和46.3%。最后跟踪田间随机采样路径,当速度为2.5 m/s时,横向偏差标准差为0.06 m。本文方法有效提高了农机曲线路径跟踪精度,满足需要曲线作业的农业生产需求。

求解测地线边界值问题的均匀B样条配点法

曲面上的测地线在图像处理、机器人学、数控加工等领域有着广泛的应用.针对参数曲面,提出了采用二阶、三阶均匀B样条配点法求解测地线边界值问题.首先建立了测地线边界值问题的离散控制方程,在给定初始逼近后,该方程可采用近似牛顿迭代法进行求解;然后推导了B样条配点法的计算精度;最后在Matlab2016b软件环境下,结合球面、圆环面以及样条曲面对所提出的方法进行了验证.实验考察了不同方法的计算精度、时间成本以及计算效率,结果表明三阶B样条配点法获得相同计算精度所需的时间通常更少,即该方法在计算效率方面具有优势.当计算测地线长度误差为0.01%时,三阶B样条配点法相较于Chen的近似测地线法节省时间成本5.5%~26.9%.对于二阶B样条配点法,其计算效率与Kasap的中心差分法相当.所提出的方法计算结果为连续曲线,无需额外的插值函数,一个潜在的应用场景为自动铺带轨迹规划.

基于B样条曲线拟合和蜉蝣算法的采煤机截割路径约束优化

实现采煤机智能化调高,关键是解决煤岩界面识别问题、截割路径优化问题及采煤机调高控制问题。即使煤岩界面被精确识别,受到实际工作中顶底板的平整性和液压支架的推移滑溜等要求的限制,采煤机滚筒无法完全跟随煤岩界面曲线,因此需要基于煤岩界面识别结果,对起伏变化的煤岩界面曲线进行截割路径优化,得到采煤机调高控制的目标轨迹。滚筒截割路径优化是基于煤岩界面估计曲线,在采煤工艺、煤质要求和设备的适应能力等限制条件的约束下,得到使回采最大化的平滑轨迹。针对上述采煤机截割路径约束优化问题,提出一种基于B样条曲线拟合和蜉蝣算法的采煤机截割路径约束优化方法。为了提高截割路径优化效果和降低计算复杂度,以B样条曲线节点系数作为设计变量,构建一种新型截割路径优化目标函数;考虑采煤机截割工艺、煤质要求等限制,使用多段赋值罚函数法处理约束,根据约束的不满足程度动态改变罚函数系数值,避免优化陷入局部最值和约束不能起到实际作用;为了进一步提高优化效果和收敛速度,使用修正蜉蝣算法寻找最优截割路径。最后,考虑实际煤岩界面中褶皱、陷落柱、断层等典型地质构造,进行仿真研究,结果表明,所提方法能在满足实际约束下快速得到平滑的截割优化路径,实时性好、适用性高。

两条B样条曲线求交的高效计算方法

曲线曲面间求交计算在CG和CAD中有着广泛的应用.牛顿法等迭代法计算效率高但需要良好的初始值;裁剪法具有良好的鲁棒性但计算效率不理想,尤其是对于相切情况的求交问题.为此,提出一种计算2条B样条曲线交点的混合方法.首先提出一种高效的线性复杂度裁剪方法,用于获得良好的初始值;然后提出一种与导数无关且效率更高的改进的割线法,用于验证贯穿性相交情况;最后提出一个相切情况下收敛阶为2的迭代公式,其性能远优于现有的牛顿法和裁剪法.理论上,混合方法若与根隔离法相结合,可以应用于更多类型曲线间的求交问题.数值实验结果表明,与现有的同类方法相比,在贯穿情况下,所提方法的计算效率提高约10%,在相切情况下则提高约100%~300%.

基于B样条曲线的心轨重构廓形参数影响分析

针对固定辙叉钢轨廓形不规则变化特点,基于B样条理论提出一种考虑固定辙叉钢轨断面廓形特征的参数化设计方法,并提出拟合钢轨廓形贴合度评价指标和关键控制参数对廓形贴合度影响权重指标;以60 kg/m钢轨12号固定辙叉为例,采用DOE(design of experiments)方法分析轨顶横坡、侧面纵坡和复合圆弧段比例系数对心轨轨头整体廓形、轨顶面廓形和侧面廓形的影响.结果表明:1)在心轨20 mm断面,轨顶横坡、侧面纵坡和复合圆弧段比例系数对心轨整体廓形变化的影响权重分别为21.08%、56.89%和22.02%,对心轨顶面廓形变化影响权重分别为8.42%、61.95%、29.63%;在心轨50 mm断面,各关键控制参数对心轨轨头整体廓形变化影响权重分别为55.9%、33.38%、10.72%;侧面纵坡对心轨20 mm和50 mm断面的侧面廓形变化影响权重分别为76.82%、66.04%.2)当心轨轨头宽度为20 mm时,侧面纵坡对各部分廓形变化影响均达到50%以上;随着心轨轨头宽度的增大,心轨轨顶横坡对整体廓形变化影响权重由21.8%增至55.9%,侧面纵坡和复合圆弧段比例系数影响权重则分别减小41.3%和51.3%.

Robust Corner Detection Based on Multi-scale Curvature Product in B-spline Scale Space

这份报纸在 B 花键弯曲规模空间的框架论述一种多尺度的弯曲产品角落察觉技术。规模产品功能在不同规模从轮廓的弯曲产品被导出。角落被 thresholding 作为本地最大值构造越过几规模的弯曲产品结果。通过规模产品，本地化精确性和察觉表演能显著地以 CNN 标准被改进。实验也证明那个建议方法显示出坚韧性到高频率细节并且提供有希望的察觉结果。

基于B样条线圈模型的段染纱针织物外观模拟

针对段染纱针织物花纹预测困难且现有织物模拟方法真实感有待提升的问题,提出了一种基于真实段染纱的针织物外观模拟方法。首先,使用图像处理技术对获取的段染纱图像进行阈值分割和形态学处理等预处理,从原始图像中提取纱线主体区域。然后,从真实织物中提取线圈点位信息,借助最小二乘拟合构建B样条线圈曲线,并根据曲线将段染纱真实图像映射为线圈图像。最后,在考虑线圈交织覆盖关系以及光照因素后,通过排列线圈实现纬平针针织物及其系列针织面料的外观模拟。结果表明:所模拟的线圈模型能够还原真实线圈中的纱线走向,且模拟织物外观花纹效果与实物一致,整体呈现出较好的真实感。

Paths of algebraic hyperbolic curves

Cubic algebraic hyperbolic （AH） Bezier curves and AH spline curves are defined with a positive parameter a in the space spanned by {1, t, sinht, cosht}. Modifying the value of a yields a family ofAH Bezier or spline curves with the family parameter α. For a fixed point on the original curve, it will move on a defined curve called ＂path of AH curve＂ （AH Bezier and AH spline curves） when a changes. We describe the geometric effects of the paths and give a method to specify a curve passing through a given point.

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.

融合改进斜四邻域A^(*)与三次B样条曲线的路径规划算法

针对传统A^(*)算法八邻域搜索路径节点多导致搜索及规划路径速度慢的问题,提出1种融合改进斜四邻域A^(*)与三次B样条曲线的路径规划算法。在传统八邻域搜索启发下,删除原本上下左右4个方向上的搜索路径,保留右上、右下、左上及左下4个方向的搜索路径,使算法在搜索时速度更快,搜索路径节点数更少;引入三次B样条曲线,优化路径上的尖锐拐点,使路径更平滑。采用提出的算法与其他2种算法在3种不同分辨率及不同障碍率的地图上进行实验验证。结果表明:相比于传统A^(*)算法,改进斜四邻域A^(*)算法的搜索时间缩短83.4%,路径节点数减少89.7%;引入的三次B样条曲线使斜四邻域A^(*)算法规划出的路径更平滑,提出的算法可极大提高路径搜索及规划的有效性。