有理二次Bézier曲线与带调节参数的三次Bézier曲线的比较

在给定三个控制点P0,P1,P2的基础上,对有理二次Bézier曲线与带调节参数的三次Bézier曲线进行了比较.一是比较二者接近控制多边形的程度;二是比较二者在控制多边形的凸包内插值一点的情况,分别给出了二者插值的条件,以及在插值条件下给出了权因子和调节参数的计算公式,计算简单,使用方便;三是比较二者偏向控制多边形边P0P1或偏向边P1P2的情况.通过对二者的比较,以后就可以根据实际需要选择适当的曲线,更加有效地对曲线的形状进行调整.     

基于Bezier函数的列车特性曲线数据处理方法研究

在列车运行计算领域, 对列车特性曲线数据处理方法的研究一直得不到应有的重视,因此利用插值法求解列车特性数据的方法沿用至今. 本文研究了插值法计算列车特性数据的误差及其影响. 对比分析了Bezier曲线与列车特性曲线特点,得出可用Bezier曲线拟合列车特性曲线,并提出一种基于Bezier函数的列车特性曲线数据求解方法. 该方法是通过人机交互方式,运用Bezier曲线拟合列车特性曲线,该Bezier曲线对应的Bezier函数为列车特性曲线的拟合函数. 用该拟合函数求解列车特性数据,计算速度与精度均明显提高. 最后对CRH3型动车组的牵引特性曲线作了实际拟合,得出的结果令人满意.     

基于Bezier曲线法对径流式涡轮机动叶的设计

根据叶轮初步设计公式,结合Bezier曲线构造方法依靠NUMECA软件Design3D模块以径流向心式涡轮机效率0.5为目标值,对叶轮子午面型线以及动叶型线进行设计。并通过NUMECA软件对所设计的叶片以及子午流面进行流体计算,得出了符合效率目标值的叶型和子午流面参数,以及子午流面的绝对温度和绝对压力的分布,提出了以径流向心式涡轮机效率为目标值,结合Bezier曲线构造法的叶片型线和子午流面型线的设计方法。     

基于Bezier曲线和B样条曲线的二维有限元模型边界表述

对Ｂｅｚｉｅｒ曲线和Ｂ样条曲线用于二维结构边界表述基本问题进行了探讨。通过对Ｂｅｚｉｅｒ曲线和Ｂ样条曲线的生成算法与特点进行分析与比较，为不同应用场合选用合适曲线进行描述提供了依据，并给出了内燃机活塞的结构边界描述的应用实例。     

隐式代数曲线的有理参数化（Ⅱ）

曲线和曲面的隐式表示和参数表示各有其优点，为了能够利用两种表示方法的优点，必须能够有效的进行曲线曲面的两种表达形式的相互转换．文章研究了隐式代数曲线的有理参数化问题．给出平面三次曲线有理参数化的有关理论，算法和实现．     

计算机曲线造型的分段保形二次样条

给出了一种新的分段保形二次样条插值算法，通过增加合适的插值点，构造分段保凸且保单调的平滑插值曲线，计算机数值实验表明该方法对所给的离散插值数据总能给出几何直观的相当漂亮的光滑曲线。算法简便易行，为计算机辅助曲线设计提供了新的有效方法。     

四次Bézier曲线形状调整方法

分析已有的带形状调节参数的扩展Bézier基生成的曲线的方法,提出带调节参数的控制点变换阵的调整曲线形状的方法.其原理是通过将原来的Bézier曲线的控制点变换为新的一组控制点,进而生成新的Bézier曲线.这组控制点的位置与参数相关联,几何意义明显.     

隐式代数曲线的有理参数化(II)

曲线和曲面的隐式表示和参数表示各有其优点,为了能够利用两种表示方法的优点,必须能够有效的进行曲线曲面的两种表达形式的相互转换.文章研究了隐式代数曲线的有理参数化问题.给出平面三次曲线有理参数化的有关理论,算法和实现.     

隐式代数曲线的有理参数化(Ⅱ)

曲线和曲面的隐式表示和参数表示各有其优点,为了能够利用两种表示方法的优点,必须能够有效的进行曲线曲面的两种表达形式的相互转换.文章研究了隐式代数曲线的有理参数化问题.给出平面三次曲线有理参数化的有关理论,算法和实现.     

用曲线坐标计算细临界型一般n次系统后继函数公式

采用曲线坐标将细临界型一般n次系统,转化为曲线坐标系统．并利用曲线坐标给出后继函数公式中的Fn2″（s,n）｜n=0。为进一步讨论全三次系统的细焦点量上界问题,给出更一般的方法．利用这种方法,通过进一步的运算,可能会发现一些系统所固有的特征,以避免采用极坐标带来的不必要的运算式子的繁杂．极坐标是一般曲线坐标的极特殊的情形．     

Five-Axis Interpolation of Continuous Short Linear Trajectories for 3[PP]S-XY Hybrid Mechanism by Dual Bezier Blending

A novel five-axis real-time interpolation algorithm for 3[PP]S-XY hybrid mechanism is proposed in this paper. In the algorithm, the five-axis tool path for controlling this hybrid mechanism is separated into two sub-paths. One sub-path describes the movement of 3[PP]S parallel kinematic mechanism module, and the other one describes the movement of XY platform. A pair of cubic Bezier curves is employed to smooth the corners in those two sub-paths. Based on the homogenous Jacobian matrix of 3[PP]S mechanism, a relationship between the position errors of every driving joint in hybrid mechanism and the position deviation of the tool tip center point at the moving platform is established. This relationship is used to estimate the approximation error for the corners smoothing according to the accuracy requirement of tool tip center in interpolation. Due to the high computational efficiency of this corner smoothing method, it is integrated into the look-ahead module of computer numerical control(CNC) system to perform online tool path smoothing. By performing the speed planning based on a floating window scheme, a jerk limited S-shape speed profile can be generated efficiently. On this basis, a realtime look-ahead scheme, which is comprised of path-smoothing and feedrate scheduling, is developed to acquire a speed profile with smooth acceleration. A monotonic cubic spline is employed for synchronization between those two smoothed sub-paths in tool path interpolation. This interpolation algorithm has been integrated into our own developed CNC system to control a 3PRS-XY experimental instrument(P, R and S standing for prismatic,revolute and spherical, respectively). A club shaped trajectory is adopted to verify the smoothness and efficiency of the five-axis interpolator for hybrid mechanism control.     

Five-axis interpolation of continuous short linear trajectories for 3[PP]S-<Emphasis Type="Italic">XY</Emphasis> hybrid mechanism by dual Bezier blending

A novel five-axis real-time interpolation algorithm for 3[PP]S-XY hybrid mechanism is proposed in this paper. In the algorithm, the five-axis tool path for controlling this hybrid mechanism is separated into two sub-paths. One sub-path describes the movement of 3[PP]S parallel kinematic mechanism module, and the other one describes the movement of XY platform. A pair of cubic Bezier curves is employed to smooth the corners in those two sub-paths. Based on the homogenous Jacobian matrix of 3[PP]S mechanism, a relationship between the position errors of every driving joint in hybrid mechanism and the position deviation of the tool tip center point at the moving platform is established. This relationship is used to estimate the approximation error for the corners smoothing according to the accuracy requirement of tool tip center in interpolation. Due to the high computational efficiency of this corner smoothing method, it is integrated into the look-ahead module of computer numerical control (CNC) system to perform online tool path smoothing. By performing the speed planning based on a floating window scheme, a jerk limited S-shape speed profile can be generated efficiently. On this basis, a realtime look-ahead scheme, which is comprised of path-smoothing and feedrate scheduling, is developed to acquire a speed profile with smooth acceleration. A monotonic cubic spline is employed for synchronization between those two smoothed sub-paths in tool path interpolation. This interpolation algorithm has been integrated into our own developed CNC system to control a 3PRS-XY experimental instrument (P, R and S standing for prismatic, revolute and spherical, respectively). A club shaped trajectory is adopted to verify the smoothness and efficiency of the five-axis interpolator for hybrid mechanism control.     

基于三角函数内插法的波动反应谱计算精度分析

以反应谱基本概念和线性插值法为理论基础提出了求解波动反应谱的三角函数内插法。推导了反应谱计算公式,建立了时间间隔相等的三角函数内插法的连锁递推反应谱计算公式。对简谐波动荷载进行三角函数内插法、解析法和"精确法"的反应谱计算,结果表明:采用三角函数内插法的反应谱计算值比反应谱计算方法(精确法)计算值更接近解析解,且计算精度更高。利用三角函数内插法对两条实际记录的波动加速度时程曲线进行反应谱的数值计算。分析表明:基于三角函数内插法得到的各反应谱值是稳定的,其反应谱值一般稍大于线性内插法所得结果,精度满足要求,能在一定程度上简化计算。     

船舶靠泊操纵模拟过程中的计算方法研究

在船舶靠泊操纵仿真中,由于船舶不能视为质点运动,因此船岸距离的计算不能简单地归结为点线距离,而应该用多边形间距方法进行计算。本文对这一问题进行了专门研究,找到一种将计算与判别合二为一的数值计算方法。该方法能避免坐标的组合判别,减少出错可能,而且简单易用。经仿真实践使用,能正确有效地完成多边形间距离的计算,具有一定的实用价值。     

车载紧急制动触发曲线计算模型分析

列车安全防护曲线计算是车载ATP的关键技术之一。IEEE1474．1^TM标准规定ATP安全制动曲线由紧急制动曲线和紧急制动触发曲线组成。紧急制动触发曲线的速度能够保证列车在侵犯该速度时能在目标点前停车,以保证行车安全。分析CBTC控车模式下,列车从超速、制动到完全静止过程中能量的转移关系,并利用能量守恒原则建立紧急制动触发曲线的计算模型。仿真结果表明,提出的计算模型满足IEEE1474．1^TM中的相关要求,具有一定的实际借鉴意义。     

跑道容量仿真模型分析

跑道容量是指在一定的运行条件下,跑道在特定时段内所能服务的起降飞机的最大架次数,对正确地估计跑道容量,减少机场延误有重要作用。在回顾以往的跑道容量计算模型的基础上,使用仿真软件建立单跑道机场的仿真模型,计算仪表飞行条件下单条跑道的容量和延误,并绘制出相应的容量一延误曲线。     

A Novel Model of F0 Contours Prediction for Continuous Speech

F0 （fundamental frequency） contour was studied under different prosodic environment in continuous speech and a novel model of F0 contours prediction was proposed. It describes syllabic F0 contour with two points, one curve and duration. The curve represents two optimal points of controlling parameters. The duration represents the syllabic duration. The prosodic characters of controlling parameters were analyzed by CART （Class and Regression Tree）. A set of controlling parameters was analyzed, which reflects the linguistic environment and prosodic structure. Then it sets up the model of F0 contours prediction with the two optimal controlling parameters and F0 templates. The end pitch value of previous syllable as special prosodic parameters was used to keep the continuity of fore-and-aft syllable. It focuses on looking out the main prosodic clues hiding in F0 contours and applying it to simplify the model for prediction. The results of synthesis experiment show that the performance of the prediction method is appreciated.