平面NURBS曲线的等距线算法：圆弧法矢近似法

本文根据产生曲线的特征点与它的等距线的特征点的对应关系,给出了一种平面NURBS曲线的等距线表示方法——圆弧法矢近似法。这种方法的特点是:(1)等距线与产生曲线具有统一的NURBS表示;(2)计算简单、几何意义明确、近似精度高。     

平面NURBS曲线的导矢及其等距线

本文首先给出了计算NURBS曲线导矢的递推公式,在此基础上,给出了生成平面NURBS曲线等距线的算法。     

NURBS曲线的无自交近似等距曲线计算EI北大核心CSCD

NURBS曲线是CAGD中的标准工具,其等距曲线的计算是CAGD中的重要内容,对异常情况包括自交(或自交环)、奇点等的处理是等距曲线计算的关键技术.基于2阶导数采样和NURBS曲线的单值性,提出一种NURBS曲线的无自交近似等距曲线计算算法.首先提出并证明了NURBS曲线无自交等距曲线的最大偏移距离;然后通过计算最大偏移距离,以NURBS曲线的单值性为约束条件计算NURBS曲线的无自交近似等距曲线.2次和3次NURBS曲线无自交近似等距曲线计算的数值实例的结果表明,所提算法可以快速、有效地生成无自交的NURBS曲线的近似等距曲线,保证剩余控制顶点数尽量少且不依赖于权因子的选择,保留了NURBS曲线的权因子对曲线形状的调整性.     

基于仿射变换的等距线逼近方法

对于Ｃ＾１的具有任意函数类型的平面曲线,利用分段仿射变换方法,生成近似的等距线。它的每一段与原曲线的相应曲线段具有相同的函数类型,具有仿射意义下的几何性质,能较好的逼近原曲线的等距线。     

基于遗传算法的NURBS曲线降阶

采用遗传算法实现NURBS曲线直接降多阶。提出并证明了NURBS曲线保端点降阶的必要条件,在此基础上将NURBS曲线的节点序列、控制顶点和权用浮点数编码为基因个体,运用遗传算法,通过循环执行选择、交叉、变异求解得到最优解或者次优解。实例说明了采用该方法实现NURBS曲线降阶有较高的精确度。     

NURBS曲面的等距曲面算法

本文将ＮＵＲＢＳ曲线的有理ｄｅＢｏｏｒ算法推广到ＮＵＲＢＳ曲面点的计算，由此可以得到ＮＵＲＢＳ曲面上点的单位法矢量，供其应用于ＮＵＲＢＳ曲面等曲面的生成。该算法几何意义明显，算法简洁，易于编程实现。     

用导矢叉乘法对NURBS曲线进行形状调整

提出用新旧曲线上对应点的两个导矢叉乘平方的积分定义目标函数的方法．通过极小化目标函数使新曲线偏离原曲线的程度最小，从而使新曲线在满足修改条件的前提下更符合原曲线所定义的形状．用实例对该方法和其它几种方法构造的曲线的形状及其误差进行了比较．     

曲线轮廓汉字等距晕线效果的实现算法

本文提出了一种基于曲线轮廓汉字的等距晕线效果的生成算法。文中通过分析实现过程中可能出现的异常情况，提出了针对这些异常的修正算法。     

CAD模型截面Voronoi图生成与分层面的等距线填充

目前快速成型中层面制作都是采用行扫描方式进行分层截面的填充，该扫描方式的缺点是：熔丝冷却后产生的收缩对上一层面形成切内应力，使得物理容易产生翘曲变形，另外对于注重外表面的形体，行扫描方式的填充效率较低，为此提出环扫描的填充方式，将VORONOI图的理论引入模型的分层制作，用外轮廓与它的等距线为轨迹完成截面的扫描填充，基于CAD模型分层后的轮廓线及其数据结构，研究了对该区域进行VORONOI图分割的算法，在此基础上规划出它的环扫描轨迹。     

用三次PH曲线构造平面Bézier曲线的等距线算法

通过加入参数节点离散B啨ｚｉｅｒ曲线 ,根据原B啨ｚｉｅｒ曲线的始末端点及其切向量 ,加入节点构造一条G1 连续的三次PH样条曲线 ,以此作为原B啨ｚｉｅｒ曲线的逼近曲线 ,并进一步产生等距线 估计了原B啨ｚｉｅｒ曲线与ＰＨ样条曲线的整体逼近误差和等距线误差     

NURBS曲线曲率连续延拓的一种有效算法

提出了一种局部延拓NURBS曲线的算法。从理论上探讨了使NURBS曲线获得曲率连续的延拓应满足的条件，同时又给出了在实际应用中使NURBS曲线获得曲率连续的延拓的基本算法。     

等距曲面的NURBS放样插值方法

本文给出了等距曲面的一种NURBS放样插值生成方法，该方法主要是在原始NURBS曲面上取得一个能较好反映曲面特征的型值点阵，再交这个型值点阵按某种算法矢方向外推，从而得到原始曲面的等距曲面上的型值点阵，然后，再用NURBS放样插值曲面来逼近等距曲面，本文给出的算法几何意义明显，易于编程实现，且得到的等距曲面其u向和v向参数曲线仍是NURBS曲线，且具有C^2连续性，最后，给出了一个实例。     

NURBS曲线自动光顺的一种有效算法

提出了一种局部光顺NURBS曲线的算法。算法建立在重复删除和插入节点的过程中,这个重复删除和插入的节点通过一个光顺准则自动选择。此算法自动找出NURBS曲线需要修改的那一点,局部修改控制多边形,使生成的新曲线更加光顺。     

Tool-path generation of planar NURBS curves

It has been widely used in CAD field for many years and gradually applied in CAM area with the prevalence of NURBS interpolator equipped in CNC controllers. But few of them provide the tool radius compensation function. In order to achieve the goal of generating tool-path, an algorithm was presented to offset NURBS curves by an optimum process for CAD/CAM systems in this paper. NURBS format is ideal for HSM applications, but not all NURBS outputs are equal and standard. Basically, there are two different ways to generate NURBS tool-paths; one is to fit a NURBS curve to the conventional tool-path output, the other one is to generate a NURBS tool-path from the start. The main targets for the tool-path of this paper are: (1) To keep a constant distance d between progenitor curve C(t) and offset curve C_d(t) on the normal direction of C(t); (2) to alternate the order k of the basis function in offset curve C_d(t); (3) to oscillate the number of control points of offset curve C_d(t) and compare it with progenitor curve C(t). In order to meet the tolerance requirements as specified by the design, this study offsets the NURBS curves by a pre-described distance d. The principle procedure consists of the following steps: (1) construct an evaluating bound error function; (2) sample offset point-sequenced curves based on first derivatives; (3) give the order of NURBS curve and number of control points to compute all initial conditions and (4) optimize the control points by a path searching algorithm.     

基于NURBS方法的气动外形优化设计

采用NURBS曲线曲面,对钝锥弹头和钝双锥弹体建立参数化曲面模型,取NURBS曲线控制点作为设计参数,应用高超声速面元法求解气动力特性,在给定设计约束下,采用遗传算法进行气动外形优化设计,并对优化结果进行了比较分析。结果表明,采用NURBS方法构造参数化外形,并结合优化技术可方便快速地获得所需最优外形;与应用二次曲线构造参数化外形相比,该方法对弹体形状控制更加灵活,并可局部修改弹头曲线形状。因此,基于NURBS方法发展整套的系统优化设计算法很有现实意义和应用价值。     

Offset of curves on tessellated surfaces

Geodesic offset of curves on surfaces is an important and useful tool of computer aided design for applications such as generation of tool paths for NC machining and simulation of fibre path on tool surfaces in composites manufacturing. For many industrial and graphic applications, tessellation representation is used for curves and surfaces because of its simplicity in representation and for simpler and faster geometric operations. The paper presents an algorithm for computing offset of curves on tessellated surfaces. A curve on tessellation (COT) is represented as a sequence of 3D points, with each line segment of every two consecutive points lying exactly on the tessellation. With an incremental approach of the algorithm to compute offset COT, the final offset curve position is obtained through several intermediate offset curve positions. Each offset curve position is obtained by offsetting all the points of COT along the tessellation in such a way that all the line segments gets offset exactly along the faces of tessellation in which the line segments are contained. The algorithm, based entirely on tessellation representation, completely eliminates the formation of local self-intersections. Global self-intersections if any, are detected and corrected explicitly. Offset of both open and closed tessellated curves, either in a plane or on a tessellated surface, can be generated using the proposed approach. The computation of offset COT is very accurate within the tessellation tolerance.     

Modifying free-formed NURBS curves and surfaces for offsetting without local self-intersection

This paper presents an algorithm of modifying free-formed NURBS curve/surface for offsetting without local self-intersecting. The method consists of (1) sampling a number of points from a progenitor curve/surface based on second derivatives; (2) checking the curvature or maximum curvature of the progenitor curve/surface at the sampled points; (3) inserting corresponding knots of sampled points; (4) repositioning control points till the curvature/maximum curvature of the curve/surface everywhere are less than the reciprocal of offset distance. The method is efficient and is able to obtain better offsetting results.     

改进的NURBS曲线预估校正插补方法

现行的NURBS曲线参数预估校正插补方法不能预估最开始的两个参数,而且不能控制预估参数迭代修正的次数。提出改进的NURBS预估校正插补方法,该方法预估插补点参数,根据最大进给步长约束、轮廓误差约束以及法向加速度约束,判定预估参数与实际参数的误差,当误差在允许范围内,则对参数步长增量进行调整,否则进行迭代修正。仿真实验结果表明,新方法通过对参数步长增量的调整,使得预估参数更加接近实际参数,较现有方法有效减少了参数迭代修正的次数,利于实时插补的实现。     

基于遗传算法优化的跳汰机排料系统PID控制仿真

针对传统PID控制方法应用于跳汰机排料系统时难以获得最优控制参数、控制效果差的问题,提出一种基于遗传算法的PID控制参数优化方法,介绍了基于遗传算法优化的PID控制结构、参数优化方法及步骤,并以某矿井跳汰机排料系统为例,对基于该方法的PID控制器的控制性能进行了仿真研究。仿真结果表明,该方法能够实现PID控制参数的在线优化,收敛速度快,具有较强的鲁棒性;基于该方法的PID控制器具有良好的动、静态性能,无超调现象,控制精度高。