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    A Class of B-spline Curves Approximating to Its Control Polygons
    一类可逼近控制多边形的B样条曲线
    The Research of the Bounds on the Deviation between Curves and the Corresponding Control Polygons
    曲线与控制多边形之间偏差的界的研究
    Thirdly, we obtain the representations of integral circle, cycloid and sinusoid on a period by uniform C-B-splines of degree 3, along with adding control points the control polygons approach the generated curves, the approximation accuracies are better than that in [16] and [18].
    3.给出了整圆、一个周期上的摆线及正弦曲线的三次均匀C-B样条表示,随着样条节点的增加,控制多边形越来越逼近生成曲线,比文[16]与[18]的逼近度优越的多。
    A simple algorithm of constructing planar piecewise 4-order HBézier-like curves with all edges tangent to given control polygons is described.
    提出了构造与多边形各边都相切的平面分段 4 阶 H Bézier-like 曲线的简便算法.
    Based on the study of the bounds on the deviation between curves and surfaces and the corresponding control polygons and nets, a new algorithm is presented to reduce the bounds on the deviation between the former curves and the corresponding control polygons.
    本文在研究了以往关于曲线曲面与控制多边形及控制网格之间偏差界的基础上,提出了一种新的算法,缩小了原有的曲线与控制多边形之间偏差的界。
    In this paper conception and current research of bounding box is firstly introduced, and necessity of the research about the bounds on the deviation between curves and surfaces and the corresponding control polygons and nets is pointed out.
    本文首先介绍了包围盒的概念和研究现状,指出了对曲线曲面与控制多边形及控制网格之间偏差的界的研究的必要性。
    In the second chapter brief introduction about the development and basic conceptions of curves and surfaces is presented. Meanwhile, it is illustrated that characteristic of curves and surfaces is one of the important foundations in the research of the bounds on the deviation between curves and surfaces and the corresponding control polygons and nets.
    第二章对曲线曲面的发展及基本概念作了比较简短的概括性介绍,阐明了曲线曲面的性质是研究曲线曲面与控制多边形及控制网格之间偏差的界的重要基础。
    We present the bounds on the deviation between univariate polynomials, tensor product polynomials, univariate splines, and tensor product splines and the corresponding control polygons and nets. The bounds on the Lp-norm are given in terms of the maximal absolute second differences of the control point sequence.
    最后分别介绍了一元多项式、张量积多项式、一元样条和张量积样条同相应的控制多边形或者控制网格之间偏差的界,给出了Lp-norm范数空间下,根据控制顶点序列的最大绝对二阶差分得出的界。
    In the case of the bounds on the deviation between cubic Bezier curves and the corresponding control polygons, we analyse the effects of the bounds by different norm and the shape of curve.
    以三次Bézier曲线和控制多边形之间偏差的界为例,分析了不同的范数空间和曲线形状对界的影响。
 

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