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 control polygons 控制多边形(3)
 控制多边形
 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。 短句来源 An effective subdivision formula for C-curves of degree five is presented. Furthermore,it is proved that the control polygons generated by the subdivision converge to the original C-curve of degree five. 给出了五次C-曲线的细分公式,并且证明了细分过程产生的控制多边形序列收敛于原曲线. 短句来源 In this paper we discuss the distribution of singular points and inflection points on a planar C-Bezier curve in details, and give the necessary and sufficient conditions for having one or two inflection points, or a loop, or a cusp, or none of the above points on the curve in terms of their control polygons. 本文完全地讨论了平面C-曲线和平面C-Bezier曲线的奇拐点和凸性性质:曲线段为且必为下列情形之一:有一各拐点,两个拐点,一个尖点,一个二重结点,处处为凸; 并给出了相应的用控制多边形相对位置表示的充分必要条件. 短句来源
 “control polygons”译为未确定词的双语例句
 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 短句来源 Furthermore, it is proved that the control polygons generated by the subdivision converge to the original H-Bezier curves. Some important properties are proved for H-Bezier curves, such as convexity preserving and the variation diminishing properties. Fourthly, G' and G2 continuous conditions of H-Bezier curves are presented. 2.基于所构造的H-Bezier基函数定义了H-Bezier曲线,讨论了H-Bezier曲线的几何性质,如端点插值性、几何不变性、凸包性、变差缩减性等几何性质。 短句来源 An altering Bezier (F-Bezier) curve with coefficient of derivatives of vector being 4 has been proposed from general Bezier curves. The rate approximating control polygons of the two bicubic F-Bezier is 1.78 times faster than those of the general Bezicr curves. 从普通贝齐尔曲线推导出了导矢系数为4的另一种变形贝齐尔曲线，由它形成的双三次贝齐尔曲面逼近多面体的速度是普通双三次贝齐尔曲面的1．78倍。 短句来源

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 control polygons
 It is known that non-self-intersecting regular Bézier curves have non-self-intersecting control polygons, after sufficiently many uniform subdivisions. It is known that the sequence of control polygons of a Bézier-De Casteljau curve or surface obtained by the "degree elevation" process converges towards the underlying curve and surface. Bernstein bases, control polygons and corner-cutting algorithms are defined for C1 Merrien's curves introduced in [7]. This paper presents a short, simple, and general proof showing that the control polygons generated by subdivision and degree elevation converge to the underlying splines, box-splines, or multivariate Bézier polynomials, respectively. The paper analyses the convergence of sequences of control polygons produced by a binary subdivision scheme of the form 更多
 In this paper,a new method for fast finding intersection of two bicubic surface patches is de- scribed.Based on subdivision algorithm,two control polygons are first made to approximate the surfaces with arbitrary precision,then the curve of intersection can be fast found by a series of triangles and lines defined in a particular way. 本文提出了一种新的曲面求交方法,这种方法基于曲面控制网格的“子”分方法,只要控制网格足够逼近曲面,则通过对控制网格处理一系列特殊的直线与三角形求交问题,就可迅速、逼近地求出两张双三次曲面片的交线。 A shape blending algorithm of 2-D curved shapes is presented in this paper. A curvedshape is represented by a closed Non-Uniform Rational B-Spline(NURBS). We determine the inter-mediate shapes by interpolating the intrinsic definitions of the initial and final control polygons. Thisalgorithm can avoid shrinkage resulted from linear vertex interpolation and produce smcoth intermedi-ate shapes. Aliasing problems can also be easily eliminated. ２－ＤＳＨＡＰＥＢＬＥＮＤＩＮＧＯＦＮＵＲＢＳＣＵＲＶＥＳＨＡＰＥＳＪｉｎＸｉａｏｇａｎｇ；ＢａｏＨｕｊｕｎ；ＰｅｎｇＱｕｎｓｈｅｎｇ２－ＤＳＨＡＰＥＢＬＥＮＤＩＮＧＯＦＮＵＲＢＳＣＵＲＶＥＳＨＡＰＥＳ￥ＪｉｎＸｉａｏｇａｎｇ；ＢａｏＨｕｊｕｎ；Ｐｅ... An altering Bezier (F-Bezier) curve with coefficient of derivatives of vector being 4 has been proposed from general Bezier curves. The rate approximating control polygons of the two bicubic F-Bezier is 1.78 times faster than those of the general Bezicr curves.Conditions ensuring the smoothness of two surfaces is presented. The method, which enable to decrease fitting time and form free surface more rapiderly will be of some value in building an efficient geometric modelling system. 从普通贝齐尔曲线推导出了导矢系数为４的另一种变形贝齐尔曲线，由它形成的双三次贝齐尔曲面逼近多面体的速度是普通双三次贝齐尔曲面的１．７８倍。并且提出了保证两张曲面片连接光顺性的条件。为减少拟合时间、较快地生成自由曲面提供了一种策略，对建造有效的几何造型系统具有一定的参考价值。 << 更多相关文摘
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