有理曲线

We also develope the corresponding rational composite Bezier curve with geometric continuous design facility.

本文还将这一方法推广到有理情形，提出了有理组合Bezier曲线的几何连续设计方法。

A new method of finding the points on an elliptic curve by Maple is supplied; Maple is applied to the addition operation, the scalar product operation and the method of seeking the order of a basic point on the elliptic curve are proposed; the applications of Maple on ECC including encryption and decryption are supplied.

利用Maple编程求出椭圆曲线上有理点，用Maple实现椭圆曲线上两点的加法、点的数乘运算及求某个基点阶数的算法，利用Maple实现椭圆曲线密码体制的加密及解密。相比C语言，Maple语言更接近于平时说话的语法。同时，Maple语言可以方便地转化成C语言。

Ythagorean hodograph curves enjoy a number of remarkable properties, such as, its offset curves have exact rational representations; the arc length function of a Pythagorean hodograph curve is simply a polynomial function of the curve parameter; and the lower degree Pythagorean hodograph curves have intuitive geometrical interpretation.

H曲线具有诸如有精确的有理 Offset、弧长函数可由多项式函数表示以及几何解释优美等一系列优良性质。基于复分析方法，避免了实分析讨论中出现的复杂表示及繁琐计算，构造了满足给定 C1 Hermite插值条件且以C1拼接连续的三次 PH曲线偶。该曲线偶可灵活处理拐点，从而克服了一般三次 PH曲线因恒凸而无法处理拐点的缺陷。

In chapter 3, we discuss a novel parametric curve representation scheme on 1D manifold in-depth.

然后，本文分别对广义有理参数曲线和广义有理参数曲面进行了深入的研究。

Furthermore,it can represent the elliptic curves,parabola and other quadratic curves without using rational form.

给出了一种基于三角函数的类三次参数曲线，该曲线不仅具有类似于三次Bézier曲线的诸多性质，而且无需有理形式即可精确地表示椭圆、抛物线等二次曲线。

A method to construct an interpolation curve of rational quadratic B-spline G continuity is given.

给出二次有理B样条G2连续拼接的条件，提出一种二次有理B样条G2连续插值曲线的构造方法。

The relationship between the transformation of weights on rational Bézier curve and parameterization of the curve with the shape unchanged is discussed.

研究了在曲线形状保持不变的条件下，有理n次Bézier曲线的权因子改变与曲线参数化的关系。

The significance of rational interpolation of NURBS curve is obvious. But people often adopt non-rational interpolation. The study of rational interpolation is very little.

有理插值在构造NURBS曲线曲面以进行形状表示与设计中有着重要的意义，但是目前大多数都采用相对简单的非有理插值，关于复杂的有理插值的研究不多。

Introduced is a kind of space uniform rational spline curve, which possesses tension parameters and is based on hyperbolic spline functions.

引入了基于双曲样条函数的、具有张力参数的空间有理等距节点样条参数曲线，给出了这种曲线在每个样条子区间上为挠曲线段的充分必要条件；分析了这种挠曲线段没有尖点、重结点和泛拐点的特性；因而在用于空间曲线几何造型时可避免奇异性。

As an application,generating quasi arc-length parameterization of PH curves is also discussed.

在CAGD中，曲线曲面一般用多项式或有理多项式表示，因此求解多项式函数的反函数是CAGD中的一个基本问题，它在曲线的准弧长参数化、曲线隐式化、曲线求交等问题中都有非常重要的作用[1-2]。

I'm strongly against the death penalty — it's an eye for an eye.

我不赞成死刑——这是以牙还牙的报复行为。

And to get you the support you need, we're enlisting all elements of our national power: our diplomacy and development, our economic might and our moral suasion, so that you and the rest of our military do not bear the burden of our security alone.

并给你们所须的支援，我们正徵召国家所有各种的力量：我们的外交及发展，我们的经济力量与道德劝说，所以你们与其他军人不须要孤独地负起国家安全的责任。