The motions of curves and surfaces have a wide range of applications.
曲线和曲面运动有着广泛的应用。
There are currently almost all the general curves and surfaces implemented.
目前几乎所有的曲线和曲面都实现过了。
Then the theory of TBSC and TBBC curves and surfaces are discussed in details.
BSC曲线曲面论，这是本文的重点内容之一。
It is significative for the smooth property of approximating curves and surfaces.
这对于研究逼近曲线曲面的光滑性是很有意义的。
In this paper, the main work is about the modification of NURBS curves and surfaces.
本文的主要工作就是围绕NURBS曲线曲面的形状修改展开的。
In particular, many integrable equations arise naturally from motions of curves and surfaces.
特别地，许多可积方程都自然地产生于曲线和曲面运动。
This thesis studies modeling and the simple application of the fractal approximation of curves and surfaces.
本文研究曲线曲面分形逼近的数学模型及其简单应用。
So many nonlinear evolution equations have been shown to be closely related to motions of curves and surfaces.
因此，很多非线性演化方程都与曲线和曲面运动有着密切的关系。
Nowadays, the construction module of free curves and surfaces is still the core one of the key parts in CAD/CAM.
至今，曲线曲面造型模块仍是CAD/CAM系统的最关键部分之一。
Currently the smoothing of curves and surfaces has become an important method of technology in car body modeling.
目前曲线曲面的光顺处理已成为轿车车身外表面造型方法中非常重要的一项技术。
B-Spline curves and curve surfaces are the most commonly used parametric curves and surfaces in Computer Graphics.
样条曲线曲面是在计算机图形学中应用最广泛的参数曲线曲面类型。
The shape of the curves and surfaces can be adjusted entirely or locally by changing the values of the shape parameters.
改变形状参数的值能整体或局部调控曲线与曲面的形状。
The problems include modifying the local shape for subdivision curves and surfaces, the subdivision schemes for NURBS etc.
细分曲线曲面的可局部修形性，对NURBS细分算法的研究等。
CAGD mainly researches the complex way to change the freedom of curves and surfaces, the so-called freedom of curves and surfaces.
CAGD主要研究以复杂方式自由变化的曲线曲面，即所谓的自由型曲线曲面。
Among the modeling methods used in the CAD parametric curves and surfaces, the technique of blending curves and surfaces is being wildly study.
在CAD参数曲线曲面造型方法中，混合曲线曲面技术正被广泛研究，本文分两大部分。
After briefly reviewing the classification and respective characters of curves and surfaces modeling, the paper expatiates its history in CAGD.
本文首先回顾了曲线曲面造型方法的分类以及各自的特点。
The extended algorithm is simple, convenient and can solve the problems of position adjustment and shape control of curves and surfaces that exist in engineering.
本文提出的算法简单、易于操作，可方便地解决工程实际中曲面位置调整和形状控制问题。
It systemically summarizes the geometry meanings of weights and the principle of the shape modification of curves and surfaces. This paper gives a method of implementing.
系统总结了权因子的几何意义，及对曲线、曲面的修型原理，并给出了其实现方法。
An important topic of Computer Aided geometric design and Computer Graphics is geometric modeling, whose major components are free-form curves and surfaces design and modeling.
几何造型是计算机辅助几何设计和计算机图形学的一项重要内容，而曲线曲面的设计与造型又是几何造型的一个主要内容。
In the classical differential geometry which deals with the theory of curves and surfaces of three dimensional Euclidean space, the most distinctive study is the Weingarten surface.
经典微分几何研究三维欧氏空间中曲线曲面理论，其最具有特色的研究是主曲率函数满足某些关系的魏因加吞曲面。
However, due to the advantages of implicit curves and surfaces which the parametric curves and surfaces don't have, sometime we need to use the implicit form of a rational curves and surfaces.
然而由于曲线曲面的隐式形式具有参数形式所不具有的优点，有时我们还需要求参数曲线曲面的隐式表达式。
As we know, it is both convenient and practical to describe curves and surfaces by matrix representation in CAGD, such as facilitating the evaluation and conversion of the curves and surfaces.
我们知道，曲线曲面的矩阵形式在计算机辅助几何设计的实际应用中是非常必要的并且存在很好的应用价值，例如方便于曲线曲面的求值和转换等。
The convexity of curves and surfaces is an important property in the field of Computer Aided Geometric Design (CAGD). This paper tries to tackle the positive and convex problem of polynomials.
在计算机辅助几何设计(CAGD)中，曲面曲线的凸性是一种重要的特性旨在解决多项式的正性和凸性问题。
With the deeper research of interval curves and interval surfaces, people begin to approximate curves (surfaces) with interval curves (surfaces).
随着对区间曲线曲面的深入研究，人们开始用区间曲线曲面来逼近曲线曲面。
Rational curves and rational surfaces, which are a class of important approximation functions, are extensive applied in CAD/CAM.
有理曲线和曲面作为一类重要的逼近函数，在计算机辅助设计与制造中有着广泛的应用。
The principles, methods and evaluation of the fairing of surfaces and curves are also discussed.
研究了曲线和曲面的光顺准则、方法和评估手段。
In computer drawing, generally, curves are represented by line segments and surfaces are tessellated up with small plane patches.
在计算机绘图中，一般来说，曲线实际上是由折线代替，而曲面实为小平面拼接而成。
It introduced imitating surfaces with bicubic parametric curves, feed length, cutter location and vector of cutter location.
介绍用双三次参数曲线拟合曲面、平头铣刀的直径、铣削的步长及行距选择、刀位点和刀轴矢量的计算。
Also the curves can express the circle arc and ellipse arc and can construct rotate surfaces.
同时它还能精确表示圆弧、椭圆弧等二次曲线，推广到空间即可以表示旋转曲面。
Also the curves can express the circle arc and ellipse arc and can construct rotate surfaces.
同时它还能精确表示圆弧、椭圆弧等二次曲线，推广到空间即可以表示旋转曲面。
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