有理曲线

一类有理曲线&RB曲线

A Kind of Rational Curve & RB Curve

此有理曲线是两个二阶锥面的交线，锥面类型由权系数组成的两个形状因子所决定。

This rational curve is the line of intersection of two conicoids and the type of the conicoidsis determined by two shape factors made up by the weights .

利用非均匀B样条小波的正交性、局部性和振动性，研究基于非均匀B样条小波分解的有理曲线的光顺算法。

Taking advantage of orthogonality , locality and oscillation of non-uniform B-spline wavelets , a new fairing algorithm for rational B-spline curve was studied .

平面有理曲线几何连续隐式化的优化方法

An optimal method of geometric continuous implicitization for planar rational curves

参数有理曲线代数表示的连分式方法

The Continued Fractions Method on Algebraic Representation of Parametric Rational Curve

一种精度可控制的有理曲线拟合算法

An algorithm for rational curves fitting with control accuracy

有理曲线和曲面的分片多项式逼近

Piecewise polynomial Approximation of Rational Curves and Surfaces

一类有理曲线曲面的修改方法及计算机实现

The Modifying Methods and Implementation with Computer of a Class of Rational Curves and Surfaces

从直线束到有理曲线

From pencil of lines to rational curves

关于复流形上的有理曲线的存在性

Existence of rational curves in complex manifolds

有理曲线的均匀区间隐式化

Uniform Interval Implicitization of Rational Surfaces

区间有理曲线的降阶

Degree reduction of interval rational curves

有理曲线的多项式逼近

Polynomial approximation of rational curves

有理曲线由直线束确定，直线束由两个或多个直线经调配得出。

The constructions of rational curves depend on the pencil of lines which may be blended in two or more straight lines .

采用射影几何学方法，研究从直线束生成有理曲线的技术方案。

By using the projective geometry , some schemes for generating rational curves from pencil of lines are investigated in this paper .

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。

Rational curves and rational surfaces , which are a class of important approximation functions , are extensive applied in CAD / CAM .

进而给出了一种曲面内部形状可调而边界连接条件不受影响的有理曲线网格插值方法。

Futhermore , another approach is developed to allow modifying the inner shape of interpolation surface patches without changing the G ￣ 1 continuity between adjacent interpolation patches .

本论文中，第一章首先介绍了有理曲线曲面的多项式逼近研究工作的发展情况和区间曲线曲面一些相关知识。

In this paper , we survey the development of polynomial approximation of rational curves ( surfaces ) and state the knowledge of interval curves ( surfaces ) in the first chapter .

利用样条曲线和原曲线加权组合构造一条新的有理曲线，该曲线通过插值原曲线的等距曲线上的采样点，从而逼近等距曲线。

Spline curve and base curve are combined to generate a new rational curve by adding the weight . This curve approximates offset curve by interpolating some sample nodes on the offset curve .

而且除直线、圆、平面、圆柱面、圆锥面和圆环面以外，有理曲线的等距曲线一般无法表示为有理形式，所以为了使CAD/CAM系统能有效处理，就必须用各种方法对等距曲线进行逼近。

Special cases for curves include straight lines and circles while planes , spheres , circular cylinders , circular cones , toruses and cyclides are the special cases for surfaces . Many methods approximating the offset curves should be used to make CAD / CAM systems operated effectively .

一种将一般有理参数曲线转化为有理Bézier曲线的方法

A Method for Converting a General Rational Parametric Curve to a Rational B é zier Curve

有理Bezier曲线导矢的第三种形式

The Third Expresses of the Derivative of a Rational Bezier Curve

该文提出了一种有理Bezier曲线的快速逐点生成算法。

A fast point-by-point generating algorithm for rational Bezier curve is presented .

有理Bezier曲线曲面的形状控制及调整

Shape Control and Modification of Rational Bezier Curve and Surface

一个n次有理参数曲线一般不能转化为权值都不为0的n次有理Bézier曲线。

In general a rational parametric curve of degree n cannot be converted into a rational B é zier curve of degree n with nonzero weights .

本文研究区间有理Bezier曲线、曲面的降阶逼近。

Degree reductions of interval rational Bezier curves and surfaces are studied in this thesis .

曲线的二次有理Bezier曲线拟合

Quadratic rational Bezier curve fitting

本文提出了一套全新的曲线曲面理论体系，称为广义有理参数曲线曲面（GeneralizedRationalParametricCurveandSurface）。

In the dissertation , a novel theoretical framework is proposed to represent and construct parametric curves and surfaces on manifold , named as generalized rational parametric curve and surface ( abbreviated as GRPCS ) .

基于齐次坐标空间，提出了一种NURBS曲线曲面和有理Bezier曲线曲面降阶的简便方法。

Based on homogeneous coordinates , this paper presents a convenient algorithm for approximate degree reduction of NURBS and rational Bezier curves and surfaces .

接着用几何方法定义了变差减缩性质，并且推得空间有理Bezier曲线具有这种性质。

Then a geometric definition of variation diminishing property is given , and it is proved that 3D Rational Bezier curves have this property .