By using the projective geometry,some schemes for generating rational curves from pencil of lines are investigated in this paper.
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。
In this paper, a new concept called uniform interval implicitization of rational curves is proposed, which is finding an uniform interval curve with lower degree bounding a given rational curve and mini.
故此提出了参数式有理曲线均匀区间隐式化的一种新方法,利用区间算术和空间重心坐标的定义,可以用一个低阶区间多项式隐式曲线来逼近所给的参数式有理曲线,同时使一些目标函数最小化,达到用隐式多项式曲线来逼近参数式有理曲线的很好效果,并提供了一些算法和实例。
In this paper, a new approach based on perturbation method is proposed for the piecewise polynomial approximation of rational curves and surfaces.
本文利用摄动的思想，以摄动有理曲线（曲面）的系数的无穷模作为优化目标，给出了用多项式曲线（曲面）逼近有理曲线（曲面）的一种新方法。
Let X be a n dimensional projective variety,x be a fixed point in X,and let C_t(X,_X(1)) be the set of rational curves C of degree t passing through x in X,p_t(X)=dimC_t(X,_X(1)) for any positive integer.
设X是n维射影代数簇,取定X中一点x,设Ct(X,X(1))表示X中的过x点的t次有理曲线的集合,pt(X)=d imCt(X,X(1))。
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.
有理曲线和曲面作为一类重要的参数曲线曲面,在计算机辅助设计与制造中有着广泛的应用。
However, due to the complex of computation and the need of the design, sometime we need to use polynomial approximation for a rational curves and surfaces.
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。
Some Methods for Shape Modification of Cubic Rational Bézier Curves;
三次有理Bézier曲线的形状调整方法
Convergence of hybrid polynomial approximation of rational Bézier curves;
有理Bézier曲线hybrid逼近收敛性
This paper gives the operator representation of rational Bézier curves′ derivatives,and the operator representation of the necessary and sufficient conditions of G1 and G2 continuous connexion between two adjacent random degree rational Bézier curves according to G1 and G2 continuous conditions.
文章给出了有理Bézier曲线各阶导矢的算子表示,并根据G1和G2连续条件,给出了两条邻接任意次有理Bézier曲线间G1和G2连续拼接充要条件的算子表示。
Approximating a kind of rational Bézier curves and their integral computation and derivatives using polynomial curves;
一类有理Bézier曲线及其求积求导的多项式逼近
Simultaneous blending of arbitrary plane topology with the quadric rational Bézier curve;
用二次有理Bézier曲线同时磨光任意平面拓扑结构
New way of approximating rational Bézier curve with polynomial curve
有理Bézier曲线的多项式逼近新方法
A new class of rational Bezier curves based on rational Bernstein function class;
基于有理Bernstein函数类的一类有理Bezier曲线
As the special example of rational B-spline curves,rational Bezier curves are becoming increasingly widespread.
有理Bezier曲线作为有理B样条曲线的特例,正得到越来越多的研究,并在CAD/CAM领域中得到越来越广泛的应用。
The rational Bezier curves are used widely in the CAD/CAM technologies, and as the shape parameters, their weights bring great flexibility in the shape design systems.
在控制顶点和节点已定的情况下,有理Bezier曲线的权因子可作为形状参数为外形设计带来了很大的灵活性。
Research on the Multiple Products Theory of B-splines and Polynomial Approximation Techniques of Rational Curves and Surfaces;
B样条多重乘积理论与有理曲线曲面多项式逼近技术的研究
Rational Approximation of Offset Curves of Rational Bézier Curves
有理Bézier曲线的等距曲线有理逼近
The Rational Approximation of Planar Bézier Offset Curve;
平面Bézier曲线的等距曲线有理逼近
NURBS (Non-Uniform Rational B-Splines)
不均匀有理B样条曲线
Curvature monotony condition Tor the quadratic rational B spline curves.
二次有理B样条曲线曲率单调条件
Study of Rational Spline & Algebraic Curves and Surfaces Splines;
有理样条和代数曲线曲面样条的研究
Research on Approximate Degree Reduction for Interval Rational Bezier Curves and Surfaces;
区间有理Bezier曲线、曲面的降阶逼近研究
A Method for the Modification of Curves and Surfaces with Rational Bezier;
一类基于有理Bezier的曲线曲面修正方法
Modeling Research on Quartic Rational Bézier Curve and Surface
四次有理Bézier曲线曲面造型的研究
An efficient extending algorithm for quadric rational Bézier curve
一种二次有理Bézier曲线延拓的有效算法
Parametric Projective Transformation and Weights of Rational Bézier Curves
有理Bézier曲线的权因子与参数射影变换
AN UNEVEN ALGORITHM FOR THE SUBDIVISION OF RATIONAL BE ′[DD)〗ZIER CURVES
有理bézierb>曲线b>的非均匀细分算法
NURB surfaces
NURBS(非一致有理B样条曲线)
Some Research on the Weights of Rational Bézier Curves
有理Bézier曲线权因子的研究
EXACT EVALUATION OF THE INTERPOLATORY SUBDIVISION CURVES AT RATIONAL PARAMETER VALUES
插值细分曲线有理参数点的精确求值
Study on shape of G~2 continuity for quartic rational Bézier curve
G~2连续的有理四次Bézier曲线的造型
Operator Representation of Smooth Jointing between Rational Bézier Curves
有理Bézier曲线光滑拼接的算子表示
New way of approximating rational Bézier curve with polynomial curve
有理Bézier曲线的多项式逼近新方法