曲线

And then, by regarding the curve and surface as a map from differential manifold to topological manifold, we present the framework of GRPCS and discussed its basic properties in detail. GRPCS provides a unified framework for parametric curve and surface.

然后通过势函数来构造微分流形上的单位分解，将曲线曲面看作微分流形到拓扑流形的映射，给出了广义有理参数曲线曲面的整体理论框架，并对广义有理参数曲线曲面的基本性质进行了讨论。

A had given another new form of curve, which is constructed by a new totally positive basis (DP-NTP basis). This kind of curve shows obvious advantage in computing, for the reason that it has linear complexity. Meanwhile, it has good shape preserving property. But regretfully it is not locally adjustable as how B-spline curves do.

a提出了另一类用标准全正基构造的新曲线表示形式，这种曲线在求值运算中具有线性时间复杂度的明显优势，同时像B样条曲线那样具有模拟或保持控制多边形形状的保形性质，但没有形状局部可调性。

This paper presents a new class of piecewise trigonometric polynomial curves and a weighted trigonometric polynomial curve which has simple structure and can be used to design curves.

提出了一类新的分段三角多项式曲线，给出了加权三角多项式曲线，表示式结构简单，能用于曲线设计。

Experiments show that C-B spline curve, uniform B-spline with shape parameter, hyperbolic polynomial uniform B-spline with shape parameter and trigonometric polynomial uniform B-spline with shape parameter can be used to produce some frequently used free form curves in the industrial field when the shape parameter is assigned with some specific values.

通过调整形状参数来修改曲线形状是计算机辅助几何设计中一个非常活跃的研究课题，研究形状参数的变化对样条曲线形状的影响，对于增加曲线造型的灵活性是非常必要的。

The trigonometric uniform polynomial curve constructed in this paper has two advantages. One is that the curve can be continuous and the shape can be adjusted with the fixed tangents. The other is that only adding one new knot, the curve can pass through the tangent, which reduces excess points.

利用绘出的三角均匀多项式曲线来逼近多边形，主要有2个特点：一是曲线能达到连续，并且在切点固定时曲线的形状可以进行调整，二是只需增加一个新节点就可以通过切点，减少了额外点。

With the shape parameter, the trigonometric polynomial curves can be close to the cubic Bécurves or close to the given control polygon then the cubic Bécurves.

由四个控制顶点生成的曲线具有与三次B zier曲线类似的性质，但具有比三次B zier曲线更好的逼近性。

Interpolating trigonometric polynomial parametric curves with C~2 (or G~1) continuity can be automatically generated without having to solve any system of equations or do any iterative computation. Then, the convexity of the constructed curves can be guaranteed by the appropriate value of the shape parameter.

在无需反求方程组、迭代计算和最值求解的前提下，即可产生插值给定点列的C~2或G~1连续的一族三角多项式样条曲线；进一步研究了该类曲线的保凸性，得到插值曲线保凸时形状参数的取值范围。

With the shape parameters, the trigonometric polynomial curves can approach more to the quadratic Bézier curves or to the given control polygon than the quadratic Bézier curves.

由三个控制顶点生成的曲线具有与二次Bézier曲线类似的性质，但具有比二次Bézier曲线更好的逼近性。

This paper narrates the theory method to determine measuring point s in the ubiety of center of road of first easement curve segment,circle curve segment and second easement curve segment,gives the source program of PC-E500 computer and explains data format in it.

讲述判定测点在道路中线第一缓和曲线段、圆曲线段、第二缓和曲线段的位置关系的理论方法，给出相应的PC-E500源程序，并对数据格式进行说明。

A length of straight line and a length of undamped sinusoid of 1/4 period replace the envelop as the response. By the new methods, calculation error is greatly reduced and system character analysis is completed with advantage.

新方法使取代曲线由包络线改为与响应曲线非常接近的一段直线和一段1／4周期的不衰减正弦曲线，从而使计算误差大大减小，这将有益于提高系统性能分析的质量。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。