参数曲线

Thesis is devoted to construct and analysis piecewise rational splines, algebraic curve and surface for interpolation.

首先对参数曲线曲面、代数曲线曲面等问题的历史背景和研究现状进行了综述，并归纳了本文所做的工作。

Set up a child in a plane curve walk along this curve by the time parameter curve.

详细说明：设一个小孩在平面上沿着某曲线行走，此曲线由时间参数曲线确定。

Set up a child in a plane curve walk along this curve by the time parameter curve....

设一个小孩在平面上沿着某曲线行走，此曲线由时间参数曲线确定。

This problem of planar parametric polynomial curve of degree 3 had been discussed perfectly many years ago, making use of invariant of affine transformation.

关于三次代数多项式参数曲线的这一问题早已解决，然而所用的几何不变量方法对于非代数曲线失效。

Properness of a parameterization is a basic property of rational parametric curves and it has been well studied when the coefficients of the parameterization are rational. However, such coefficients in engineering and CAGD are often represented with float numbers with errors.

有理参数曲线的恰当性是曲线的基本性质，虽然其在有理系数情况下已经有完备的结果，但在工程和CAGD应用中常常得到带误差浮点系数的有理表示形式。

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。

Hence the study of geometric properties, which include the distribution of singular and inflection points and the convexity of parametric curves, is the key for designer to control the curves shape.

在计算机辅助几何设计的光顺曲线造型中，不希望曲线带有二重结点、尖点及多余拐点，因此对参数曲线的几何性质(包括奇、拐点分布及凸性等)的研究是控制其曲线形状的关键。

The following central point within a small local region of current tracing point can be obtained based on the influence of neighboring points as well as the smoothness and fairness principle. Finally, a sequential of central points can be traced out efficiently without any iteration and a parametric curve can be reconstructed by interpolating the central points.

该方法仅从当前跟踪点的邻近点集与曲线重建光顺准则出发，无须迭代，可快速、有效地跟踪得到无序点集的一个中轴点列，最后再由此点列拟合出参数曲线。

The main content reads as follows: Chapter 1 gives a survey on the three methods by which regular geometric modeling can be rended, including parametric curves/surfaces modeling method, algebraic curves/surfaces modeling method and subdivision. Moreover we introduce in greater detail about two means for subdivision which fit into two class: geometric subdivision and algebraic subdivision.

全文主要内容如下：第一章首先对CAGD中构造&规则几何形体&的三类造型方法：参数曲线、曲面造型方法，代数曲线、曲面造型方法及细分法——曲线、曲面的离散化造型方法，作了较系统的综述，并对两类主要的细分法——几何方法与代数方法，作了较详细的介绍。

The result shows that the convergence of active contour curve is not only depended on the image gradient,but also the target region.

简单地讲，主动轮廓模型是一条由相应能量函数控制的可形变参数曲线，以能量函数最小化为目标，控制曲线变形，具有最小能量的闭合曲线就是目标轮廓。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。