参数方程

If the surface isrepresented by an implicit algebraic equation,the mapping can be constructed bythe theory of parametrization of algebraic surfaces;If the surface is represented byan parametric equation,the parameter values on the parameter plane can be solvedby numerical method or Grobner Basis method.

若曲面由代数隐式方程给出，可通过代数曲面参数化理论构造映射；若曲面由参数方程给出，可通过数值方法或Grobner基方法求解参数型值点。

In present textbook,for curvilinear parameter equation,there is no defined methods to solve characteristic of graph ,copy methods and the area of self-closed planar graph .

在现行教材中，有关参数方程所示曲线的图像特点、描绘方法以及自身封闭所围成的平面图形的面积等都未给出明确的求法，为此，文中给出了关于曲线参数方程的两个教学注记，以弥补教材中的不足。

The program developed with the formula enable the coordinates for points and the parametric formula for curves in the orthographic projection to be transferred into ones in the axonometric projection, which can be directly displayed on the screen. In addition, except for assigned different values to elastic coefficient of the axial direction and the angles of the axes, it is generally adapted in drawing any of the axonometric projections.

用它编程，可以把正投影中点的坐标或曲线的参数方程，转换成屏幕上能够直接显示点的轴测投影的坐标或曲线的轴测投影的参数方程，而且除了赋轴向伸缩系数和轴间角的大小、正负不同的参数值外，对绘任一种轴测投影和相应正投影都具有通用性。

We build the model for the enveloping worm helix parametric equation and then analyze its relations with the enveloping worm helix tooth surface equation,thus establishing the characteristic model of the involute helicoid enveloping worm′s generative gears.

渐开面环面蜗杆的三维构建属复杂曲面造型，文章在环面蜗杆螺旋线参数方程建模的基础上，分析讨论了其与渐开面环面蜗杆螺旋齿面方程的对应关系，建立了渐开面包络环面蜗杆产型齿的特征模型。

An algorithm which can draw any complex surfaces expressed by explicit equation or parametric equation was given.

提出了显式方程和参数方程表示的曲面的一种绘制算法，该算法可以绘制任意复杂的方程曲面。

From commonly used equation of calculating plane figure quadrature, formulas of calculating plane figure quadrature by applying curve parametric equation can be deduced.

从由曲线普通方程求平面图形面积的公式出发推出在各种情形下由曲线参数方程求平面图形面积的公式。

First, the algrithm classify the measurement characteristics as point, line and surface which can be classified to conicoid and free surface. Then, this algorithm establishes the parametric equation according to various features. After that this paper brings forward the characteristic parameters utilising least square method with several characteristic points. Finally high precision probe radius compensation is carried out according to the features.

该算法首先把测量特征分为点、线、面3种基本特征（其中面特征又分为二次曲面和自由曲面），然后建立各种特征的参数方程，利用测量得到的少量特征点，采用最小二乘法拟合得到被测特征的参数，最后根据被测特征参数进行高精度半径补偿。

The ellipse curre equation of circular image is derived based on the theory of spatial analytic geometry and rotation matrix s representation with unit quaternion then a mathematical model of the distortion error is established which relates the distortion error to the foca length of the used CCD camera,the radius as well as the position and the attitude of the inspected circle directly.

研究三维视觉检测中圆的中心经针孔摄像机成像后存在畸变误差的问题，首先基于空间解析几何理论和旋转矩阵的四元数表示法推导出像平面上投影椭圆的参数方程；然后根据参数方程建立圆中心成像畸变误差的数学模型；最后对影响畸变误差的主要因素进行分析。

As it can be expressed easily by argument equations, we use the conicoid as the criteria of points" classification. Based on the point"s normal and the adjacent field, corresponding to the conicoid equation such as plane, ball and cylinder, we search the points that fit the equation along the adjacent field. Using this method, we realized the automatic classification of unorganized points.The experiments using the algoritlim and criteria approved from this thesis are also carried out.

本文采用了可以比较方便地用参数方程表示的二次曲面作为数据点的分类标准，根据点的法向量以及其邻域结点的各种属性，对应于平面、球面、柱面等二次曲面，依据曲面方程的特点，从起始点开始沿邻域深度优先递归寻找符合方程的数据点，实现了散乱数据点的自动分类。

The relations of parametric equations with the route coordinates and the part coordinates are found out according to the curve model,the parametric equations of middle and side stakes in circular curve and easement curve are derived,thence the value of parameters is obtained,the solution procedure is got.

根据曲线模型，找出线路控制坐标系与局部坐标系坐标之间的参数方程关系，推出了缓和曲线及圆曲线中边桩坐标的参数方程，代入已知量求得参数的值，给出了求解步骤。

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。