实际上，直线的参数方程总是这个样子的。
In fact, parametric equations of lines always look like that.
我们主要还是关注，参数方程的运用，主要是一维的，比如直线、曲线等。
So, we have mostly focused on the use of parametric equations just for one dimensional objects, lines, and curves.
而当我们考虑运动点的轨迹的时候，轨迹可以称作是参数方程。
And, so when we think of the trajectory of the moving point, that's called a parametric equation.
现在我们可以做很多事情了，因为我们有了参数方程，现在有一件神秘的事。
So, now, just to show you that we can do a lot of things when we have a parametric equation, here is a small mystery.
我不准备写参数方程。
我们马上就要学习直线的参数方程。
OK, so we are going to learn about parametric equations of lines.
我希望在这明白,参数方程是考虑直线的一个很好办法。
So, I hope you've seen here that parametric equations are a great way to think about lines.
再来深入研究一下参数方程，我们以前还学过速度和加速度的。
Ok, so let me move on a bit and point out that with parametric equations, we've looked also at things like velocity and acceleration.
我们建立有两个变量φ和θ的球面的参数方程,它们恰好是,球坐标系统的一部分。
We are finding a parametric equation for the sphere using two variables phi and theta which happen to be part of the spherical coordinate system.
当然也有另一种方法，就是用参数方程表示这两条直线，用两条直线的方向向量作外积，从而得到切平面的法向量。
Another way to do it, of course, would provide actually parametric equations of these lines, get vectors along them and then take the cross-product to get the normal vector to the plane.
我们还学过怎样理解直线方程，它们有些特性，因为我们是从参数方程角度理解。
Ok, we've also seen how to look at equations of lines, and those were of a slightly different nature because we've been doing them as parametric equations.
利用椭圆的参数方程，给出了以等分角度为增量的绘椭圆的一种算法，并分析了算法的误差。
This paper makes use of the elliptical parameter equation, present a generation algorithm of ellipse with division Angle increments, and makes error analysis.
凡是可以表示为矢量参数方程的正则曲线，都可以用该方法进行插补。
Any regular curve that can be expressed by the vector parameter equation may be interpolated by this method.
提出了任意转角位置的渐开线齿轮齿廓的参数方程。
The parameter equation of involute tooth profile on any angular position is presented.
采用加权曲面参数方程拟合型腔侧壁曲面的算法，实现了子午线轮胎活络模模具型腔曲面的构造。
Apply the weighted surface parameter equation to fit the algorithm of cavity lateral surface, and realize the cavity surface construction of radial parting mold of meridian tire.
首先，我们运用流体力学的原理，分析推导出流曲线曲面的参数方程，实现了挤压型腔的数学建模。
First, we realize the mathematic model through getting the parameterized equation by analyzing the fluid mechanics and make use of Bezier curve to approximate stream curve.
第6周隐函数的导数。由参数方程所确定的函数的倒数。数学实验一。 二。
Week 6 The derivative of implicit function. the function's derivate by parameter equation.
运用毕奥萨伐尔定律和椭圆参数方程，计算出椭圆环电流中心的磁感强度。
The magnetic induction intensity at the center of elliptic current ring is derived based on the Biot-Savart law and elliptic parameter equation intensity.
文中的曲面或用参数方程表达或用符号距离函数表达。
In this paper, the surface is presented with a parameterized equation or a signed distance function.
基于这种裂纹单元，作者引入椭圆参数方程，推出一种计算裂纹前缘点应力强度因子的新方法。
Based on this kind of crack element, and by introducing parametric equation of ellipse, a new method for estimating stress intensity factor is proposed.
当单调函数的反函数不能显性表示时，连续型随机变量的分布密度曲线仍可通过参数方程的形式获得。
When a inverse function of monotone function can not show the explicit formula, the distribution density curve of continuous randon variable can be gained with a parametric equation.
椭圆的参数方程的几何意义是众所周知的(见例1)。
The geometric meaning for the parametric equation of ellipse is a familiar thing (See example 1).
通过试验和数值研究推导了完全叠接管节点试件在轴向力作用下应力集中因子的参数方程。
This paper presents the parametric equations on stress concentration factor(SCF) of completely overlapped tubular joints under axial loading using experimental and numerical analysis.
同时，对具有参数方程形式表示的非圆曲线进行了等间距直线逼近的节点误差分析。
While there is the analysis of node tolerance with parameter equation on approaching along a straight line with equal step.
本文将分别对双曲线、抛物线的参数方程阐述几何意义(见例2、例3)。
This paper describes the geometric meaning for the parametric equation of hyperbola and parabola, respectively (see examples 2 and 3).
本文推导出计算机绘图中的二次B一样条曲线的参数方程，介绍二次B一样条曲线的性质，并给出在逼近曲线时的特殊处理方法。
This paper infers the parametric equation of the quadric B-spline curve, introduces its character, and gives the special method of process when the curve is approximated.
各向异性的伤演规律可由能量平衡及当量单参数方程所确定。
The anisotropic damage evolution law is obtained by the virtue of energy equilibrium and an equivalent singe variable equation.
首先说明了参数方程的基本定义，了解什么是参数方程。
Firstly illustrates the basic definition parameter equation, understand what is the parameter equation.
本文给出了抛物环面天线的参数方程和辐射场公式。
In this paper, the parametric equation and radiation field formulas for a parabolic torus reflector antenna are given.
通过对此数学模型的求解，导出了相交双管相贯线上各点局部二面角的计算公式，给出了相交双管装配接触线的参数方程，并解释了其数学本质。
By the solution of the model, a calculating formula of the local dihedral angel of intersecting line and a parametric equation of contacting line are given.
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