That's the equation of a tangent plane. 这就是切平面的方程。
Now, if I have two lines tangent to the surface, well, then together they determine for me the tangent plane to the surface. Let's try to see how that works. 现在,假设曲面上有两条相交切线,那么这两条切线可以确定一个切平面,我们来看看这个平面是怎么搞出来的。
That is how we get the tangent plane. 这样我们就得到了切平面。
And, in particular, this approximation is called the tangent plane approximation because it tells us, in fact, it amounts to identifying the graph of the function with its tangent plane. 这个近似办法称作,切平面近似,因为它告诉我们,可以通过切平面,来反映函数的图像。
Well, that means the gradient is actually perpendicular to the tangent plane or to the surface at this point. 那意味着,梯度向量在这点上,垂直于切平面或者是等值面。
OK, and that's going to be the normal vector to the surface or to the tangent plane. 这就是切平面的,或者说这个曲面的法向量。
Then, if I choose any vector in that tangent plane. 那么如果我选择了任何位于切平面的向量。
Mean Value Coordinates on Tangent Plane for Laplacian Mesh Deformation 基于切平面中值坐标的Laplacian网格变形算法
And so, in particular, if we set this equal to zero instead of approximately zero, it means we'll actually be moving on the tangent plane to the level set. 而且,特别地,如果我们令此函数为零,而不是近似为零,它意味着我们在水平集的切平面上移动。
Say you have a minimum, well, the tangent plane at this point, at the bottom of the graph is going to be horizontal. 如果你说这是个极小值,那么这点的切平面应该是水平的。
And, at this point, I have the tangent plane to the level surface OK, so this is tangent plane to the level. 在这点上,我们有一个切于等值面的切面,这就是等值面的切平面。
Being perpendicular to the surface means that you are perpendicular to its tangent plane. 垂直于曲面也意味着垂直于它的切平面,垂直于曲面也意味着垂直于它的切平面。
Research on stereo vision measuring method for tire tangent plane 轮胎切平面的立体视觉测量方法研究
It is really the tangent plane. 它确实就是切平面。
If we were moving on the tangent plane, this would be an actual equality. 如果我们在切平面上移动,这将会是一个真正的等式。
Study of Solving Normal Line and Tangent Plane of Archimedes Helicoid Based on MATLAB 基于MATLAB的阿基米德螺旋面法线和切平面的求解研究
And, here's a tangent plane at the given point. 在这个给定的点有一个切平面。
OK, so now if you have a surface given by an evil equation, and a point on the surface, well, you know how to find the tangent plane to the surface at that point OK, any questions? 如果有一个由有点恶心的方程确定的曲面,以及在曲面上的一个点,你应该知道,如何找到这点处的切平面了,有问题么?
Let's think about the tangent plane with regard to a function f. 我们来考虑,关于函数f的一个切平面。
And now what this approximation formula here says is that, in fact, the graph of a function is close to the tangent plane. 这里这个近似式的意思是,函数图象和切平面靠得很近。
That's one way to define the tangent plane. 这是定义切平面的方法。
Well, one way to think about it is in terms of tangent plane approximation. 我们可以从用切平面逼近的想法来入手。
We are replacing the graph by its tangent plane. 我们用函数的切平面来替代它的图像。
In fact, when we turn this into an equality, that would mean that we replace f by the tangent plane. 其实,看这个等式,就是用切平面上的值来近似f的值。
This paper derives navigation error equations of tangent plane inertial coordinate. 本文推导了切平面惯性系统的导航误差方程;
A SPECIAL TANGENT PLANE OF RING SURFACES Family of Osculating Planes, Rectifying Planes, Normal Planes of Space Curves 环面的一种特殊切面空间曲线的密切面族、从切面族和法面族
Tangent Plane Approximation of Homogeneous Constraints and Its Application to Optimal Design 齐次约束的切平面近似及在优化设计中的应用
This paper analyses the tangent equation of space curve and the derivation process of the curved tangent plane equation in the higher-mathematics teaching-materials, and shows another method to extract the tangent equation of space curve. 分析高等数学教材中空间曲线的切线方程和曲面的切平面方程的推导过程,给出求空间曲线的切线方程的另一种方法。
By the aid of local-tangent-planes-based method, the tangent plane is estimated, the normal vector is adjusted and the directional distance function is calculated. 利用基于局部切平面簇的方法对数据点云进行切平面的估算、法向量的调整和计算有向距离函数,提高了重建速度,改善了重建效果。
All satellite image are tangent plane projection obtained along the flight direction of satellite. 卫星图像都是沿卫星飞行方向而获取的切平面投影图像。