显示两条曲线的交点 [英] Show the intersection of two curves

问题描述

如果我有两个由两个不同方程定义的图：

  x = 0：0.01：30; 
 y1 = x。^ 2 + 2; 
 y2 = x。^ 3; 
  

我将它们绘制为

  plot（x，y1，x，y2）; 
  

如何以编程方式在交叉点周​​围形成一个小环（如下图所示）？

解决方案

您必须找到交点（p _x ，p _y ）：

  idx = find（y1  -  y2  px = x（idx）; 
 py = y1（idx）;请记住，我们正在比较浮点数表示法中的两个数字，所以不是  
> 
 
> > y1 == y2 我们必须设置一个容差。我选择它作为 eps ，但这取决于您决定。
 
 
 
要围绕此画一个圆点，你可以计算它的点，然后绘制它们，但更好的方法是用一个圆圈标记来绘制一个点（归功于乔纳斯对此建议）：
 $ b $ pre $  plot（px，py，'ro'，'MarkerSize'，18） 
  

通过这种方式，圆的尺寸不受坐标轴和纵横比的影响。

示例

  x = 0：0.01：30; 
 y1 = x。^ 2 + 2; 
 y2 = x。^ 3; 
 
％//找到交点
 idx = find（y1  -  y2  px = x（idx）; 
 py = y1（idx）; 
 
 figure 
 plot（x，y1，x，y2，px，py，'ro'，'MarkerSize'，18）
 axis（[0 10 0 10]） 
  

这应该会产生以下图表：

If I have two plots defined by two different equations:

x = 0:0.01:30;
y1 = x .^2 + 2;
y2 = x .^3 ;

and I plot them as

plot(x, y1, x, y2);

How do I get a small ring around the point of intersection programatically (as in the following plot)?

解决方案

You'll have to find the point of intersection (p_x, p_y) manually:

idx = find(y1 - y2 < eps, 1); %// Index of coordinate in array
px = x(idx);
py = y1(idx);

Remember that we're comparing two numbers in floating point representation, so instead of y1 == y2 we must set a tolerance. I've chosen it as eps, but it's up to you to decide.

To draw a circle around this point, you can compute its points and then plot them, but a better approach would be to plot one point with a blown-up circle marker (credit to Jonas for this suggestion):

plot(px, py, 'ro', 'MarkerSize', 18)

This way the dimensions of the circle are not affected by the axes and the aspect ratio of the plot.

Example

x = 0:0.01:30;
y1 = x .^ 2 + 2;
y2 = x .^ 3;

%// Find point of intersection
idx = find(y1 - y2 < eps, 1);
px = x(idx);
py = y1(idx);

figure
plot(x, y1, x, y2, px, py, 'ro', 'MarkerSize', 18)
axis([0 10 0 10])

This should produce the following plot:

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