水平线与函数的交点 [英] points of intersection of horizontal line with a function

问题描述

我有这段代码会生成以下图像(图像)，我将如何继续检测该线与函数的交点?

i have this code that generate the following (image), how would i proceed to detect the intersections of the line with the function ?`

import numpy as np
import matplotlib.pyplot as plt

y = 0.4*np.ones(100)                
x = np.arange(0, 100)           

t = np.linspace(0,100,100)
Fs = 6000
f = 200
func = np.sin(2 * np.pi * f * t / Fs)

idx = np.where(func == y) # how i think i should do to detect intersections

print(idx)

plt.plot(x, y)        # the horizontal line
plt.plot(t,func)      # the function
plt.show()

推荐答案

您可以使用以下表达式获取最接近交点的数组t的索引.

You can use the following expression to get the indices of the array t that is closest to the intersection points.

idx = np.argwhere(np.diff(np.sign(y - func))).flatten()

此表达式选择列表中符号变化的索引.但是，这仅是真实交点的近似值.减小t的步长以提高精度.

This expression selects indices where there is a change of sign in the list. However, this is only an approximation of the real intersection points. Decrease the step-size of t to increase precision.

由于方程式相对简单，另一种方法是手工求解并实现封闭形式的绘图公式.

Since the equations are relatively simple, another way would be to solve it by hand and implement the closed-form formula for plotting.

您具有方程式y = 0.4和y = sin(2*pi*t*f/Fs).交叉点的值在t处，这样0.4 = sin(2*pi*t*f/Fs).解决t有两个答案:

You have the equations y = 0.4 and y = sin(2*pi*t*f/Fs). Intersection points are at values of t such that 0.4 = sin(2*pi*t*f/Fs). Solving for t gives two answers:

t = (arcsin(0.4) + 2*pi*k) / (2*pi*f/Fs)
t = (pi - arcsin(0.4) + 2*pi*k) / (2*pi*f/Fs)

其中k是任何整数.简而言之，遍历给定范围内的所有所需整数，并使用上述两个方程式计算坐标t.您将获得一组可以在图形上绘制的点(t,0.4).

where k is any integer. In short, loop through all desired integers in a given range and compute the coordinates t using the two equations above. You will get a set of points (t,0.4) that you can plot on your graph.

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