Matplotlib绘制y上限可变（y=0.1cos(x)）的等高线图方法求助

核心逻辑是对超出目标区域的数值进行掩码屏蔽，Matplotlib在绘制等高线时会自动跳过值为NaN的区域，天然支持不规则边界的绘制。

完整可运行代码 #

import numpy as np
from numpy import sqrt, cos, sin, sinh, cosh, exp
import matplotlib
from matplotlib import pyplot as plt

# 1. 生成网格
delta = 0.025
X = np.arange(0, 6, delta)
Y = np.arange(-1, 0.2, delta)
x, y = np.meshgrid(X, Y)

# 2. 计算复函数值
I = 1j  # 虚数单位
Psi = (0.1743261076e-2-0.1743261076e-2*I)*sin(x)*((1.318639968*I)*cosh((0.7071067812e-1+0.7071067812e-1*I)*(10.+cos(x)))*sin(0.7071067812e-1*cos(x))*sinh(0.7071067812e-1*cos(x))*y-(.6752336213*I)*cosh((0.7071067812e-1+0.7071067812e-1*I)*(10.+cos(x)))*cosh(0.7071067812e-1*cos(x))*sin(0.7071067812e-1*cos(x))*y-1.*cosh((0.7071067812e-1+0.7071067812e-1*I)*(10.+cos(x)))*exp((0.7071067812e-1*I)*cos(x)+1.414213562+.7071067812*I+0.7071067812e-1*cos(x))-(3.887320974*I)*sinh(.7071067812*y+(.7071067812*I)*y-0.7071067812e-1*cos(x)-(0.7071067812e-1*I)*cos(x))*sin(0.7071067812e-1*cos(x))*sinh(0.7071067812e-1*cos(x))-(3.321756325*I)*sinh(.7071067812*y+(.7071067812*I)*y-0.7071067812e-1*cos(x)-(0.7071067812e-1*I)*cos(x))*cos(0.7071067812e-1*cos(x))*sinh(0.7071067812e-1*cos(x))+cosh((0.7071067812e-1+0.7071067812e-1*I)*(10.+cos(x)))*exp(-(0.7071067812e-1*I)*cos(x)-.7071067812*I-0.7071067812e-1*cos(x))+(4.022439224*I)*cosh((0.7071067812e-1+0.7071067812e-1*I)*(10.+cos(x)))*cos(0.7071067812e-1*cos(x))*sinh(0.7071067812e-1*cos(x))*y+(4.178862074*I)*cosh((0.7071067812e-1+0.7071067812e-1*I)*(10.+cos(x)))*cosh(0.7071067812e-1*cos(x))*cos(0.7071067812e-1*cos(x))*y-(2.366831780*I)*sinh(.7071067812*y+(.7071067812*I)*y-0.7071067812e-1*cos(x)-(0.7071067812e-1*I)*cos(x))*cosh(0.7071067812e-1*cos(x))*sin(0.7071067812e-1*cos(x))-(2.022482447*I)*sinh(.7071067812*y+(.7071067812*I)*y-0.7071067812e-1*cos(x)-(0.7071067812e-1*I)*cos(x))*cosh(0.7071067812e-1*cos(x))*cos(0.7071067812e-1*cos(x))-(.6752336213*I)*cosh((0.7071067812e-1+0.7071067812e-1*I)*(10.+cos(x)))*cosh(0.7071067812e-1*cos(x))*sin(0.7071067812e-1*cos(x))+(4.022439224*I)*cosh((0.7071067812e-1+0.7071067812e-1*I)*(10.+cos(x)))*cos(0.7071067812e-1*cos(x))*sinh(0.7071067812e-1*cos(x))+(4.178862074*I)*cosh((0.7071067812e-1+0.7071067812e-1*I)*(10.+cos(x)))*cosh(0.7071067812e-1*cos(x))*cos(0.7071067812e-1*cos(x))+(1.318639968*I)*cosh((0.7071067812e-1+0.7071067812e-1*I)*(10.+cos(x)))*sin(0.7071067812e-1*cos(x))*sinh(0.7071067812e-1*cos(x))-4.022439224*cosh((0.7071067812e-1+0.7071067812e-1*I)*(10.+cos(x)))*cosh(0.7071067812e-1*cos(x))*sin(0.7071067812e-1*cos(x))*y+1.318639968*cosh((0.7071067812e-1+0.7071067812e-1*I)*(10.+cos(x)))*cosh(0.7071067812e-1*cos(x))*cos(0.7071067812e-1*cos(x))*y-4.178862074*cosh((0.7071067812e-1+0.7071067812e-1*I)*(10.+cos(x)))*sin(0.7071067812e-1*cos(x))*sinh(0.7071067812e-1*cos(x))*y-.6752336213*cosh((0.7071067812e-1+0.7071067812e-1*I)*(10.+cos(x)))*cos(0.7071067812e-1*cos(x))*sinh(0.7071067812e-1*cos(x))*y-4.178862074*cosh((0.7071067812e-1+0.7071067812e-1*I)*(10.+cos(x)))*sin(0.7071067812e-1*cos(x))*sinh(0.7071067812e-1*cos(x))-.6752336213*cosh((0.7071067812e-1+0.7071067812e-1*I)*(10.+cos(x)))*cos(0.7071067812e-1*cos(x))*sinh(0.7071067812e-1*cos(x))+1.318639968*cosh((0.7071067812e-1+0.7071067812e-1*I)*(10.+cos(x)))*cosh(0.7071067812e-1*cos(x))*cos(0.7071067812e-1*cos(x))-4.022439224*cosh((0.7071067812e-1+0.7071067812e-1*I)*(10.+cos(x)))*cosh(0.7071067812e-1*cos(x))*sin(0.7071067812e-1*cos(x))+2.022482447*sinh(.7071067812*y+(.7071067812*I)*y-0.7071067812e-1*cos(x)-(0.7071067812e-1*I)*cos(x))*sin(0.7071067812e-1*cos(x))*sinh(0.7071067812e-1*cos(x))-3.887320974*sinh(.7071067812*y+(.7071067812*I)*y-0.7071067812e-1*cos(x)-(0.7071067812e-1*I)*cos(x))*cosh(0.7071067812e-1*cos(x))*cos(0.7071067812e-1*cos(x))-2.366831780*sinh(.7071067812*y+(.7071067812*I)*y-0.7071067812e-1*cos(x)-(0.7071067812e-1*I)*cos(x))*cos(0.7071067812e-1*cos(x))*sinh(0.7071067812e-1*cos(x))+3.321756325*sinh(.7071067812*y+(.7071067812*I)*y-0.7071067812e-1*cos(x)-(0.7071067812e-1*I)*cos(x))*cosh(0.7071067812e-1*cos(x))*sin(0.7071067812e-1*cos(x)))/(cosh((0.7071067812e-1+0.7071067812e-1*I)*(10.+cos(x)))*(.9583581328*cosh(0.7071067812e-1*cos(x))*cos(0.7071067812e-1*cos(x))-.8189270221*cosh(0.7071067812e-1*cos(x))*sin(0.7071067812e-1*cos(x))+(.8189270221*I)*sinh(0.7071067812e-1*cos(x))*cos(0.7071067812e-1*cos(x))+(.9583581328*I)*sinh(0.7071067812e-1*cos(x))*sin(0.7071067812e-1*cos(x))+.5835053242*sinh(0.7071067812e-1*cos(x))*cos(0.7071067812e-1*cos(x))-.4986113867*sinh(0.7071067812e-1*cos(x))*sin(0.7071067812e-1*cos(x))+(.4986113867*I)*cosh(0.7071067812e-1*cos(x))*cos(0.7071067812e-1*cos(x))+(.5835053242*I)*cosh(0.7071067812e-1*cos(x))*sin(0.7071067812e-1*cos(x))))
AA = Psi.real

# 3. 掩码超出y上限的区域：y > 0.1*cos(x)的位置设为NaN
y_upper = 0.1 * np.cos(x)
AA[y > y_upper] = np.nan

# 4. 绘制等高线
fig, ax = plt.subplots() 
plt.xlabel(r'x')
plt.ylabel(r'y')
CS = ax.contour(x, y, AA)
ax.clabel(CS, inline=True, fontsize=10)
# 可选：绘制y上限边界线验证效果
ax.plot(X, 0.1*np.cos(X), 'r--', label='y=0.1cos(x) 上限')
ax.legend()
plt.show()

关键逻辑说明 #

• 原有函数计算逻辑完全不需要修改，只需要在获取实部数值后增加一行掩码操作即可
• Matplotlib的contour函数会自动忽略值为NaN的网格点，等高线只会在y ≤ 0.1cos(x)的区域内生成，边界处会自动截断
• 可以通过调整网格步长delta控制绘图精度，步长越小边界越平滑，计算耗时也会相应增加

内容的提问来源于stack exchange，提问作者John