使用Python与Mayavi可视化复函数z1^n+z2^n=1无显示问题求助

Hey there, I've looked into your code and found a couple of key issues that are causing Mayavi to show nothing. Let's break down what's wrong and fix it step by step:

What's Going Wrong? #

1. 1D Grid Can't Generate a Surface: Your line theta = np.mgrid[0:pi/2] creates a 1D array, but mlab.mesh() requires 2D arrays to render a surface. Without a 2D grid, there's no surface for Mayavi to draw.
2. Unnecessary Complexity in Complex Math: The expression np.cos(theta*xi*1j) is mathematically equivalent to np.cosh(theta*xi) (since $\cos(ix) = \cosh(x)$). Using the hyperbolic cosine directly avoids confusion and potential issues with complex exponentiation.
3. Unused Variables: You defined z14 and z24 but didn't plot them—this isn't the main issue, but it's a waste of code.

Fixed Code #

import numpy as np
from mayavi import mlab

pi = np.pi
n = 2
xi = 3
# Create a 2D grid with 100 samples along each axis for a smooth surface
theta, phi = np.mgrid[0:pi/2:100j, 0:pi/2:100j]
k1 = np.array([2, 3])
k2 = np.array([0, 1])

# Precompute the complex phases to clean up the code
phase_k1_0 = np.exp((2 * k1[0] * pi / n) * 1j)
phase_k1_1 = np.exp((2 * k1[1] * pi / n) * 1j)
phase_k2_0 = np.exp((2 * k2[0] * pi / n) * 1j)
phase_k2_1 = np.exp((2 * k2[1] * pi / n) * 1j)

# Simplify using hyperbolic functions instead of complex cosine/sine
cosh_term = np.cosh(theta * xi) ** (2 / n)
sinh_term = np.sinh(theta * xi) ** (2 / n)

# Calculate coordinates for each of the four solution sets
# Set 1
z11 = phase_k1_0 * cosh_term
z21 = phase_k2_0 * sinh_term
x11, x21, x31 = z11.real, z11.imag, z21.real
# Set 2
z12 = phase_k1_0 * cosh_term
z22 = phase_k2_1 * sinh_term
x12, x22, x32 = z12.real, z12.imag, z22.real
# Set 3
z13 = phase_k1_1 * cosh_term
z23 = phase_k2_0 * sinh_term
x13, x23, x33 = z13.real, z13.imag, z23.real
# Set 4
z14 = phase_k1_1 * cosh_term
z24 = phase_k2_1 * sinh_term
x14, x24, x34 = z14.real, z14.imag, z24.real

# Plot each surface with a unique color for clarity
mlab.mesh(x11, x21, x31, color=(1, 0, 0))
mlab.mesh(x12, x22, x32, color=(0, 1, 0))
mlab.mesh(x13, x23, x33, color=(0, 0, 1))
mlab.mesh(x14, x24, x34, color=(1, 1, 0))

# Add axis labels to make the plot easier to interpret
mlab.xlabel('Re(z₁)')
mlab.ylabel('Im(z₁)')
mlab.zlabel('Re(z₂)')

mlab.show()

Key Fixes Explained #

• 2D Grid: By using np.mgrid[0:pi/2:100j, 0:pi/2:100j], we create a 2D grid of points. The 100j tells NumPy to generate 100 evenly spaced points along each axis, which gives a smooth surface.
• Simplified Hyperbolic Functions: Replacing complex cosine with np.cosh() makes the code easier to read and avoids any unexpected behavior from complex number operations.
• Color-Coded Surfaces: Assigning different colors to each surface helps you distinguish between the four different solution sets defined by your k1 and k2 values.
• Axis Labels: These make it clear which axis corresponds to the real/imaginary parts of your complex variables.

When you run this fixed code, you should see the four surfaces for $z_1^2 + z_2^2 = 1$ render correctly in Mayavi.

内容的提问来源于stack exchange，提问作者Silvio