How to create a line on a surface with "matplotlib" in python

Question

I would like to draw two lines on a surface (the pink surface) to represent the two cutting lines of this pink surface and two 2d planes (x = y and x = -y), like the blue lines in the figure below. Does anyone know how to do it?

The code to generate the pink surface is as below:

import numpy as NP
import matplotlib.pyplot as PLT

def f(x1, x2):
    return 0.5 * x1 + 0.6 * x2 + 0.2 * x1 * x1 + 0.1 * x1 * x2 + 0.3 * x2 * x2 + 4

x = NP.linspace(-3, 3, 100)
y = NP.linspace(-3, 3, 100)
xx, yy = NP.meshgrid(x,y)
z = f(xx, yy)

# set up the figure
fig = PLT.figure()
ax = fig.gca(projection='3d')
ax.set_xlim(-3, 3)
ax.set_ylim(3, -3)
ax.set_xlabel("x")
ax.set_ylabel("y")
ax.set_zlabel("z")

# plot the figure
ax.plot_surface(xx, yy, z, cmap="spring", alpha = 0.7)

# add the x=y line to the ground plane
ax.plot([-3, 3], [-3, 3], color = 'grey', linewidth = 1, linestyle='dashed')

# add the x=-y line to the ground plane
ax.plot([3, -3], [-3, 3], color = 'grey', linewidth = 1, linestyle='dashed')

PLT.show()

JohanC · Accepted Answer · 2020-03-03 16:40:16Z

3

You can just use plot(x, -x, f(x, -x)) and plot(x, x, f(x, x)) to draw the curves. Note that matplotlib doesn't perfectly hide elements that are partially obscured by other elements.

from mpl_toolkits.mplot3d import Axes3D
from matplotlib import pyplot as plt
import numpy as np

def f(x1, x2):
    return 0.5 * x1 + 0.6 * x2 + 0.2 * x1 * x1 + 0.1 * x1 * x2 + 0.3 * x2 * x2 + 4

x = np.linspace(-3, 3, 100)
y = np.linspace(-3, 3, 100)
xx, yy = np.meshgrid(x,y)
z = f(xx, yy)

# set up the figure
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.set_xlim(-3, 3)
ax.set_ylim(3, -3)
ax.set_xlabel("x")
ax.set_ylabel("y")
ax.set_zlabel("z")

# plot the figure
ax.plot_surface(xx, yy, z, cmap="spring", alpha = 0.7)

# add the x=y line to the ground plane
ax.plot([-3, 3], [-3, 3], color='grey', linewidth=1, linestyle='dashed')

# add the x=-y line to the ground plane
ax.plot([3, -3], [-3, 3], color='grey', linewidth=1, linestyle='dashed')

ax.plot(x, x, f(x, x), color='dodgerblue')
ax.plot(x, -x, f(x, -x), color='dodgerblue')

plt.show()

answered Mar 3, 2020 at 16:40

JohanC

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4 Comments

wh41e Over a year ago

man, your solution is great! Thanks much. I have another question, could you help me again? stackoverflow.com/questions/60517183/…

JohanC Over a year ago

It seems the other question is already answered satisfactory. Optionally, you could label the x-axis as x,y and x,-y respectively, and the y-axis as z, to be consistent with the 3D plot.

wh41e Over a year ago

upvoted, do you know how to label as (X,Y) or (X,-Y)?

JohanC Over a year ago

plt.xlabel('(X,-Y)'); plt.ylabel('Z') ?

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