Python 3D Plots over non-rectangular domain

Question

I have some z=f(x,y) data which i would like to plot. The issue is that (x,y) are not part of a "nice" rectangle, but rather arbitrary parallelograms, as shown in the attached image (this particular one is also a rectangle, but you could think of more general cases). So I am having a hard time figuring out how I can use plot_surface in this case, as this usually will take x and y as 2d arrays, and here my x-and y-values are 1d. Thanks.

Answer 1

Abritrary points can be supplied as 1D arrays to matplotlib.Axes3D.plot_trisurf. It doesn't matter whether they follow a specific structure.

Other methods which would depend on the structure of the data would be

• Interpolate the points on a regular rectangular grid. This can be accomplished using scipy.interpolate.griddata. See example here
• Reshape the input arrays such that they live on a regular and then use plot_surface(). Depending on the order by which the points are supplied, this could be a very easy solution for a grid with "parallelogramic" shape.
  As can be seen from the sphere example, plot_surface() also works in cases of very unequal grid shapes, as long as it's structured in a regular way.

Here are some examples:

For completeness, find here the code that produces the above image:

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

f = lambda x,y: np.sin(x+0.4*y)*0.23+1

fig = plt.figure(figsize=(5,6))
plt.subplots_adjust(left=0.1, top=0.95,wspace=0.01)


ax0 = fig.add_subplot(322, projection="3d")

ma = 6*(np.random.rand(100)-0.5)
mb = 6*(np.random.rand(100)-0.5)
phi = np.pi/4
x = 1.7*ma*np.cos(phi) + 1.7*mb*np.sin(phi)
y = -1.2*ma*np.sin(phi) +1.2* mb*np.cos(phi)
z = f(x,y)
ax0.plot_trisurf(x,y,z)

ax1 = fig.add_subplot(321)
ax0.set_title("random plot_trisurf()")
ax1.set_aspect("equal")
ax1.scatter(x,y, marker="+", alpha=0.4)
for i  in range(len(x)):
    ax1.text(x[i],y[i], i  , ha="center", va="center", fontsize=6)


n = 10
a = np.linspace(-3, 3, n)
ma, mb = np.meshgrid(a,a)
phi = np.pi/4
xm = 1.7*ma*np.cos(phi) + 1.7*mb*np.sin(phi)
ym = -1.2*ma*np.sin(phi) +1.2* mb*np.cos(phi)
shuf = np.c_[xm.flatten(), ym.flatten()]
np.random.shuffle(shuf)
x = shuf[:,0]
y = shuf[:,1]
z = f(x,y)

ax2 = fig.add_subplot(324, projection="3d")
ax2.plot_trisurf(x,y,z)

ax3 = fig.add_subplot(323)
ax2.set_title("unstructured plot_trisurf()")
ax3.set_aspect("equal")
ax3.scatter(x,y, marker="+", alpha=0.4)
for i  in range(len(x)):
    ax3.text(x[i],y[i], i  , ha="center", va="center", fontsize=6)


x = xm.flatten()
y = ym.flatten()
z = f(x,y)

X = x.reshape(10,10)
Y = y.reshape(10,10)
Z = z.reshape(10,10)

ax4 = fig.add_subplot(326, projection="3d")
ax4.plot_surface(X,Y,Z)

ax5 = fig.add_subplot(325)
ax4.set_title("regular plot_surf()")
ax5.set_aspect("equal")
ax5.scatter(x,y, marker="+", alpha=0.4)
for i  in range(len(x)):
    ax5.text(x[i],y[i], i  , ha="center", va="center", fontsize=6)


for axes in [ax0, ax2,ax4]:
    axes.set_xlim([-3.5,3.5])
    axes.set_ylim([-3.5,3.5])
    axes.set_zlim([0.9,2.0])
    axes.axis("off")
plt.savefig(__file__+".png")
plt.show()

Answer 2

If your data is in order, and you know the size of the parallgram, a reshape will probably suffice:

ax.surface(x.reshape(10, 10), y.reshape(10, 10), z.reshape(10, 10))

Will work if the parallelogram has 10 points on each side, and the points are ordered in a zigzag pattern