Plotting concave shape (lens focus) using mplot3d

Question

I am currently trying to visualize the focal shape of a lens using matplotlib, specifically the mplot3d toolbox. I obtained the data from fitting ellipses to a set of microscope images at different focal lengths as major major and minor minor radius, as well as the rotation angle ang of said ellipses. From this, I'm generating x , y and z arrays containing the coordinates of the ellipses like this.

i = 100
omega = np.linspace(0, 2 * np.pi, i, endpoint=True)

x = [major * np.cos(omega) * np.cos(np.deg2rad(ang + 90)) - minor * np.sin(omega) * np.sin(np.deg2rad(ang + 90)) for major, minor, ang in zip(maj_avg, min_avg, ang_avg)]
y = [major * np.cos(omega) * np.sin(np.deg2rad(ang + 90)) + minor * np.sin(omega) * np.cos(np.deg2rad(ang + 90)) for major, minor, ang in zip(maj_avg, min_avg, ang_avg)]
z = [np.full(i, zi) for zi in zs]

If I now plot the individual ellipses in 3D space, everything works as intended.

fig = plt.figure(figsize=(16, 12))
ax = fig.add_subplot(111, projection='3d')
for x_arr, y_arr, z_arr in zip(x, y, z):
    ax.plot(x_arr, y_arr, z_arr)

plt.show()

What I am trying to do is generate a surface plot from this dataset which shows the focal shape of the lens. Up to now, I tried plot_surface together with meshgrid / griddata like this:

xi = np.arange(-300, 300, 0.1)
yi = np.arange(-300, 300, 0.1)

xgrid, ygrid = np.meshgrid(xi, yi)
zgrid = griddata(np.ravel(x), np.ravel(y), np.ravel(z), xi, yi, interp='linear')

fig = plt.figure(figsize=(16, 12))
ax = fig.add_subplot(111, projection='3d')

surf = ax.plot_surface(xgrid, ygrid, zgrid)
plt.show()

And also plot_trisurf is giving similarly unsatisfactory results:

triang = mtri.Triangulation(np.ravel(x), np.ravel(y))

fig = plt.figure(figsize=(16, 12))
ax = fig.add_subplot(111, projection='3d')
ax.plot_trisurf(triang, np.ravel(z), cmap=plt.cm.CMRmap)
plt.show()

Could someone suggest a way to properly show the high-z region of my dataset in the surface plots?

Answer 1

The problem is that you are trying to interpolate a parametric curve on a grid. Since the shape to draw is a non-bijective, non-sujective one, you get a complete mess.

Instead of trying to interpolate the points you may directly plot them.

X = np.array(x)
Y = np.array(y)
Z = np.array(z)
ax.plot_surface(X,Y,Z, cmap="RdYlBu")
plt.show()

Complete example for reproduction:

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

maj_avg = 50*(np.linspace(0,1,20)-0.6)**2+50
min_avg = 60*(np.linspace(0,1,20)-0.7)**2+60
ang_avg = np.linspace(0,90,20)
zs = np.arange(0,40,2)

i = 100
omega = np.linspace(0, 2 * np.pi, i, endpoint=True)

x = [major * np.cos(omega) * np.cos(np.deg2rad(ang + 90)) \
     - minor * np.sin(omega) * np.sin(np.deg2rad(ang + 90)) \
     for major, minor, ang in zip(maj_avg, min_avg, ang_avg)]
y = [major * np.cos(omega) * np.sin(np.deg2rad(ang + 90)) \
     + minor * np.sin(omega) * np.cos(np.deg2rad(ang + 90)) \
     for major, minor, ang in zip(maj_avg, min_avg, ang_avg)]
z = [np.full(i, zi) for zi in zs]


fig = plt.figure(figsize=(16, 12))
ax = fig.add_subplot(111, projection='3d')
#for x_arr, y_arr, z_arr in zip(x, y, z):
#    ax.plot(x_arr, y_arr, z_arr)

X = np.array(x)
Y = np.array(y)
Z = np.array(z)
ax.plot_surface(X,Y,Z, cmap="RdYlBu")

plt.show()