Unstructured Spherical and Cylindrical Coordinates

Using an unstructured dataset in spherical coordinates is similar to using a planar coordinated system shown in Unstructured coordinates example.

import numpy as np
import matplotlib.pyplot as plt
from matplotlib import colormaps,colors
import s3dlib.surface as s3d

#.. Unstructured spherical coordinates

sixColors = colormaps['Blues'](np.linspace(0, 1, 6))
sixColor_cmap = colors.ListedColormap(sixColors)

# make data:  <--- copy from matplotlib examples
np.random.seed(1)
x = np.random.uniform(-3, 3, 256)
y = np.random.uniform(-3, 3, 256)
z = (1 - x/2 + x**5 + y**3) * np.exp(-x**2 - y**2)

# transform to a spherical dataset, (r,t,p)
t = (x/3 +1)*np.pi
p = (y/3 +1)*np.pi/2
r = z + 2   # <-- shift the radius
rtp = np.array([r,t,p])
xyz = s3d.SphericalSurface.coor_convert(rtp,True)  # <-- for scatter plot

# 2. Setup and map surface .........................................

surface = s3d.SphericalSurface.pntsurf(rtp.T)
edges = surface.edges
surface.map_cmap_from_op( cmap='Blues') # <-- to set contour colors, next
contours = surface.contourLineSet(5) # default: spherical contours
surface.map_cmap_from_op( cmap=sixColor_cmap)

# 3. Construct figure, add surface, and plot ......................

fig = plt.figure(figsize=(10,3))
fig.text(0.5,0.975,str(surface), ha='center', va='top', fontsize='smaller')
minmax,ticks = (-3,3), [-3,0,3]
for i in range(3) :
    ax = fig.add_subplot(131+i, projection='3d')
    ax.set(xticks=ticks,yticks=ticks,zticks=ticks,
            xlim=minmax, ylim=minmax, zlim=minmax ) 
    ax.tick_params(labelcolor='w')
    ax.set_proj_type('ortho')
    ax.xaxis.set_pane_color([1,1,1])
    ax.yaxis.set_pane_color([1,1,1])
    ax.zaxis.set_pane_color([1,1,1])
    ax.view_init(azim=-145)
    if i==0 : ax.scatter(*xyz, s=3, c='darkgrey')
    ax.add_collection3d(contours.fade(0.3,ax=ax) \
    if i==0 else edges.fade(0.1,ax=ax) if i==1 else surface.shade(.4,ax=ax))

fig.tight_layout(pad=0)

plt.show()

Using a cylindrical dataset results in the following.

The only change to the script to produce the 3D figure in cylindrical coordinates is the following:

# transform to a cylindrical dataset, (r,t,z)
t = (x/3 +1)*np.pi
Z = y
r = z + 2   # <-- shift the radius
rtz = np.array([r,t,Z])
xyz = s3d.CylindricalSurface.coor_convert(rtz,True)  # <-- for scatter plot

# 2. Setup and map surface .........................................

surface = s3d.CylindricalSurface.pntsurf(rtz.T)
edges = surface.edges
surface.map_cmap_from_op( cmap='Blues') # <-- to set contour colors, next
contours = surface.contourLineSet(5) # default: cylincrical contours
surface.map_cmap_from_op( cmap=sixColor_cmap)

These visualization are enhanced using a varying hue colormap instead of uniform hue, as shown below. The number of contours was increased from 5 to 10 to further enhance the interpretation.