Polar Coordinates to XYZ

Documentation on Dini’s surface can be found in Wikipedia where this function definition is located.

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

#.. Polar Coordinates to XYZ

# 1. Define function to examine .....................................

def dinisurf(rtz) :
    r,t,z = rtz
    a, b = 1, 0.2
    T = 2*t
    x = a*np.cos(T)*np.sin(r)
    y = a*np.sin(T)*np.sin(r)
    z = a*(np.cos(r) + np.log(np.tan(r/2))) + b*T
    return x,y,z

# 2. Setup and map surfaces .........................................
rez = 4

surface = s3d.PolarSurface(rez, basetype='hex_c', minrad=0.01)
surface.map_cmap_from_op( lambda rtz: rtz[0] , cmap='inferno' )
surface.map_geom_from_op( dinisurf, returnxyz=True )

# 3. Construct figures, add surface, plot ...........................

fig = plt.figure(figsize=plt.figaspect(1))
fig.text(0.975,0.975, "Dini's Surface", ha='right', va='top', fontsize='larger', multialignment='right')
ax = plt.axes(projection='3d', aspect='equal')
ax.set(xlim=(-.75,.75), ylim=(-.75,.75), zlim=(-3,1) )
ax.set_axis_off()
ax.view_init(elev=20)
ax.add_collection3d(surface)

fig.tight_layout()
plt.show()