Klein Bottle

The Klein Bottle, Spherical to XYZ example surface.

import numpy as np
import s3dlib.surface as s3d

#.. Klein Bottle obj export

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

def klein(rtp) :
    r,t,p = rtp
    u = p
    v = t
    cU, sU = np.cos(u), np.sin(u)
    cV, sV = np.cos(v), np.sin(v)
    x = -(2/15)*cU* \
        (  ( 3 )*cV + \
           ( -30 + 90*np.power(cU,4) - 60*np.power(cU,6) + 5*cU*cV )*sU \
        )
    y = -(1/15)*sU* \
        (  ( 3 - 3*np.power(cU,2) -48*np.power(cU,4) +48*np.power(cU,6) )*cV + \
           (-60 + ( 5*cU - 5*np.power(cU,3) - 80*np.power(cU,5) + 80*np.power(cU,7) )*cV  )*sU \
        )
    z = (2/15)*( 3 + 5*cU*sU )*sV
    return x,y,z

# 2. Setup and map surface .........................................
rez=6

surface = s3d.SphericalSurface(rez,basetype='octa_c')
surface.map_geom_from_op( klein, returnxyz=True )
surface.transform(s3d.eulerRot(0,-90),translate=[0,0,2])

s3d.save_surfgeom_to_obj('obj_files/klein_bottle.obj',surface)