import numpy as np
from matplotlib import pyplot as plt
import matplotlib.colors as colors
import s3dlib.surface as s3d
import s3dlib.cmap_utilities as cmu
#.. #3 - influenced by M.C.Escher - Knots
# https://mcescher.com/gallery/mathematical/
# 1. Define functions to examine ....................................
wdth = 1
elev, azim = 90, 0
illum = s3d.rtv([1,-1,1],elev,azim)
def Torus(rez,width=wdth ) :
def fold(rtz,width) :
r,t,z = rtz
Z = width*np.sin(z*np.pi)/2
R = 1 + width*np.cos(z*np.pi)/2
return R,t,Z
surface = s3d.CylindricalSurface(rez,basetype='tri_s')
surface.map_geom_from_op( lambda rtz : fold(rtz,width) )
return surface
def Trefoil(rtz) :
r,t,z = rtz
rw = 1-wdth/2
X = rw*(np.sin(t)+2*np.sin(2*t))
Y = rw*(np.cos(t)-2*np.cos(2*t))
R0,T,Z = s3d.PolarSurface.coor_convert([X,Y,z])
R = R0 + r - rw
Z = z - np.sin(3*t)
return R,T,Z
# 2. Setup and map surfaces .........................................
rez = 6
aa = colors.rgb_to_hsv( [ 0.659, 0.502, 0.400 ] )
ab = colors.rgb_to_hsv( [ 0.886, 0.706, 0.576 ] )
cmap = cmu.hsv_cmap_gradient(aa,ab)
surface1 = Torus(rez)
surface1.map_geom_from_op( Trefoil )
surface1.map_cmap_from_normals(cmap,direction=illum)
surface1.set_surface_alpha(.3)
surface2 = Torus(rez,wdth/3)
surface2.map_geom_from_op( Trefoil )
surface2.map_cmap_from_normals(cmap,direction=illum)
ring = surface1+surface2
ring.set_linewidth(0)
ring.shade(.2,direction=illum).hilite(.8,direction=illum)
# 3. Construct figure, add surfaces, and plot ......................
fig = plt.figure(figsize=plt.figaspect(1))
info, infocolor = 'S3Dlib.org', [0.898,0.843,0.800]
text = fig.text(0.11, 0.04, info, color=infocolor, fontsize=45, fontweight='bold' )
ax = plt.axes(projection='3d', aspect='equal')
minmax = (-1.8,1.8)
ax.set(xlim=minmax, ylim=minmax, zlim=minmax )
ax.set_axis_off()
ax.set_proj_type('ortho')
ax.set_facecolor( [ 0.933, 0.902, 0.859 ] )
ax.view_init(elev,azim)
ax.add_collection3d(ring)
fig.tight_layout(pad=0)
plt.show()
