def klein_bottle(draw=True,
show=True,
figure8=False,
endpoint=True,
uv=False,
wireframe=False,
texture=None):
import ipyvolume.pylab as p3
# http://paulbourke.net/geometry/klein/
u = np.linspace(0, 2 * pi, num=40, endpoint=endpoint)
v = np.linspace(0, 2 * pi, num=40, endpoint=endpoint)
u, v = np.meshgrid(u, v)
if figure8:
#u -= np.pi
#v -= np.pi
a = 2
s = 5
x = s * (a + cos(u / 2) * sin(v) -
sin(u / 2) * sin(2 * v) / 2) * cos(u)
y = s * (a + cos(u / 2) * sin(v) -
sin(u / 2) * sin(2 * v) / 2) * sin(u)
z = s * (sin(u / 2) * sin(v) + cos(u / 2) * sin(2 * v) / 2)
else:
r = 4 * (1 - cos(u) / 2)
x = 6 * cos(u) * (1 + sin(u)) \
+ r * cos(u) * cos(v) * (u < pi) \
+ r * cos(v + pi) * (u >= pi)
y = 16 * sin(u) + r * sin(u) * cos(v) * (u < pi)
z = r * sin(v)
if draw:
if texture:
uv = True
if uv:
mesh = p3.plot_mesh(x,
y,
np.array([z]),
wrapx=not endpoint,
wrapy=not endpoint,
u=u / (2 * np.pi),
v=v / (2 * np.pi),
wireframe=wireframe,
texture=texture)
else:
mesh = p3.plot_mesh(x,
y,
np.array([z]),
wrapx=not endpoint,
wrapy=not endpoint,
wireframe=wireframe,
texture=texture)
if show:
p3.show()
return mesh
else:
return x, y, z, u, v
def klein_bottle(draw=True, show=True, figure8=False, endpoint=True, uv=True, wireframe=False, texture=None, both=False, interval=1000):
"""Show one or two Klein bottles"""
import ipyvolume.pylab as p3
# http://paulbourke.net/geometry/klein/
u = np.linspace(0, 2 * pi, num=40, endpoint=endpoint)
v = np.linspace(0, 2 * pi, num=40, endpoint=endpoint)
u, v = np.meshgrid(u, v)
if both:
x1, y1, z1, u1, v1 = klein_bottle(endpoint=endpoint, draw=False, show=False)
x2, y2, z2, u2, v2 = klein_bottle(endpoint=endpoint, draw=False, show=False, figure8=True)
x = [x1, x2]
y = [y1, y2]
z = [z1, z2]
else:
if figure8:
#u -= np.pi
#v -= np.pi
a = 2
s = 5
x = s * (a + cos(u / 2) * sin(v) - sin(u / 2) * sin(2 * v)/2) * cos(u)
y = s * (a + cos(u / 2) * sin(v) - sin(u / 2) * sin(2 * v)/2) * sin(u)
z = s * (sin(u / 2) * sin(v) + cos(u / 2) * sin(2 * v)/2)
else:
r = 4 * (1 - cos(u) / 2)
x = 6 * cos(u) * (1 + sin(u)) \
+ r * cos(u) * cos(v) * (u < pi) \
+ r * cos(v + pi) * (u >= pi)
y = 16 * sin(u) + r * sin(u) * cos(v) * (u < pi)
z = r * sin(v)
if draw:
if texture:
uv = True
if uv:
mesh = p3.plot_mesh(x, y, z, wrapx=not endpoint, wrapy=not endpoint, u=u/(2*np.pi), v=v/(2*np.pi), wireframe=wireframe, texture=texture)
else:
mesh = p3.plot_mesh(x, y, z, wrapx=not endpoint, wrapy=not endpoint, wireframe=wireframe, texture=texture)
if show:
if both:
p3.animation_control(mesh, interval=interval)
p3.squarelim()
p3.show()
return mesh
else:
return x, y, z, u, v