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from manimlib import *
import numpy as np
from scipy.special import sph_harm
# configure style
config.background_color = '#202020'
# config.tex_template.add_to_preamble(
# r"\usepackage[p,osf]{scholax}"
# r"\usepackage{amsmath}"
# r"\usepackage[scaled=1.075,ncf,vvarbb]{newtxmath}"
# )
class FourierOnS1(ThreeDScene):
@staticmethod
def harmonic_cos(m, n, theta, phi):
# get only the cos() part
r = np.real(sph_harm(m, n, theta, phi)) * 5 # Y_n^m
# coordinates transformation
x = r * np.cos(theta) * np.sin(phi)
y = r * np.sin(phi) * np.sin(theta)
z = r * np.cos(phi)
return [x, y, z]
@staticmethod
def harmonic_surf(m, n):
surf = Surface(uv_func=lambda u, v: FourierOnS1.harmonic_cos(m, n, u, v),
u_range=[0, 2 * PI], v_range=[-PI, PI],
color=GREY, resolution=(101, 101), shadow=0.1)
surf.mesh = SurfaceMesh(surf)
surf.mesh.set_stroke(BLACK, 1, opacity=0.7)
return surf
def construct(self):
axes = ThreeDAxes(x_range=[-2, 2], y_range=[-2, 2], z_range=[-3, 3])
self.add(axes)
frame = self.camera.frame
frame.set_euler_angles(theta=-30*DEGREES, phi=70*DEGREES)
frame.add_updater(lambda m, dt: m.increment_theta(-0.1 * dt))
last_surf = None
last_label = None
for n in range(0, 5):
for m in range(0, n):
surf = FourierOnS1.harmonic_surf(m, n)
label = Tex(r"Y_{%d}^{%d}(\theta, \phi)" % (n, m))
if last_surf is None:
self.play(ShowCreation(surf))
self.play(ShowCreation(surf.mesh, lag_ratio=0.01))
else:
self.play(FadeOut(last_surf), FadeOut(last_surf.mesh))
self.play(ShowCreation(surf))
self.play(ShowCreation(surf.mesh, lag_ratio=0.01))
if last_label is not None:
self.remove(last_label)
label.to_corner(UL)
last_surf = surf
last_label = label
self.wait(3)
self.wait(5)
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