1 files changed, 67 insertions, 0 deletions
diff --git a/manim/harmonics.py b/manim/harmonics.py
new file mode 100644
index 0000000..a908e25
--- /dev/null
+++ b/manim/harmonics.py
@@ -0,0 +1,67 @@
+from manim import *
+from manim.mobject.opengl.opengl_surface import OpenGLSurface
+from manim.mobject.opengl.opengl_three_dimensions import OpenGLSurfaceMesh
+
+
+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(lambda u, v: FourierOnS1.harmonic_cos(m, n, u, v),
+                       u_range=[0, 2 * PI], v_range=[-PI, PI], resolution=[50, 50],
+                       fill_opacity=.8, checkerboard_colors=[BLUE_D, BLUE_E])
+
+        return surf
+
+    def construct(self):
+        axes = ThreeDAxes(x_range=[-1, 1], y_range=[-1, 1])
+        self.add(axes)
+
+        self.set_camera_orientation(theta=30 * DEGREES, phi=75 * DEGREES)
+        self.begin_ambient_camera_rotation(rate=.1)
+
+        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 = MathTex(r"Y_{%d}^{%d}(\theta, \phi)" % (n, m))
+
+                if last_surf is not None:
+                    self.play(ReplacementTransform(last_surf, surf))
+
+                if last_label is not None:
+                    self.remove(last_label)
+
+                self.play(Create(surf))
+                self.add_fixed_in_frame_mobjects(label)
+                label.to_corner(UL)
+
+                last_surf = surf 
+                last_label = label
+
+                self.wait()
+
+        self.wait(5)