1 files changed, 71 insertions, 0 deletions
diff --git a/manimgl/harmonics.py b/manimgl/harmonics.py
new file mode 100644
index 0000000..0a15566
--- /dev/null
+++ b/manimgl/harmonics.py
@@ -0,0 +1,71 @@
+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)