From 8c5929532abe52fef7e8b29d7b5ded3e344b71a2 Mon Sep 17 00:00:00 2001
From: Grant Sanderson <grantsanderson7@gmail.com>
Date: Sun, 20 Dec 2015 16:43:22 -0800
Subject: [PATCH] Turned VibratingString animation into more general Vibrate

---
 animation/playground.py           | 62 +++++++++++++++++--------------
 old_projects/music_and_measure.py | 16 ++++----
 2 files changed, 43 insertions(+), 35 deletions(-)

diff --git a/animation/playground.py b/animation/playground.py
index e3d24e4c..34fa492e 100644
--- a/animation/playground.py
+++ b/animation/playground.py
@@ -1,42 +1,50 @@
 import numpy as np
+import operator as op
 
 from animation import Animation
 from transform import Transform
-from mobject import Mobject1D
+from mobject import Mobject1D, Mobject
+from topics.geometry import Line
 
 from helpers import *
 
-class VibratingString(Animation):
+class Vibrate(Animation):
     DEFAULT_CONFIG = {
-        "num_periods" : 1,
-        "overtones"   : 4,
-        "amplitude"   : 0.5,
-        "radius"      : SPACE_WIDTH/2,
-        "center"      : ORIGIN,
-        "color"       : "white",
-        "run_time"    : 3.0,
-        "alpha_func"  : None
+        "spatial_period"  : 6,
+        "temporal_period" : 1,
+        "overtones"       : 4,
+        "amplitude"       : 0.5,
+        "radius"          : SPACE_WIDTH/2,
+        "run_time"        : 3.0,
+        "alpha_func"      : None
     }
-    def __init__(self, **kwargs):
-        digest_config(self, kwargs)
-        def func(x, t):
-            return sum([
-                (self.amplitude/((k+1)**2.5))*np.sin(2*mult*t)*np.sin(k*mult*x)
-                for k in range(self.overtones)
-                for mult in [(self.num_periods+k)*np.pi]
+    def __init__(self, mobject = None, **kwargs):
+        if mobject is None:
+            mobject = Line(3*LEFT, 3*RIGHT)
+        Animation.__init__(self, mobject, **kwargs)
+
+    def wave_function(self, x, t):
+        return sum([
+            reduce(op.mul, [
+                self.amplitude/(k**2), #Amplitude
+                np.sin(2*np.pi*(k**1.5)*t/self.temporal_period), #Frequency
+                np.sin(2*np.pi*k*x/self.spatial_period) #Number of waves
             ])
-        self.func = func
-        Animation.__init__(self, Mobject1D(color = self.color), **kwargs)
+            for k in range(1, self.overtones+1)
+        ])
+
 
     def update_mobject(self, alpha):
-        self.mobject.init_points()
-        epsilon = self.mobject.epsilon
-        self.mobject.add_points([
-            [x*self.radius, self.func(x, alpha*self.run_time)+y, 0]
-            for x in np.arange(-1, 1, epsilon/self.radius)
-            for y in epsilon*np.arange(3)
-        ])
-        self.mobject.shift(self.center)
+        time = alpha*self.run_time
+        families = map(
+            Mobject.get_full_submobject_family,
+            [self.mobject, self.starting_mobject]
+        )
+        for mob, start in zip(*families):
+            mob.points = np.apply_along_axis(
+                lambda (x, y, z) : (x, y + self.wave_function(x, time), z),
+                1, start.points
+            )
 
 
 class TurnInsideOut(Transform):
diff --git a/old_projects/music_and_measure.py b/old_projects/music_and_measure.py
index 4dd60846..3999b9a6 100644
--- a/old_projects/music_and_measure.py
+++ b/old_projects/music_and_measure.py
@@ -126,7 +126,7 @@ class Piano(ImageMobject):
         return keys
 
 
-class VibratingString(Animation):
+class Vibrate(Animation):
     DEFAULT_CONFIG = {
         "num_periods" : 1,
         "overtones" : 4,
@@ -302,7 +302,7 @@ class MeasureTheoryToHarmony(IntervalScene):
         line = Line(radius*LEFT, radius*RIGHT).highlight("white")
         self.play(DelayByOrder(Transform(all_mobs, line)))
         self.clear()
-        self.play(VibratingString(alpha_func = smooth))
+        self.play(Vibrate(alpha_func = smooth))
         self.clear()
         self.add(line)
         self.dither()
@@ -313,12 +313,12 @@ class ChallengeOne(Scene):
         title = TextMobject("Challenge #1").to_edge(UP)
         start_color = Color("blue")
         colors = start_color.range_to("white", 6)
-        self.bottom_vibration = VibratingString(
+        self.bottom_vibration = Vibrate(
             num_periods = 1, run_time = 3.0, 
             center = DOWN, color = start_color
         )
         top_vibrations = [
-            VibratingString(
+            Vibrate(
                 num_periods = freq, run_time = 3.0,
                 center = 2*UP, color = colors.next()
             )
@@ -415,8 +415,8 @@ class QuestionAndAnswer(Scene):
     def construct(self):
         Q = TextMobject("Q:").shift(UP).to_edge(LEFT)
         A = TextMobject("A:").shift(DOWN).to_edge(LEFT)
-        string1 = VibratingString(center = 3*UP, color = "blue")
-        string2 = VibratingString(num_periods = 2, center = 3.5*UP, color = "green")
+        string1 = Vibrate(center = 3*UP, color = "blue")
+        string2 = Vibrate(num_periods = 2, center = 3.5*UP, color = "green")
         twotwenty = TexMobject("220").scale(0.25).next_to(string1.mobject, LEFT)
         r220 = TexMobject("r\\times220").scale(0.25).next_to(string2.mobject, LEFT)
         question = TextMobject(
@@ -466,11 +466,11 @@ class PlaySimpleRatio(Scene):
         return str(fraction).replace("/", "_to_")
 
     def construct(self, fraction, color):
-        string1 = VibratingString(
+        string1 = Vibrate(
             num_periods = 1, run_time = 5.0, 
             center = DOWN, color = "blue"
         )
-        string2 = VibratingString(
+        string2 = Vibrate(
             num_periods = fraction, run_time = 5.0,
             center = 2*UP, color = color
         )