Beginning music and measure theory

animation/simple_animations.py

@@ -52,7 +52,7 @@ class Rotating(Animation):
             alpha_func = alpha_func,
             *args, **kwargs
         )
-        self.axes = [axis] if axis else axes
+        self.axes = [axis] if axis is not None else axes
         self.radians = radians
 
     def update_mobject(self, alpha):

animation/transform.py

@@ -39,7 +39,7 @@ class Transform(Animation):
         self.interpolation_function = interpolation_function
         count1, count2 = mobject1.get_num_points(), mobject2.get_num_points()
         if count2 == 0:
-            mobject2 = Point((SPACE_WIDTH, SPACE_HEIGHT, 0))
+            mobject2.add_points([(SPACE_WIDTH, SPACE_HEIGHT, 0)])
             count2 = mobject2.get_num_points()
         Mobject.align_data(mobject1, mobject2)
         Animation.__init__(self, mobject1, run_time = run_time, *args, **kwargs)

mobject/image_mobject.py

@@ -16,12 +16,14 @@ class ImageMobject(Mobject2D):
                  image_file, 
                  filter_color = "black", 
                  invert = True,
+                 use_cache = True,
                  *args, **kwargs):
         Mobject2D.__init__(self, *args, **kwargs)
         self.filter_rgb = 255 * np.array(Color(filter_color).get_rgb()).astype('uint8')
         self.name = to_cammel_case(
             os.path.split(image_file)[-1].split(".")[0]
         )
+        self.use_cache = use_cache
         possible_paths = [
             image_file,
             os.path.join(IMAGE_DIR, image_file),
@@ -35,7 +37,7 @@ class ImageMobject(Mobject2D):
         raise IOError("File not Found")
                 
     def generate_points_from_file(self, path, invert):
-        if self.read_in_cached_attrs(path, invert):
+        if self.use_cache and self.read_in_cached_attrs(path, invert):
             return
         image = Image.open(path).convert('RGB')
         if invert:

mobject/mobject.py

@@ -32,13 +32,16 @@ class Mobject(object):
         if not hasattr(self, "name"):
             self.name = name or self.__class__.__name__
         self.has_normals = hasattr(self, 'unit_normal')
+        self.init_points()
+        self.generate_points()
+        if center:
+            self.center().shift(center)
+
+    def init_points(self):
         self.points = np.zeros((0, 3))
         self.rgbs   = np.zeros((0, 3))
         if self.has_normals:
             self.unit_normals = np.zeros((0, 3))
-        self.generate_points()
-        if center:
-            self.center().shift(center)
 
     def __str__(self):
         return self.name
@@ -79,6 +82,7 @@ class Mobject(object):
             self.add_points(mobject.points, mobject.rgbs)
         return self
 
+
     def repeat(self, count):
         #Can make transition animations nicer
         points, rgbs = deepcopy(self.points), deepcopy(self.rgbs)
@@ -86,6 +90,13 @@ class Mobject(object):
             self.add_points(points, rgbs)
         return self
 
+    def do_in_place(self, method, *args, **kwargs):
+        center = self.get_center()
+        self.shift(-center)
+        method(*args, **kwargs)
+        self.shift(center)
+        return self
+
     def rotate(self, angle, axis = OUT):
         t_rotation_matrix = np.transpose(rotation_matrix(angle, axis))
         self.points = np.dot(self.points, t_rotation_matrix)
@@ -94,10 +105,7 @@ class Mobject(object):
         return self
 
     def rotate_in_place(self, angle, axis = OUT):
-        center = self.get_center()
-        self.shift(-center)
-        self.rotate(angle, axis)
-        self.shift(center)
+        self.do_in_place(self.rotate, angle, axis)
         return self
 
     def shift(self, vector):
@@ -144,13 +152,21 @@ class Mobject(object):
         self.shift(shift_val)
         return self
 
+    def next_to(self, mobject, direction = RIGHT, buff = EDGE_BUFFER):
+        self.shift(
+            mobject.get_edge_center(direction) - \
+            self.get_edge_center(-direction) + \
+            buff * direction
+        )
+        return self
+
     def scale(self, scale_factor):
         self.points *= scale_factor
         return self
 
     def scale_in_place(self, scale_factor):
-        center = self.get_center()
-        return self.center().scale(scale_factor).shift(center)
+        self.do_in_place(self.scale, scale_factor)
+        return self
 
     def stretch(self, factor, dim):
         self.points[:,dim] *= factor

mobject/three_dimensional_mobjects.py

@@ -9,9 +9,12 @@ from helpers import *
 class Stars(Mobject):
     DEFAULT_COLOR = "white"
     SHOULD_BUFF_POINTS = False
-    def __init__(self, num_points = DEFAULT_NUM_STARS, 
+    def __init__(self,
+                 radius = SPACE_WIDTH,
+                 num_points = DEFAULT_NUM_STARS, 
                  *args, **kwargs):
         self.num_points = num_points
+        self.radius = radius
         Mobject.__init__(self, *args, **kwargs)
 
     def generate_points(self):
@@ -23,7 +26,7 @@ class Stars(Mobject):
             )
             for x in range(self.num_points)
             for r, phi, theta in [[
-                max(SPACE_HEIGHT, SPACE_WIDTH) * random(),
+                self.radius * random(),
                 np.pi * random(),
                 2 * np.pi * random(),
             ]]

sample_script.py

@@ -10,29 +10,13 @@ from animation import *
 from mobject import *
 from constants import *
 from region import *
-from scene import Scene, SceneFromVideo
+from scene import Scene
 from script_wrapper import command_line_create_scene
 
 
-class SampleScene(SceneFromVideo):
+class SampleScene(Scene):
     def construct(self):
-        path = os.path.join(MOVIE_DIR, "EdgeDetectedCountingInBinary35-75.mp4")
-        SceneFromVideo.construct(self, path, time_range = (3, 5))
-        self.apply_gaussian_blur(sigmaX = 10)
-        self.make_all_black_or_white()
-        self.name = "BlurEdgeBlurBold"
-
-        # self.animate_over_time_range(
-        #     0, 3,
-        #     ApplyMethod(Dot().to_edge(LEFT).to_edge, RIGHT)
-        # )
-       
-    def make_all_black_or_white(self):
-        self.frames = [
-            255*(frame != 0).astype('uint8')
-            for frame in self.frames
-        ]
-        
+        pass
 
 if __name__ == "__main__":
     command_line_create_scene()

scripts/music_and_measure.py

@@ -0,0 +1,261 @@
+#!/usr/bin/env python
+
+import numpy as np
+import itertools as it
+from copy import deepcopy
+import sys
+from fractions import Fraction, gcd
+
+from animation import *
+from mobject import *
+from constants import *
+from region import *
+from scene import Scene
+from script_wrapper import command_line_create_scene
+
+import random
+
+MOVIE_PREFIX = "music_and_measure/"
+
+INTERVAL_RADIUS = 6
+NUM_INTERVAL_TICKS = 16
+TICK_STRETCH_FACTOR = 4
+INTERVAL_COLOR_PALETTE = [
+    "yellow",
+    "green",
+    "skyblue",
+    "#AD1457",
+    "#6A1B9A",
+    "#26C6DA",
+    "#FF8F00",
+]
+
+def rationals():
+    curr = Fraction(1, 2)
+    numerator, denominator = 1, 2
+    while True:
+        yield curr
+        if curr.numerator < curr.denominator - 1:
+            new_numerator = curr.numerator + 1
+            while gcd(new_numerator, curr.denominator) != 1:
+                new_numerator += 1
+            curr = Fraction(new_numerator, curr.denominator)
+        else:
+            curr = Fraction(1, curr.denominator + 1)
+
+def fraction_mobject(fraction):
+    n, d = fraction.numerator, fraction.denominator
+    return tex_mobject("\\frac{%d}{%d}"%(n, d))
+
+
+def zero_to_one_interval():
+    interval = NumberLine(
+        radius = INTERVAL_RADIUS,
+        interval_size = 2.0*INTERVAL_RADIUS/NUM_INTERVAL_TICKS
+    )
+    interval.elongate_tick_at(-INTERVAL_RADIUS, TICK_STRETCH_FACTOR)
+    interval.elongate_tick_at(INTERVAL_RADIUS, TICK_STRETCH_FACTOR)
+    interval.add(tex_mobject("0").shift(INTERVAL_RADIUS*LEFT+DOWN))
+    interval.add(tex_mobject("1").shift(INTERVAL_RADIUS*RIGHT+DOWN))
+    return interval
+
+class OpenInterval(Mobject):
+    def __init__(self, center = ORIGIN, width = 2, **kwargs):
+        Mobject.__init__(self, **kwargs)
+        self.add(tex_mobject("(").shift(LEFT))
+        self.add(tex_mobject(")").shift(RIGHT))
+        scale_factor = width / 2.0
+        self.stretch(scale_factor, 0)
+        self.stretch(0.5+0.5*scale_factor, 1)
+        self.shift(center)
+
+class VibratingString(Animation):
+    def __init__(self, 
+                 num_periods = 1,
+                 overtones = 4,
+                 amplitude = 0.5,
+                 radius = INTERVAL_RADIUS, 
+                 center = ORIGIN,
+                 color = "white",
+                 run_time = 3.0, 
+                 alpha_func = None,
+                 **kwargs):
+        self.radius = radius
+        self.center = center
+        def func(x, t):
+            return sum([
+                (amplitude/((k+1)**2))*np.sin(2*mult*t)*np.sin(k*mult*x)
+                for k in range(overtones)
+                for mult in [(num_periods+k)*np.pi]
+            ])
+        self.func = func
+        kwargs["run_time"] = run_time
+        kwargs["alpha_func"] = alpha_func
+        Animation.__init__(self, Mobject1D(color = color), **kwargs)
+
+    def update_mobject(self, alpha):
+        self.mobject.init_points()
+        self.mobject.add_points([
+            [x*self.radius, self.func(x, alpha*self.run_time), 0]
+            for x in np.arange(-1, 1, self.mobject.epsilon/self.radius)
+        ])
+        self.mobject.shift(self.center)
+
+
+class IntervalScene(Scene):
+    def construct(self):
+        self.interval = zero_to_one_interval()
+        self.add(self.interval)
+
+    def show_all_fractions(self, 
+                           num_fractions = 27, 
+                           pause_time = 1.0,
+                           remove_as_you_go = True):
+        shrink = not remove_as_you_go
+        for fraction, count in zip(rationals(), range(num_fractions)):
+            frac_mob, tick  = self.add_fraction(fraction, shrink)
+            self.dither(pause_time)
+            if remove_as_you_go:
+                self.remove(frac_mob, tick)
+
+    def add_fraction(self, fraction, shrink = False):
+        point = self.num_to_point(fraction)
+        tick_rad = self.interval.tick_size*TICK_STRETCH_FACTOR        
+        frac_mob = fraction_mobject(fraction)
+        if shrink:
+            scale_factor = 2.0/fraction.denominator
+            frac_mob.scale(scale_factor)
+            tick_rad *= scale_factor
+        frac_mob.shift(point + frac_mob.get_height()*UP)
+        tick = Line(point + DOWN*tick_rad, point + UP*tick_rad)
+        tick.highlight("yellow")
+        self.add(frac_mob, tick)
+        return frac_mob, tick
+
+    def cover_fractions(self, 
+                        epsilon = 0.3, 
+                        num_fractions = 9, 
+                        run_time_per_interval = 0.5):
+        for fraction, count in zip(rationals(), range(num_fractions)):
+            self.add_open_interval(
+                fraction,
+                epsilon / 2**(count+1),
+                run_time = run_time_per_interval
+            )
+
+    def add_open_interval(self, num, width, color = None, run_time = 0):
+        width *= 2*self.interval.radius
+        center_point = self.num_to_point(num)
+        open_interval = OpenInterval(center_point, width)
+        if color:
+            open_interval.highlight(color)
+        interval_line = Line(open_interval.get_left(), open_interval.get_right())
+        interval_line.scale_in_place(0.9)#Silliness
+        interval_line.do_in_place(interval_line.sort_points, np.linalg.norm)
+        interval_line.highlight("yellow")
+        if run_time > 0:
+            squished_interval = deepcopy(open_interval).stretch_to_fit_width(0)
+            self.animate(
+                Transform(squished_interval, open_interval),
+                ShowCreation(interval_line),
+                run_time = run_time
+            )
+            self.remove(squished_interval)
+        self.add(open_interval, interval_line)
+        return open_interval, interval_line
+
+    def num_to_point(self, num):
+        assert(num <= 1 and num >= 0)
+        radius = self.interval.radius
+        return (num*2*radius - radius)*RIGHT
+
+
+class TwoChallenges(Scene):
+    def construct(self):
+        two_challenges = text_mobject("Two Challenges", size = "\\Huge").to_edge(UP)
+        one, two = map(text_mobject, ["1.", "2."])
+        one.shift(UP).to_edge(LEFT)
+        two.shift(DOWN).to_edge(LEFT)
+        notes = ImageMobject("musical_notes").scale(0.3)
+        notes.next_to(one)
+        notes.highlight("blue")
+        measure = text_mobject("Measure Theory").next_to(two)
+        probability = text_mobject("Probability")
+        probability.next_to(measure).shift(DOWN+RIGHT)
+        integration = tex_mobject("\\int")
+        integration.next_to(measure).shift(UP+RIGHT)
+        arrow_to_prob = Arrow(measure, probability)
+        arrow_to_int = Arrow(measure, integration)
+        for arrow in arrow_to_prob, arrow_to_int:
+            arrow.highlight("yellow")
+
+
+        self.add(two_challenges)
+        self.dither()
+        self.add(one, notes)
+        self.dither()
+        self.add(two, measure)
+        self.dither()
+        self.animate(ShowCreation(arrow_to_int))
+        self.add(integration)
+        self.dither()
+        self.animate(ShowCreation(arrow_to_prob))
+        self.add(probability)
+        self.dither()
+
+class MeasureTheoryToHarmony(IntervalScene):
+    def construct(self):
+        IntervalScene.construct(self)
+        self.cover_fractions()
+        self.dither()
+        all_mobs = CompoundMobject(*self.mobjects)
+        all_mobs.sort_points()
+        self.clear()
+        radius = self.interval.radius
+        line = Line(radius*LEFT, radius*RIGHT).highlight("white")
+        self.animate(DelayByOrder(Transform(all_mobs, line)))
+        self.clear()
+        self.animate(VibratingString(alpha_func = smooth))
+        self.clear()
+        self.add(line)
+        self.dither()
+
+
+class ChallengeOne(Scene):
+    def construct(self):
+        title = text_mobject("Challenge #1").to_edge(UP)
+        bottom_vibration = VibratingString(
+            num_periods = 1, run_time = 1.0, 
+            center = DOWN, color = "blue"
+        )
+        top_vibration = VibratingString(
+            num_periods = 2, run_time = 1.0,
+            center = 2*UP, color = "lightgreen"
+        )
+        freq_num1 = text_mobject("220 Hz")
+        freq_num2 = text_mobject("$r\\times$220 Hz")
+        freq_num1.shift(1.5*DOWN)
+        freq_num2.shift(1.5*UP)
+        r_constraint = tex_mobject("1<r<2")
+        # self.add(title, freq_num1, freq_num2, r_constraint)
+        self.animate(top_vibration, bottom_vibration)
+
+
+
+class SampleIntervalScene(IntervalScene):
+    def construct(self):
+        IntervalScene.construct(self)
+        self.cover_fractions()
+        self.dither()
+
+
+class ShowAllFractions(IntervalScene):
+    def construct(self):
+        IntervalScene.construct(self)
+        self.show_all_fractions(remove_as_you_go = False, pause_time = 0.3)
+
+
+if __name__ == "__main__":
+    command_line_create_scene(MOVIE_PREFIX)
+
+