starting main moser video

animation.py

@@ -10,6 +10,7 @@ import inspect
 from images2gif import writeGif
 
 from helpers import *
+from constants import *
 from mobject import Mobject
 
 class Animation(object):

constants.py

@@ -1,15 +1,15 @@
 import os
 
 PRODUCTION_QUALITY = True
-GENERALLY_BUFF_POINTS = False
+GENERALLY_BUFF_POINTS = True
 
 DEFAULT_POINT_DENSITY_2D = 25  #if PRODUCTION_QUALITY else 20
-DEFAULT_POINT_DENSITY_1D = 200 #if PRODUCTION_QUALITY else 50
+DEFAULT_POINT_DENSITY_1D = 150 #if PRODUCTION_QUALITY else 50
 
 DEFAULT_HEIGHT = 1440 if PRODUCTION_QUALITY else 480
 DEFAULT_WIDTH  = 2560 if PRODUCTION_QUALITY else 640
 #All in seconds
-DEFAULT_FRAME_DURATION = 0.04 #if PRODUCTION_QUALITY else 0.1
+DEFAULT_FRAME_DURATION = 0.04 if PRODUCTION_QUALITY else 0.1
 DEFAULT_ANIMATION_RUN_TIME = 3.0 
 DEFAULT_TRANSFORM_RUN_TIME = 1.0
 DEFAULT_DITHER_TIME = 1.0

generate_logo.py

@@ -5,6 +5,8 @@ from animation import *
 from mobject import *
 from constants import *
 from helpers import *
+from scene import *
+from image_mobject import *
 import itertools as it
 import os
 
@@ -14,12 +16,12 @@ import numpy as np
 DARK_BLUE = "#236B8E"
 DARK_BROWN = "#8B4513"
 LIGHT_BROWN = "#CD853F"
+LOGO_RADIUS = 1.5
 
 
 if __name__ == '__main__':
-    size = 1.5
-    circle = Circle(color = 'skyblue').repeat(4).scale(size)
-    sphere = Sphere(density = 100, color = DARK_BLUE).scale(size)
+    circle = Circle(density = 100, color = 'skyblue').repeat(5).scale(LOGO_RADIUS)
+    sphere = Sphere(density = 100, color = DARK_BLUE).scale(LOGO_RADIUS)
     sphere.rotate(-np.pi / 7, [1, 0, 0])
     sphere.rotate(-np.pi / 7)
     alpha = 0.3
@@ -27,20 +29,21 @@ if __name__ == '__main__':
     Mobject.interpolate(circle, sphere, iris, alpha)
     for mob, color in [(iris, LIGHT_BROWN), (circle, DARK_BROWN)]:
         mob.highlight(color, lambda (x, y, z) : x < 0 and y > 0)
-        mob.highlight("black", lambda point: np.linalg.norm(point) < size/2)
+        mob.highlight("black", lambda point: np.linalg.norm(point) < 0.55*LOGO_RADIUS)
 
-    #TODO, reimplement all of this.
-    name = tex_mobject("3Blue1Brown").center()
+    name = tex_mobject(r"\text{3Blue1Brown}").center()
     name.highlight("gray")
-    # name.highlight(DARK_BROWN, lambda (x, y, z) : x < 0 and y > 0)
     name.shift((0, -2, 0))
-    create_eye = Transform(
+    sc = Scene()
+    sc.animate(Transform(
         circle, iris, 
-        run_time = DEFAULT_ANIMATION_RUN_TIME,
-        name = "LogoGeneration"
-    ).then(
-        Animation(name, dither_time = 0)
-    ).drag_pixels()
-    create_eye.write_to_movie()
-    index = int(DEFAULT_ANIMATION_RUN_TIME / DEFAULT_ANIMATION_PAUSE_TIME)
-    create_eye.frames[index].save(LOGO_PATH)
+        run_time = DEFAULT_ANIMATION_RUN_TIME
+    ))
+    sc.add(name)
+    sc.dither()
+    sc.frames = drag_pixels(sc.frames)
+    sc.write_to_movie("LogoGeneration", end_dither_time = 0)
+
+
+    # index = int(DEFAULT_ANIMATION_RUN_TIME / DEFAULT_ANIMATION_PAUSE_TIME)
+    # create_eye.frames[index].save(LOGO_PATH)

helpers.py

@@ -4,6 +4,7 @@ from PIL import Image
 from colour import Color
 from random import random
 import string
+
 from constants import *
 
 def hash_args(args):
@@ -25,13 +26,13 @@ def to_cammel_case(name):
     ]
     return "".join(parts)
 
-def drag_pixels(images):
-    curr = np.array(images[0])
-    new_images = []
-    for image in images:
-        curr += (curr == 0) * np.array(image)
-        new_images.append(Image.fromarray(curr))
-    return new_images
+def drag_pixels(frames):
+    curr = frames[0]
+    new_frames = []
+    for frame in frames:
+        curr += (curr == 0) * np.array(frame)
+        new_frames.append(np.array(curr))
+    return new_frames
 
 def invert_image(image):
     arr = np.array(image)

mobject.py

@@ -4,6 +4,7 @@ import os
 from PIL import Image
 from random import random
 from copy import deepcopy
+from colour import Color
 
 from constants import *
 from helpers import *
@@ -264,6 +265,11 @@ class Vector(Arrow):
 class Dot(Mobject1D): #Use 1D density, even though 2D
     DEFAULT_COLOR = "white"
     def __init__(self, center = (0, 0, 0), radius = 0.05, *args, **kwargs):
+        center = np.array(center)
+        if center.size == 1:
+            raise Exception("Center must have 2 or 3 coordinates!")
+        elif center.size == 2:
+            center = np.append(center, [0])
         self.center = center
         self.radius = radius
         Mobject1D.__init__(self, *args, **kwargs)

moser/intro.py

@@ -17,27 +17,15 @@ RADIUS = SPACE_HEIGHT - 0.1
 CIRCLE_DENSITY = DEFAULT_POINT_DENSITY_1D*RADIUS
 
 
-####
-def moser_function(n):
-    return choose(n, 4) + choose(n, 2) + 1
-
-def choose(n, r):
-    if n < r: return 0
-    r = min(r, n-r)
-    if r == 0: return 1
-    numer = reduce(op.mul, xrange(n, n-r, -1), 1)
-    denom = reduce(op.mul, xrange(1, r+1), 1)
-    return numer//denom
-####
-
-
 def logo_to_circle():
-    from generate_logo import LIGHT_BROWN
+    from generate_logo import DARK_BROWN, LOGO_RADIUS
     sc = Scene()
     small_circle = Circle(
         density = CIRCLE_DENSITY,
         color = 'skyblue'
-    ).highlight(LIGHT_BROWN, lambda (x, y, z) : x < 0 and y > 0)
+    ).scale(LOGO_RADIUS).highlight(
+        DARK_BROWN, lambda (x, y, z) : x < 0 and y > 0
+    )
     big_circle = Circle(density = CIRCLE_DENSITY).scale(RADIUS)
     sc.add(small_circle)
     sc.dither()
@@ -102,7 +90,7 @@ def summarize_pattern(*radians):
         new_lines = CompoundMobject(*[
             Line(points[x], points[y]) for y in xrange(x)
         ])
-        num = tex_mobject(str(moser_function(x + 1)))
+        num = tex_mobject(str(moser_function(x + 1))).center()
         sc.animate(
             Transform(last_num, num) if last_num else ShowCreation(num),
             FadeIn(new_lines),
@@ -270,6 +258,7 @@ def next_few_videos(*radians):
     return sc
 
 
+
 if __name__ == '__main__':
     radians = [1, 3, 5, 2, 4, 6]
     more_radians = radians + [10, 13, 20, 17, 15, 21, 18.5]
@@ -282,13 +271,20 @@ if __name__ == '__main__':
     # connect_points(*radians).write_to_movie("moser/ConnectPoints")
     # response_invitation().write_to_movie("moser/ResponseInvitation")
     # different_points(radians, different_radians).write_to_movie("moser/DifferentPoints")
-    next_few_videos(*radians).write_to_movie("moser/NextFewVideos")
-
+    # next_few_videos(*radians).write_to_movie("moser/NextFewVideos")
+    # summarize_pattern(*different_radians).write_to_movie("moser/PatternWithDifferentPoints")
 
     #Images
     # tex_mobject(r"""
     #     \underbrace{1, 2, 4, 8, 16, 31, \dots}_\text{What?}
-    # """).save_image("moser/NumberList")
+    # """).save_image("moser/NumberList31")
+    # tex_mobject("""
+    #     1, 2, 4, 8, 16, 32, 63, \dots
+    # """).save_image("moser/NumberList63")
+    # tex_mobject("""
+    #     1, 2, 4, 8, 15, \dots
+    # """).save_image("moser/NumberList15")
+    
 
 
 

moser/main.py

@@ -0,0 +1,137 @@
+#!/usr/bin/env python
+
+import numpy as np
+import itertools as it
+import operator as op
+from copy import deepcopy
+
+
+from animation import *
+from mobject import *
+from image_mobject import *
+from constants import *
+from region import *
+from scene import Scene
+
+from moser_helpers import *
+
+RADIUS = SPACE_HEIGHT - 0.1
+CIRCLE_DENSITY = DEFAULT_POINT_DENSITY_1D*RADIUS
+
+
+class CircleScene(Scene):
+    def __init__(self, radians, *args, **kwargs):
+        Scene.__init__(self, *args, **kwargs)
+        self.radius = RADIUS
+        self.circle = Circle(density = CIRCLE_DENSITY).scale(self.radius)
+        self.points = [
+            (self.radius * np.cos(angle), self.radius * np.sin(angle), 0)
+            for angle in radians
+        ]
+        self.dots = [Dot(point) for point in self.points]
+        self.lines = [Line(p1, p2) for p1, p2 in it.combinations(self.points, 2)]
+        self.add(self.circle, *self.dots + self.lines)
+
+
+##################################################
+
+def count_lines(*radians):
+    sc = CircleScene(radians)
+    text = tex_mobject(r"\text{How Many Lines?}", size = r"\large")
+    text_center = (sc.radius + 1, sc.radius -1, 0)
+    text.scale(0.4).shift(text_center)
+    x = text_center[0]
+    new_lines = [
+        Line((x-1, y, 0), (x+1, y, 0))
+        for y in np.arange(
+            -(sc.radius - 1), 
+            sc.radius - 1, 
+            (2*sc.radius - 2)/len(sc.lines)
+        )
+    ]
+    sc.add(text)
+    sc.dither()
+    sc.animate(*[
+       Transform(line1, line2, run_time = 2)
+       for line1, line2 in zip(sc.lines, new_lines)
+    ])
+    return sc
+
+
+def count_intersection_points(*radians):
+    radians = [r % (2*np.pi) for r in radians]
+    radians.sort()
+    sc = CircleScene(radians)
+    intersection_points = [
+        intersection([p[0], p[2]], [p[1], p[3]])
+        for p in it.combinations(sc.points, 4)
+    ]
+    intersection_dots = CompoundMobject(*[
+        Dot(point) for point in intersection_points
+    ])
+    how_many = tex_mobject(r"""
+        \text{How many}\\
+        \text{intersection points?}
+    """, size = r"\large")
+    text_center = (sc.radius + 1, sc.radius -1, 0)
+    how_many.scale(0.4).shift(text_center)
+    new_points = [
+        (text_center[0], y, 0)
+        for y in np.arange(
+            -(sc.radius - 1), 
+            sc.radius - 1, 
+            (2*sc.radius - 2)/choose(len(sc.points), 4)
+        )
+    ]
+    new_dots = CompoundMobject(*[
+        Dot(point) for point in new_points
+    ])
+
+    sc.add(how_many)
+    sc.animate(ShowCreation(intersection_dots))
+    sc.add(intersection_dots)
+    sc.animate(Transform(intersection_dots, new_dots))
+    sc.add(tex_mobject(str(len(new_points))).center())
+    return sc
+
+def non_general_position():
+    radians = np.arange(1, 7)
+    new_radians = (np.pi/3)*radians
+    sc1 = CircleScene(radians)
+    sc2 = CircleScene(new_radians)
+    center_region = reduce(
+        Region.intersect,
+        [
+            HalfPlane((sc1.points[x], sc1.points[(x+3)%6]))
+            for x in [0, 4, 2]#Ya know, trust it
+        ]
+    )
+    center_region
+    text = tex_mobject(r"\text{This region disappears}", size = r"\large")
+    text.center().scale(0.5).shift((-sc1.radius, sc1.radius-0.3, 0))
+    arrow = Arrow(
+        point = (-0.35, -0.1, 0),
+        direction = (1, -1, 0), 
+        length = sc1.radius + 1,
+        color = "white",
+    )
+
+    sc1.highlight_region(center_region, "green")
+    sc1.add(text, arrow)
+    sc1.dither(2)
+    sc1.remove(text, arrow)
+    sc1.reset_background()
+    sc1.animate(*[
+        Transform(mob1, mob2, run_time = DEFAULT_ANIMATION_RUN_TIME)
+        for mob1, mob2 in zip(sc1.mobjects, sc2.mobjects)
+    ])
+    return sc1
+
+
+##################################################
+
+if __name__ == '__main__':
+    radians = np.arange(0, 6, 6.0/7)
+    count_lines(*radians).write_to_movie("moser/CountLines")
+    count_intersection_points(*radians).write_to_movie("moser/CountIntersectionPoints")
+    non_general_position().write_to_movie("moser/NonGeneralPosition")

moser/moser_helpers.py

@@ -0,0 +1,34 @@
+import numpy as np
+import operator as op
+import itertools as it
+
+def choose(n, r):
+    if n < r: return 0
+    if r == 0: return 1
+    denom = reduce(op.mul, xrange(1, r+1), 1)
+    numer = reduce(op.mul, xrange(n, n-r, -1), 1)
+    return numer//denom
+
+def moser_function(n):
+    return choose(n, 4) + choose(n, 2) + 1
+
+def intersection(line1, line2):
+    """
+    A "line" should come in the form [(x0, y0), (x1, y1)] for two
+    points it runs through
+    """
+    p0, p1, p2, p3 = map(
+        lambda tup : np.array(tup[:2]),
+        [line1[0], line1[1], line2[0], line2[1]]
+    )
+    p1, p2, p3 = map(lambda x : x - p0, [p1, p2, p3])
+    transform = np.zeros((2, 2))
+    transform[:,0], transform[:,1] = p1, p2
+    if np.linalg.det(transform) == 0: return
+    inv = np.linalg.inv(transform)
+    new_p3 = np.dot(inv, p3.reshape((2, 1)))
+    #Where does line connecting (0, 1) to new_p3 hit x axis
+    x_intercept = new_p3[0] / (1 - new_p3[1]) 
+    result = np.dot(transform, [[x_intercept], [0]])
+    result = result.reshape((2,)) + p0
+    return result

scene.py

@@ -36,6 +36,7 @@ class Scene(object):
             )
         self.background = self.original_background
         self.shape = self.background.shape[:2]
+        #TODO, space shape
         self.name = name
 
     def __str__(self):