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295 lines
8.3 KiB
Python
295 lines
8.3 KiB
Python
#!/usr/bin/env python
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import numpy as np
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import itertools as it
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import operator as op
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from copy import deepcopy
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from big_ol_pile_of_manim_imports import *
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RADIUS = FRAME_Y_RADIUS - 0.1
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CIRCLE_DENSITY = DEFAULT_POINT_DENSITY_1D*RADIUS
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def logo_to_circle():
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from .generate_logo import DARK_BROWN, LOGO_RADIUS
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sc = Scene()
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small_circle = Circle(
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density = CIRCLE_DENSITY,
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color = 'skyblue'
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).scale(LOGO_RADIUS).set_color(
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DARK_BROWN, lambda x_y_z : x_y_z[0] < 0 and x_y_z[1] > 0
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)
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big_circle = Circle(density = CIRCLE_DENSITY).scale(RADIUS)
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sc.add(small_circle)
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sc.wait()
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sc.animate(Transform(small_circle, big_circle))
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return sc
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def count_sections(*radians):
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sc = Scene()
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circle = Circle(density = CIRCLE_DENSITY).scale(RADIUS)
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sc.add(circle)
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points = [
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(RADIUS * np.cos(angle), RADIUS * np.sin(angle), 0)
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for angle in radians
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]
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dots = [Dot(point) for point in points]
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interior = Region(lambda x, y : x**2 + y**2 < RADIUS**2)
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for x in range(1, len(points)):
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if x == 1:
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sc.animate(ShowCreation(dots[0]), ShowCreation(dots[1]))
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sc.add(dots[0], dots[1])
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else:
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sc.animate(ShowCreation(dots[x]))
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sc.add(dots[x])
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new_lines = Mobject(*[
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Line(points[x], points[y]) for y in range(x)
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])
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sc.animate(Transform(deepcopy(dots[x]), new_lines, run_time = 2.0))
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sc.add(new_lines)
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sc.wait()
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regions = plane_partition_from_points(*points[:x+1])
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for reg in regions:
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reg.intersect(interior)
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regions = [reg for reg in regions if reg.bool_grid.any()]
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last_num = None
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for reg, count in zip(regions, it.count(1)):
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number = TexMobject(str(count)).shift((RADIUS, 3, 0))
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sc.set_color_region(reg)
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rt = 1.0 / (x**0.8)
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sc.add(number)
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sc.remove(last_num)
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last_num = number
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sc.wait(rt)
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sc.reset_background()
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sc.remove(last_num)
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sc.animate(Transform(last_num, deepcopy(last_num).center()))
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sc.wait()
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sc.remove(last_num)
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return sc
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def summarize_pattern(*radians):
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sc = Scene()
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circle = Circle(density = CIRCLE_DENSITY).scale(RADIUS)
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sc.add(circle)
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points = [
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(RADIUS * np.cos(angle), RADIUS * np.sin(angle), 0)
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for angle in radians
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]
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dots = [Dot(point) for point in points]
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last_num = None
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for x in range(len(points)):
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new_lines = Mobject(*[
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Line(points[x], points[y]) for y in range(x)
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])
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num = TexMobject(str(moser_function(x + 1))).center()
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sc.animate(
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Transform(last_num, num) if last_num else ShowCreation(num),
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FadeIn(new_lines),
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FadeIn(dots[x]),
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run_time = 0.5,
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)
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sc.remove(last_num)
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last_num = num
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sc.add(num, dots[x], new_lines)
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sc.wait()
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return sc
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def connect_points(*radians):
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sc = Scene()
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circle = Circle(density = CIRCLE_DENSITY).scale(RADIUS)
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sc.add(circle)
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points = [
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(RADIUS * np.cos(angle), RADIUS * np.sin(angle), 0)
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for angle in radians
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]
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dots = [Dot(point) for point in points]
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sc.add(*dots)
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anims = []
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all_lines = []
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for x in range(len(points)):
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lines = [Line(points[x], points[y]) for y in range(len(points))]
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lines = Mobject(*lines)
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anims.append(Transform(deepcopy(dots[x]), lines, run_time = 3.0))
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all_lines.append(lines)
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sc.animate(*anims)
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sc.add(*all_lines)
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sc.wait()
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return sc
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def interesting_problems():
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sc = Scene()
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locales = [(6, 2, 0), (6, -2, 0), (-5, -2, 0)]
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fermat = Mobject(*TexMobjects(["x^n","+","y^n","=","z^n"]))
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fermat.scale(0.5).shift((-2.5, 0.7, 0))
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face = SimpleFace()
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tb = ThoughtBubble().shift((-1.5, 1, 0))
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sb = SpeechBubble().shift((-2.4, 1.3, 0))
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fermat_copies, face_copies, tb_copies, sb_copies = (
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Mobject(*[
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deepcopy(mob).scale(0.5).shift(locale)
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for locale in locales
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])
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for mob in [fermat, face, tb, sb]
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)
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sc.add(face, tb)
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sc.animate(ShowCreation(fermat, run_time = 1))
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sc.add(fermat)
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sc.wait()
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sc.animate(
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Transform(
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deepcopy(fermat).repeat(len(locales)),
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fermat_copies
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),
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FadeIn(face_copies, run_time = 1.0)
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)
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sc.animate(FadeIn(tb_copies))
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sc.wait()
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sc.animate(
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Transform(tb, sb),
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Transform(tb_copies, sb_copies)
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)
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return sc
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def response_invitation():
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sc = Scene()
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video_icon = VideoIcon()
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mini_videos = Mobject(*[
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deepcopy(video_icon).scale(0.5).shift((3, y, 0))
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for y in [-2, 0, 2]
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])
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comments = Mobject(*[
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Line((-1.2, y, 0), (1.2, y, 0), color = 'white')
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for y in [-1.5, -1.75, -2]
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])
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sc.add(video_icon)
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sc.wait()
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sc.animate(Transform(deepcopy(video_icon).repeat(3), mini_videos))
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sc.add(mini_videos)
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sc.wait()
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sc.animate(ShowCreation(comments, run_time = 1.0))
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return sc
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def different_points(radians1, radians2):
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sc = Scene()
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circle = Circle(density = CIRCLE_DENSITY).scale(RADIUS)
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sc.add(circle)
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points1, points2 = (
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[
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(RADIUS * np.cos(angle), RADIUS * np.sin(angle), 0)
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for angle in radians
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]
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for radians in (radians1, radians2)
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)
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dots1, dots2 = (
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Mobject(*[Dot(point) for point in points])
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for points in (points1, points2)
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)
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lines1, lines2 = (
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[
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Line(point1, point2)
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for point1, point2 in it.combinations(points, 2)
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]
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for points in (points1, points2)
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)
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sc.add(dots1, *lines1)
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sc.animate(
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Transform(dots1, dots2, run_time = 3),
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*[
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Transform(line1, line2, run_time = 3)
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for line1, line2 in zip(lines1, lines2)
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]
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)
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sc.wait()
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return sc
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def next_few_videos(*radians):
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sc = Scene()
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circle = Circle(density = CIRCLE_DENSITY).scale(RADIUS)
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points = [
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(RADIUS * np.cos(angle), RADIUS * np.sin(angle), 0)
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for angle in radians
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]
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dots = Mobject(*[
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Dot(point) for point in points
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])
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lines = Mobject(*[
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Line(point1, point2)
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for point1, point2 in it.combinations(points, 2)
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])
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thumbnail = Mobject(circle, dots, lines)
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frame = VideoIcon().set_color(
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"black",
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lambda point : get_norm(point) < 0.5
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)
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big_frame = deepcopy(frame).scale(FRAME_X_RADIUS)
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frame.shift((-5, 0, 0))
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sc.add(thumbnail)
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sc.wait()
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sc.animate(
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Transform(big_frame, frame),
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Transform(
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thumbnail,
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deepcopy(thumbnail).scale(0.15).shift((-5, 0, 0))
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)
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)
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sc.add(frame, thumbnail)
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sc.wait()
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last = frame
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for x in [-2, 1, 4]:
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vi = VideoIcon().shift((x, 0, 0))
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sc.animate(
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Transform(deepcopy(last), vi),
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Animation(thumbnail)#Keeps it from getting burried
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)
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sc.add(vi)
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last = vi
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return sc
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if __name__ == '__main__':
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radians = [1, 3, 5, 2, 4, 6]
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more_radians = radians + [10, 13, 20, 17, 15, 21, 18.5]
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different_radians = [1.7, 4.8, 3.2, 3.5, 2.1, 5.5]
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# logo_to_circle().write_to_movie("moser/LogoToCircle")
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# count_sections(*radians).write_to_movie("moser/CountingSections")
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# summarize_pattern(*radians).write_to_movie("moser/SummarizePattern")
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# interesting_problems().write_to_movie("moser/InterestingProblems")
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# summarize_pattern(*more_radians).write_to_movie("moser/ExtendedPattern")
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# connect_points(*radians).write_to_movie("moser/ConnectPoints")
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# response_invitation().write_to_movie("moser/ResponseInvitation")
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# different_points(radians, different_radians).write_to_movie("moser/DifferentPoints")
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# next_few_videos(*radians).write_to_movie("moser/NextFewVideos")
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# summarize_pattern(*different_radians).write_to_movie("moser/PatternWithDifferentPoints")
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#Images
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# TexMobject(r"""
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# \Underbrace{1, 2, 4, 8, 16, 31, \dots}_\text{What?}
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# """).save_image("moser/NumberList31")
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# TexMobject("""
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# 1, 2, 4, 8, 16, 32, 63, \dots
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# """).save_image("moser/NumberList63")
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# TexMobject("""
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# 1, 2, 4, 8, 15, \dots
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# """).save_image("moser/NumberList15")
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