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