mirror of
https://github.com/3b1b/manim.git
synced 2025-09-01 00:48:45 +00:00
Merge branch 'master' into eop
This commit is contained in:
Ben Hambrecht
commit
76e7623200
6 changed files with 408 additions and 73 deletions
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@ -1 +0,0 @@
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@ -1,3 +1,6 @@
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#!/usr/bin/env python2
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# -*- coding: utf-8 -*-
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from big_ol_pile_of_manim_imports import *
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NAME_WITH_SPACES = "Prime Meridian"
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@ -5,71 +8,100 @@ DIAMETER = 3.0
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RADIUS = DIAMETER / 2
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LETTER_SCALE = 1
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class NameAnimationScene(Scene):
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CONFIG = {
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"animated_name": "Prime Meridian"
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}
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def construct(self):
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name = ''.join(NAME_WITH_SPACES.split(' '))
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letters = list(name)
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nb_letters = len(letters)
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name = self.animated_name
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letter_mobs = TextMobject(name)
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nb_letters = len(letter_mobs)
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randy = PiCreature()
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randy.move_to(ORIGIN).scale_to_fit_height(0.5 * DIAMETER)
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randy.set_color(BLUE_E)
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randy.look_at(UP + RIGHT)
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self.add(randy)
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dtheta = TAU/nb_letters
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angles = np.arange(TAU/4,-3 * TAU / 4,-dtheta)
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dtheta = TAU / nb_letters
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angles = np.arange(TAU / 4, -3 * TAU / 4, -dtheta)
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name_mob = VGroup()
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for (letter, angle) in zip(letters, angles):
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letter_mob = TextMobject(letter).scale(LETTER_SCALE)
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for (letter_mob, angle) in zip(letter_mobs, angles):
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letter_mob.scale(LETTER_SCALE)
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pos = RADIUS * np.cos(angle) * RIGHT + RADIUS * np.sin(angle) * UP
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letter_mob.move_to(pos)
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name_mob.add(letter_mob)
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pos2 = RADIUS * np.cos(angles[2]) * RIGHT + RADIUS * np.sin(angles[2]) * UP
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pos2 = RADIUS * np.cos(angles[2]) * RIGHT + \
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RADIUS * np.sin(angles[2]) * UP
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times_n_label = VGroup(
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TexMobject("\\times"),
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Integer(1)
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)
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times_n_label.arrange_submobjects(RIGHT)
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times_n_label.shift(FRAME_WIDTH * RIGHT / 4)
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times_n_label.to_edge(UP)
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self.play(
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LaggedStart(Write, name_mob, run_time = 3),
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ApplyMethod(randy.look_at, pos2, run_time = 3)
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LaggedStart(FadeIn, name_mob, run_time=3),
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ApplyMethod(randy.change, "pondering", pos2, run_time=1),
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FadeIn(times_n_label)
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)
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for i in range(2,nb_letters + 2):
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for n in range(2, nb_letters + 2):
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group = []
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for (j,letter_mob) in enumerate(name_mob.submobjects):
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for (j, letter_mob) in enumerate(name_mob.submobjects):
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new_angle = TAU / 4 - i * j * dtheta
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new_pos = RADIUS * np.cos(new_angle) * RIGHT + RADIUS * np.sin(new_angle) * UP
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new_angle = TAU / 4 - n * j * dtheta
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new_pos = RADIUS * np.cos(new_angle) * \
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RIGHT + RADIUS * np.sin(new_angle) * UP
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letter_mob.target = letter_mob.copy().move_to(new_pos)
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anim = MoveToTarget(letter_mob, path_arc = - j * dtheta)
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anim = MoveToTarget(letter_mob, path_arc=- j * dtheta)
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group.append(anim)
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new_n = Integer(n)
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new_n.move_to(times_n_label[1])
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self.play(
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AnimationGroup(*group, run_time = 3),
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ApplyMethod(randy.look_at,name_mob.submobjects[2], run_time = 3)
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AnimationGroup(*group, run_time=3),
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UpdateFromFunc(randy, lambda r: r.look_at(name_mob.submobjects[2])),
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FadeOut(times_n_label[1]),
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FadeIn(new_n)
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)
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times_n_label.submobjects[1] = new_n
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self.wait(0.5)
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thank_you = TextMobject("Thank You!").next_to(randy, DOWN)
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new_randy = randy.copy()
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new_randy.change("hooray")
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new_randy.set_color(BLUE_E)
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new_randy.look_at(ORIGIN)
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self.play(
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Transform(name_mob, thank_you),
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ReplacementTransform(name_mob, VGroup(*thank_you)),
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Transform(randy, new_randy)
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)
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self.play(Blink(randy))
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def __str__(self):
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return self.animated_name.replace(" ", "") + "Animation"
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names = []
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if __name__ == "__main__":
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for name in names:
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try:
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NameAnimationScene(
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frame_duration=PRODUCTION_QUALITY_FRAME_DURATION,
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camera_config=PRODUCTION_QUALITY_CAMERA_CONFIG,
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animated_name=name,
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write_to_movie=True,
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output_directory=os.path.join(
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ANIMATIONS_DIR,
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"active_projects",
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"name_animations",
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),
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)
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except Exception as e:
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print "Could not animate %s: %s" % (name, e)
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@ -25,6 +25,26 @@ def get_chord_f_label(chord, arg="f", direction=DOWN):
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chord_f.angle = angle
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return chord_f
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def get_wallis_product(n_terms=6, show_result=True):
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tex_mob_args = []
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for x in range(n_terms):
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if x % 2 == 0:
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numerator = x + 2
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denominator = x + 1
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else:
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numerator = x + 1
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denominator = x + 2
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tex_mob_args += [
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"{%d" % numerator, "\\over", "%d}" % denominator, "\\cdot"
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]
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tex_mob_args[-1] = "\\cdots"
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if show_result:
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tex_mob_args += ["=", "{\\pi", "\\over", "2}"]
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result = TexMobject(*tex_mob_args)
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return result
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# Scenes
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@ -33,7 +53,7 @@ class DistanceProductScene(MovingCameraScene):
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"ambient_light_config": {
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"opacity_function": DEFAULT_OPACITY_FUNCTION,
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"num_levels": 100,
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"light_radius": 5,
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"radius": 5,
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"max_opacity": 0.8,
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"color": PRODUCT_COLOR,
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},
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@ -112,11 +132,15 @@ class DistanceProductScene(MovingCameraScene):
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self.lights.add(light)
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return self.lights
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def get_distance_lines(self):
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self.distance_lines = VGroup(*[
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Line(self.get_observer_point(), point)
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def get_distance_lines(self, start_point=None, line_class=Line):
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if start_point is None:
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start_point = self.get_observer_point()
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lines = VGroup(*[
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line_class(start_point, point)
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for point in self.get_lh_points()
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])
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lines.set_stroke(width=2)
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self.distance_lines = lines
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return self.distance_lines
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def get_symbolic_distance_labels(self):
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@ -145,7 +169,7 @@ class DistanceProductScene(MovingCameraScene):
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include_background_rectangle=True,
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)
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label.scale_to_fit_height(self.numeric_distance_label_height)
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max_width = 0.5 * line.get_length()
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max_width = 0.5 * max(line.get_length(), 0.1)
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if label.get_width() > max_width:
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label.scale_to_fit_width(max_width)
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angle = (line.get_angle() % TAU) - TAU / 2
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@ -185,7 +209,7 @@ class DistanceProductScene(MovingCameraScene):
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product_decimal.scale_to_fit_height(self.numeric_distance_label_height)
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product_decimal.next_to(h_line, DOWN)
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product_decimal.align_to(stacked_labels, RIGHT)
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product_decimal.set_color(BLUE)
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product_decimal[1].set_color(BLUE)
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return VGroup(stacked_labels, h_line, times, product_decimal)
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def get_circle_group(self):
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@ -1468,14 +1492,14 @@ class PlugObserverIntoPolynomial(DistanceProductScene):
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i = polynomial[1].submobjects.index(eq)
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return polynomial[1][:i], polynomial[1][i], polynomial[1][i + 1:]
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def get_lines(self):
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dot = self.observer_dot
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lines = VGroup(*[
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DashedLine(dot.get_center(), point)
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for point in self.get_lh_points()
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])
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lines.set_stroke(width=2)
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return lines
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def get_lines(self, start_point=None):
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return self.get_distance_lines(
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start_point=start_point,
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line_class=DashedLine
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)
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def get_observer_point(self, dummy_arg):
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return self.observer_dot.get_center()
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class PlugObserverIntoPolynomial5Lighthouses(PlugObserverIntoPolynomial):
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@ -1664,9 +1688,9 @@ class DistanceProductIsChordF(PlugObserverIntoPolynomial):
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self.add_plane()
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self.add_circle_group()
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self.add_polynomial("O")
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self.add_observer_and_lines()
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self.show_all_animations()
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def add_observer_and_lines(self):
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def show_all_animations(self):
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fraction = self.observer_fraction = 0.3
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circle = self.circle
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@ -1821,13 +1845,294 @@ class DistanceProductIsChordF(PlugObserverIntoPolynomial):
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self.wait()
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class ProveLemma2(PlugObserverIntoPolynomial):
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CONFIG = {
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"include_lighthouses": False,
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"num_lighthouses": 8,
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# "ambient_light_config": CHEAP_AMBIENT_LIGHT_CONFIG,
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# "add_lights_in_foreground": False,
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}
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def construct(self):
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self.add_plane()
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self.add_circle_group()
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self.add_polynomial("O")
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self.replace_first_lighthouse()
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self.rearrange_polynomial()
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self.plug_in_one()
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def replace_first_lighthouse(self):
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light_to_remove = self.lights[0]
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dot = self.observer_dot = Dot(color=self.observer_config["color"])
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dot.move_to(self.get_circle_point_at_proportion(0.5 / self.num_lighthouses))
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arrow = Vector(0.5 * DL, color=WHITE)
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arrow.next_to(dot, UR, SMALL_BUFF)
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O_label = self.O_dot_label = TexMobject("O")
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O_label.match_color(dot)
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O_label.add_background_rectangle()
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O_label.next_to(arrow, UR, SMALL_BUFF)
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|
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# First, move the lighthouse
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self.add_foreground_mobject(dot)
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self.play(
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dot.move_to, light_to_remove,
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MaintainPositionRelativeTo(arrow, dot),
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MaintainPositionRelativeTo(O_label, dot),
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path_arc=-TAU / 2
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)
|
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|
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black_rect = Rectangle(
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height=6, width=3.5,
|
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stroke_width=0,
|
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fill_color=BLACK,
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fill_opacity=1,
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)
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black_rect.to_corner(DL, buff=0)
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lines = self.get_lines(self.circle.get_right())
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labels = self.get_numeric_distance_labels()
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column_group = self.get_distance_product_column(
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black_rect.get_top() + MED_SMALL_BUFF * DOWN
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)
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stacked_labels, h_line, times, product_decimal = column_group
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q_marks = self.q_marks = TextMobject("???")
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q_marks.move_to(product_decimal, LEFT)
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q_marks.match_color(product_decimal)
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|
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zero_rects = VGroup(*map(SurroundingRectangle, [dot, stacked_labels[0]]))
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|
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self.play(
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LaggedStart(ShowCreation, lines),
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LaggedStart(FadeIn, labels),
|
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)
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self.play(
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FadeIn(black_rect),
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ShowCreation(h_line),
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Write(times),
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ReplacementTransform(labels.copy(), stacked_labels)
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)
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self.wait()
|
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self.play(ReplacementTransform(
|
||||
stacked_labels.copy(),
|
||||
VGroup(product_decimal)
|
||||
))
|
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self.wait()
|
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self.add_foreground_mobject(zero_rects)
|
||||
self.play(*map(ShowCreation, zero_rects))
|
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self.wait(2)
|
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self.play(
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VGroup(light_to_remove, zero_rects[0]).shift, FRAME_WIDTH * RIGHT / 2,
|
||||
path_arc=-60 * DEGREES,
|
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rate_func=running_start,
|
||||
remover=True
|
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)
|
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self.play(
|
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VGroup(stacked_labels[0], zero_rects[1]).shift, 4 * LEFT,
|
||||
rate_func=running_start,
|
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remover=True,
|
||||
)
|
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self.remove_foreground_mobjects(zero_rects)
|
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self.play(
|
||||
FadeOut(product_decimal),
|
||||
FadeIn(q_marks)
|
||||
)
|
||||
self.play(FadeOut(labels))
|
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self.wait()
|
||||
|
||||
def rearrange_polynomial(self):
|
||||
dot = self.observer_dot
|
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lhs, equals, rhs = self.get_polynomial_split(self.polynomial)
|
||||
polynomial_background = self.polynomial[0]
|
||||
first_factor = rhs[:5]
|
||||
remaining_factors = rhs[5:]
|
||||
equals_remaining_factors = VGroup(equals, remaining_factors)
|
||||
|
||||
# first_factor_rect = SurroundingRectangle(first_factor)
|
||||
lhs_rect = SurroundingRectangle(lhs)
|
||||
|
||||
frac_line = Line(LEFT, RIGHT, color=WHITE)
|
||||
frac_line.match_width(lhs, stretch=True)
|
||||
frac_line.next_to(lhs, DOWN, SMALL_BUFF)
|
||||
O_minus_1 = TexMobject("\\left(", "O", "-", "1", "\\right)")
|
||||
O_minus_1.next_to(frac_line, DOWN, SMALL_BUFF)
|
||||
new_lhs_background = BackgroundRectangle(VGroup(lhs, O_minus_1), buff=SMALL_BUFF)
|
||||
new_lhs_rect = SurroundingRectangle(VGroup(lhs, O_minus_1))
|
||||
|
||||
roots_of_unity_circle = VGroup(*[
|
||||
Circle(radius=0.2, color=YELLOW).move_to(point)
|
||||
for point in self.get_lh_points()
|
||||
])
|
||||
for circle in roots_of_unity_circle:
|
||||
circle.save_state()
|
||||
circle.scale(4)
|
||||
circle.fade(1)
|
||||
|
||||
self.play(ShowCreation(lhs_rect))
|
||||
self.add_foreground_mobject(roots_of_unity_circle)
|
||||
self.play(LaggedStart(
|
||||
ApplyMethod, roots_of_unity_circle,
|
||||
lambda m: (m.restore,)
|
||||
))
|
||||
self.wait()
|
||||
frac_line_copy = frac_line.copy()
|
||||
self.play(
|
||||
FadeIn(new_lhs_background),
|
||||
polynomial_background.stretch, 0.8, 0,
|
||||
polynomial_background.move_to, frac_line_copy, LEFT,
|
||||
equals_remaining_factors.arrange_submobjects, RIGHT, SMALL_BUFF,
|
||||
equals_remaining_factors.next_to, frac_line_copy, RIGHT, MED_SMALL_BUFF,
|
||||
ReplacementTransform(first_factor, O_minus_1, path_arc=-90 * DEGREES),
|
||||
ShowCreation(frac_line),
|
||||
Animation(lhs),
|
||||
ReplacementTransform(lhs_rect, new_lhs_rect),
|
||||
)
|
||||
self.play(
|
||||
roots_of_unity_circle[0].shift, FRAME_WIDTH * RIGHT / 2,
|
||||
path_arc=(-60 * DEGREES),
|
||||
rate_func=running_start,
|
||||
remover=True
|
||||
)
|
||||
|
||||
# Expand rhs
|
||||
expanded_rhs = self.expanded_rhs = TexMobject(
|
||||
"=", "1", "+",
|
||||
"O", "+",
|
||||
"O", "^2", "+",
|
||||
"\\cdots",
|
||||
"O", "^{N-1}"
|
||||
)
|
||||
expanded_rhs.next_to(frac_line, RIGHT)
|
||||
expanded_rhs.shift(LEFT)
|
||||
expanded_rhs.scale(0.9)
|
||||
expanded_rhs.set_color_by_tex("O", dot.get_color())
|
||||
|
||||
self.play(
|
||||
polynomial_background.stretch, 1.8, 0, {"about_edge": LEFT},
|
||||
FadeIn(expanded_rhs),
|
||||
equals_remaining_factors.scale, 0.9,
|
||||
equals_remaining_factors.next_to, expanded_rhs,
|
||||
VGroup(
|
||||
new_lhs_background, lhs, frac_line, O_minus_1,
|
||||
new_lhs_rect,
|
||||
).shift, LEFT,
|
||||
)
|
||||
self.wait()
|
||||
|
||||
def plug_in_one(self):
|
||||
expanded_rhs = self.expanded_rhs
|
||||
O_terms = expanded_rhs.get_parts_by_tex("O")
|
||||
ones = VGroup(*[
|
||||
TexMobject("1").move_to(O_term, RIGHT)
|
||||
for O_term in O_terms
|
||||
])
|
||||
ones.match_color(O_terms[0])
|
||||
|
||||
equals_1 = TexMobject("= 1")
|
||||
equals_1.next_to(self.O_dot_label, RIGHT, SMALL_BUFF)
|
||||
brace = Brace(expanded_rhs[1:], DOWN)
|
||||
N_term = brace.get_text("N")
|
||||
|
||||
product = DecimalNumber(
|
||||
self.num_lighthouses,
|
||||
num_decimal_points=3,
|
||||
show_ellipsis=True
|
||||
)
|
||||
product.move_to(self.q_marks, LEFT)
|
||||
|
||||
self.play(Write(equals_1))
|
||||
self.play(
|
||||
FocusOn(brace),
|
||||
GrowFromCenter(brace)
|
||||
)
|
||||
self.wait(2)
|
||||
self.play(ReplacementTransform(O_terms, ones))
|
||||
self.wait()
|
||||
self.play(Write(N_term))
|
||||
self.play(FocusOn(product))
|
||||
self.play(
|
||||
FadeOut(self.q_marks),
|
||||
FadeIn(product)
|
||||
)
|
||||
self.wait()
|
||||
|
||||
|
||||
class ArmedWithTwoKeyFacts(TeacherStudentsScene, DistanceProductScene):
|
||||
CONFIG = {
|
||||
"num_lighthouses": 6,
|
||||
"ambient_light_config": {
|
||||
"opacity_function": inverse_power_law(1, 1, 1, 6),
|
||||
"radius": 1,
|
||||
"num_levels": 100,
|
||||
"max_opacity": 1,
|
||||
},
|
||||
}
|
||||
|
||||
def setup(self):
|
||||
TeacherStudentsScene.setup(self)
|
||||
DistanceProductScene.setup(self)
|
||||
|
||||
def construct(self):
|
||||
circle1 = self.circle
|
||||
circle1.scale_to_fit_height(1.5)
|
||||
circle1.to_corner(UL)
|
||||
circle2 = circle1.copy()
|
||||
circle2.next_to(circle1, DOWN, MED_LARGE_BUFF)
|
||||
|
||||
wallis_product = get_wallis_product(n_terms=8)
|
||||
|
||||
N = self.num_lighthouses
|
||||
labels = VGroup()
|
||||
for circle, f, dp in (circle1, 0.5, "2"), (circle2, 0, "N"):
|
||||
self.circle = circle
|
||||
lights = self.get_lights()
|
||||
if f == 0:
|
||||
lights.submobjects.pop(0)
|
||||
observer = Dot(color=MAROON_B)
|
||||
frac = f / N
|
||||
point = self.get_circle_point_at_proportion(frac)
|
||||
observer.move_to(point)
|
||||
lines = self.get_distance_lines(point, line_class=DashedLine)
|
||||
|
||||
label = TextMobject("Distance product = %s" % dp)
|
||||
label.scale(0.7)
|
||||
label.next_to(circle, RIGHT)
|
||||
labels.add(label)
|
||||
|
||||
group = VGroup(lines, observer, label)
|
||||
self.play(
|
||||
FadeIn(circle),
|
||||
LaggedStart(FadeIn, VGroup(*it.chain(lights))),
|
||||
LaggedStart(
|
||||
FadeIn, VGroup(*it.chain(group.family_members_with_points()))
|
||||
),
|
||||
self.teacher.change, "raise_right_hand",
|
||||
self.get_student_changes(*["pondering"] * 3)
|
||||
)
|
||||
wallis_product.move_to(labels).to_edge(RIGHT)
|
||||
self.play(
|
||||
LaggedStart(FadeIn, wallis_product),
|
||||
self.teacher.change_mode, "hooray",
|
||||
self.get_student_changes(*["thinking"] * 3, look_at_arg=wallis_product)
|
||||
)
|
||||
self.wait(2)
|
||||
|
||||
|
||||
class KeeperAndSailor(DistanceProductScene):
|
||||
CONFIG = {
|
||||
"num_lighthouses": 9,
|
||||
"ambient_light_config": CHEAP_AMBIENT_LIGHT_CONFIG,
|
||||
}
|
||||
|
||||
def construct(self):
|
||||
self.place_lighthouses()
|
||||
self.introduce_observers()
|
||||
|
||||
|
||||
class Test(Scene):
|
||||
def construct(self):
|
||||
product = get_wallis_product(8)
|
||||
product.get_parts_by_tex("\\over").set_color(YELLOW)
|
||||
self.add(product)
|
||||
|
||||
|
||||
|
||||
|
|
|
|||
|
|
@ -39,7 +39,7 @@ class PiCreatureScene(Scene):
|
|||
}
|
||||
|
||||
def setup(self):
|
||||
self.pi_creatures = self.create_pi_creatures()
|
||||
self.pi_creatures = VGroup(*self.create_pi_creatures())
|
||||
self.pi_creature = self.get_primary_pi_creature()
|
||||
if self.pi_creatures_start_on_screen:
|
||||
self.add(*self.pi_creatures)
|
||||
|
|
|
|||
|
|
@ -439,6 +439,9 @@ class DashedLine(Line):
|
|||
|
||||
def generate_points(self):
|
||||
length = np.linalg.norm(self.end - self.start)
|
||||
if length == 0:
|
||||
self.add(Line(self.start, self.end))
|
||||
return self
|
||||
num_interp_points = int(length / self.dashed_segment_length)
|
||||
points = [
|
||||
interpolate(self.start, self.end, alpha)
|
||||
|
|
|
|||
|
|
@ -165,7 +165,7 @@ class SVGMobject(VMobject):
|
|||
# input preprocessing
|
||||
if fill_color in ["", "none", "#FFF", "#FFFFFF"] or Color(fill_color) == Color(WHITE):
|
||||
opacity = 0
|
||||
fill_color = BLACK # shdn't be necessary but avoids error msgs
|
||||
fill_color = BLACK # shdn't be necessary but avoids error msgs
|
||||
if fill_color in ["#000", "#000000"]:
|
||||
fill_color = WHITE
|
||||
if stroke_color in ["", "none", "#FFF", "#FFFFFF"] or Color(stroke_color) == Color(WHITE):
|
||||
|
|
@ -175,10 +175,6 @@ class SVGMobject(VMobject):
|
|||
stroke_color = WHITE
|
||||
if stroke_width in ["", "none", "0"]:
|
||||
stroke_width = 0
|
||||
|
||||
# is there sth to draw?
|
||||
if opacity == 0 and stroke_width == 0:
|
||||
return
|
||||
|
||||
if corner_radius in ["", "0", "none"]:
|
||||
corner_radius = 0
|
||||
|
|
@ -187,22 +183,22 @@ class SVGMobject(VMobject):
|
|||
|
||||
if corner_radius == 0:
|
||||
mob = Rectangle(
|
||||
width = float(rect_element.getAttribute("width")),
|
||||
height = float(rect_element.getAttribute("height")),
|
||||
stroke_width = stroke_width,
|
||||
stroke_color = stroke_color,
|
||||
fill_color = fill_color,
|
||||
fill_opacity = opacity
|
||||
width=float(rect_element.getAttribute("width")),
|
||||
height=float(rect_element.getAttribute("height")),
|
||||
stroke_width=stroke_width,
|
||||
stroke_color=stroke_color,
|
||||
fill_color=fill_color,
|
||||
fill_opacity=opacity
|
||||
)
|
||||
else:
|
||||
mob = RoundedRectangle(
|
||||
width = float(rect_element.getAttribute("width")),
|
||||
height = float(rect_element.getAttribute("height")),
|
||||
stroke_width = stroke_width,
|
||||
stroke_color = stroke_color,
|
||||
fill_color = fill_color,
|
||||
fill_opacity = opacity,
|
||||
corner_radius = corner_radius
|
||||
width=float(rect_element.getAttribute("width")),
|
||||
height=float(rect_element.getAttribute("height")),
|
||||
stroke_width=stroke_width,
|
||||
stroke_color=stroke_color,
|
||||
fill_color=fill_color,
|
||||
fill_opacity=opacity,
|
||||
corner_radius=corner_radius
|
||||
)
|
||||
|
||||
mob.shift(mob.get_center() - mob.get_corner(UP + LEFT))
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue