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End of Wallis project
This commit is contained in:
Grant Sanderson
parent
e31ede3393
commit
8127d9482b
2 changed files with 354 additions and 11 deletions
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@ -1,3 +1,5 @@
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# -*- coding: utf-8 -*-
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from big_ol_pile_of_manim_imports import *
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from once_useful_constructs.light import AmbientLight
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from once_useful_constructs.light import Lighthouse
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@ -11,6 +13,13 @@ CHEAP_AMBIENT_LIGHT_CONFIG = {
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"radius": 0.25,
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"opacity_function": DEFAULT_OPACITY_FUNCTION,
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}
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HIGHT_QUALITY_AMBIENT_LIGHT_CONFIG = {
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"opacity_function": DEFAULT_OPACITY_FUNCTION,
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"num_levels": 100,
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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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def get_chord_f_label(chord, arg="f", direction=DOWN):
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@ -376,6 +385,16 @@ class SourcesOfOriginality(TeacherStudentsScene):
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self.wait(5)
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class Six(Scene):
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def construct(self):
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six = TexMobject("6")
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six.add_background_rectangle(opacity = 1)
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six.background_rectangle.stretch(1.5, 0)
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six.scale_to_fit_height(7)
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self.add(six)
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class SridharWatchingScene(PiCreatureScene):
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CONFIG = {
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"default_pi_creature_kwargs": {
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@ -756,15 +775,25 @@ class ShowProduct(Scene):
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return axes
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class TeacherShowing(TeacherStudentsScene):
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def construct(self):
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screen = self.screen
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screen.scale_to_fit_height(4)
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screen.next_to(self.students, UP, MED_LARGE_BUFF, RIGHT)
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self.play(
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ShowCreation(screen),
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self.teacher.change, "raise_right_hand", screen,
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self.get_student_changes(
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*["pondering"] * 3,
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look_at_arg=screen
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)
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)
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self.wait(5)
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class DistanceProductScene(MovingCameraScene):
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CONFIG = {
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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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"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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"ambient_light_config": HIGHT_QUALITY_AMBIENT_LIGHT_CONFIG,
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"circle_color": BLUE,
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"circle_radius": 3,
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"num_lighthouses": 6,
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@ -1467,6 +1496,16 @@ class Lemma2With9Lighthouses(Lemma2):
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}
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class ConfusedPiCreature(Scene):
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def construct(self):
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randy = Randolph(color=GREY_BROWN)
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self.add(randy)
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self.play(Blink(randy))
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self.play(randy.change, "confused")
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self.play(Blink(randy))
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self.wait()
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class FromGeometryToAlgebra(DistanceProductScene):
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CONFIG = {
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"num_lighthouses": 7,
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@ -4917,9 +4956,313 @@ class KeeperAndSailorForSineProduct(KeeperAndSailor):
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self.wait()
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class Conclusion(TeacherStudentsScene):
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CONFIG = {
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"camera_config": {"background_alpha": 255},
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}
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def construct(self):
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wallis_product = get_wallis_product(6)
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wallis_product.move_to(self.hold_up_spot, DOWN)
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wallis_product.shift_onto_screen()
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for i in range(0, len(wallis_product) - 5, 4):
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color = GREEN if (i / 4) % 2 == 0 else BLUE
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wallis_product[i:i + 3].set_color(color)
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sine_formula = TexMobject(
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"\\sin(", "f", "\\pi", ")", "=", "f", "\\pi",
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"\\prod_{k \\ne 0}", "\\left(", "1", "-",
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"{f", "\\over", "k}", "\\right)"
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)
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sine_formula.set_color_by_tex("f", GREEN)
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sine_formula.set_color_by_tex("left", WHITE)
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sine_formula.move_to(self.hold_up_spot, DOWN)
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sine_formula.shift_onto_screen()
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euler = ImageMobject("Euler")
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euler.scale_to_fit_height(2.5)
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basel_problem = TexMobject(
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"\\frac{1}{1^2} + ",
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"\\frac{1}{2^2} + ",
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"\\frac{1}{3^2} + ",
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"\\cdots",
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"\\frac{\\pi^2}{6}"
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)
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basel_problem.move_to(self.hold_up_spot, DOWN)
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implication = TexMobject("\\Rightarrow")
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implication.next_to(basel_problem[0][1], LEFT)
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self.play(
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self.teacher.change, "raise_right_hand",
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FadeInFromDown(wallis_product),
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self.get_student_changes("thinking", "hooray", "surprised")
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)
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self.wait()
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self.play(
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self.teacher.change, "hooray",
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FadeInFromDown(sine_formula),
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wallis_product.to_edge, UP,
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self.get_student_changes("pondering", "thinking", "erm")
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)
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self.wait(3)
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self.play(
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sine_formula.next_to, implication, LEFT,
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{"submobject_to_align": sine_formula[-1]},
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FadeIn(implication),
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)
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euler.next_to(sine_formula, UP)
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self.play(
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FadeIn(euler),
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LaggedStart(FadeIn, basel_problem),
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self.teacher.change, "happy",
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self.get_student_changes("sassy", "confused", "hesitant")
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)
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self.wait(2)
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wallis_rect = SurroundingRectangle(wallis_product)
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wallis_rect.set_color(BLUE)
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basel_rect = SurroundingRectangle(basel_problem)
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basel_rect.set_color(YELLOW)
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self.play(
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ShowCreation(wallis_rect),
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FadeOut(implication),
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FadeOut(euler),
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FadeOut(sine_formula),
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)
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self.play(
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ShowCreation(basel_rect),
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self.teacher.change, "surprised",
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self.get_student_changes(*["happy"] * 3)
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)
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self.wait(5)
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class ByLine(Scene):
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def construct(self):
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self.add(TextMobject("""
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Written and animated by \\\\
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\\quad \\\\
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Sridhar Ramesh \\\\
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Grant Sanderson
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""").shift(2 * UP))
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class SponsorUnderlay(PiCreatureScene):
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CONFIG = {
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"default_pi_creature_start_corner": DR,
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}
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def construct(self):
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url = TextMobject("https://udacity.com/3b1b/")
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url.to_corner(UL)
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rect = ScreenRectangle(height=5.5)
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rect.next_to(url, DOWN)
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rect.to_edge(LEFT)
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url.next_to(rect, UP)
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url.save_state()
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url.next_to(self.pi_creature.get_corner(UL), UP)
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logo = SVGMobject(file_name="udacity")
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logo.set_fill("#02b3e4")
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logo.to_corner(UR)
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self.add(logo)
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self.play(
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Write(url),
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self.pi_creature.change, "raise_right_hand"
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)
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self.play(
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url.restore,
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ShowCreation(rect),
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path_arc=90 * DEGREES,
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)
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self.wait(2)
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self.change_mode("thinking")
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self.wait()
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self.look_at(url)
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self.wait(10)
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self.change_mode("happy")
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self.wait(10)
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self.change_mode("raise_right_hand")
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self.wait(10)
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self.remove(rect)
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self.play(url.next_to, self.pi_creature, UL)
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url_rect = SurroundingRectangle(url)
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self.play(ShowCreation(url_rect))
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self.play(FadeOut(url_rect))
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self.wait(3)
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class EndScreen(PatreonEndScreen):
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CONFIG = {
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"specific_patrons": [
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"Juan Benet",
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"Keith Smith",
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"Chloe Zhou",
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"Ross Garber",
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"Desmos",
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"Burt Humburg",
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"CrypticSwarm",
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"Hoang Tung Lam",
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"Sergei",
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"Devin Scott",
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"George John",
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"Akash Kumar",
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"Felix Tripier",
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"Arthur Zey",
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"David Kedmey",
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"Ali Yahya",
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"Mayank M. Mehrotra",
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"Lukas Biewald",
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"Yana Chernobilsky",
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"Kaustuv DeBiswas",
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"Yu Jun",
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"dave nicponski",
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"Damion Kistler",
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"Jordan Scales",
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"Markus Persson",
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"Fred Ehrsam",
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"Britt Selvitelle",
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"Jonathan Wilson",
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"Ryan Atallah",
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"Joseph John Cox",
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"Luc Ritchie",
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"Cooper Jones",
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"James Hughes",
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"John V Wertheim",
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"Chris Giddings",
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"Song Gao",
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"William Fritzon",
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"Alexander Feldman",
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# "孟子易",
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"Mengzi yi",
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"zheng zhang",
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"Matt Langford",
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"Max Mitchell",
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"Richard Burgmann",
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"John Griffith",
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"Chris Connett",
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"Steven Tomlinson",
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"Jameel Syed",
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"Bong Choung",
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"Ignacio Freiberg",
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"Zhilong Yang",
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"Dan Esposito (Guardion)",
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"Giovanni Filippi",
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"Eric Younge",
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"Prasant Jagannath",
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"Cody Brocious",
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"James H. Park",
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"Norton Wang",
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"Kevin Le",
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"Tianyu Ge",
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"David MacCumber",
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"Oliver Steele",
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"Yaw Etse",
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"Dave B",
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"Waleed Hamied",
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"George Chiesa",
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"supershabam",
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"Delton Ding",
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"Thomas Tarler",
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"Jonathan Eppele",
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"Isak Hietala",
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"1stViewMaths",
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"Jacob Magnuson",
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"Mark Govea",
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"Clark Gaebel",
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"Mathias Jansson",
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"David Clark",
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"Michael Gardner",
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"Mads Elvheim",
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"Awoo",
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"Dr David G. Stork",
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"Ted Suzman",
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"Linh Tran",
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"Andrew Busey",
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"John Haley",
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"Ankalagon",
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"Eric Lavault",
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"Boris Veselinovich",
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"Julian Pulgarin",
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"Jeff Linse",
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"Ryan Dahl",
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"Robert Teed",
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"Jason Hise",
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"Meshal Alshammari",
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"Bernd Sing",
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"James Thornton",
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"Mustafa Mahdi",
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"Mathew Bramson",
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"Jerry Ling",
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# "世珉 匡",
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"Shi min kuang",
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"Rish Kundalia",
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"Achille Brighton",
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"Ripta Pasay",
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]
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}
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class Thumbnail(DistanceProductScene):
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def construct(self):
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product = get_wallis_product()
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product.scale(1.5)
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product.move_to(2.5 * UP)
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frac_lines = product.get_parts_by_tex("\\over")
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frac_indices = map(product.index_of_part, frac_lines)
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parts = VGroup(*[
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product[i-1:i+2]
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for i in frac_indices
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])
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parts[::2].set_color(GREEN)
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parts[1::2].set_color(BLUE)
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parts[-1].set_color(WHITE)
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parts[-1].set_stroke(RED, 1)
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parts[-1].scale(1.5, about_edge=LEFT)
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new_proof = TextMobject("New proof")
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new_proof.scale(2.5)
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new_proof.set_color(YELLOW)
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new_proof.set_stroke(RED, 0.75)
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new_proof.next_to(product, DOWN, MED_LARGE_BUFF)
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circle = self.circle = Circle(radius=8, color=RED)
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circle.move_to(3 * DOWN, DOWN)
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bottom_dot = Dot(color=BLUE)
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bottom_dot.move_to(circle.get_bottom())
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observer = PiCreature(mode="pondering")
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observer.scale_to_fit_height(0.5)
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observer.next_to(bottom_dot, DOWN)
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lights = VGroup()
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lines = VGroup()
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light_config = dict(HIGHT_QUALITY_AMBIENT_LIGHT_CONFIG)
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# light_config = dict(CHEAP_AMBIENT_LIGHT_CONFIG)
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light_config["max_opacity"] = 1
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step = 0.03
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for frac in np.arange(step, 0.2, step):
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for u in -1, 1:
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light = AmbientLight(**light_config)
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dot = Dot(color=BLUE)
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dot.move_to(light)
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light.add_to_back(dot)
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light.move_to(self.get_circle_point_at_proportion(u * frac - 0.25))
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lights.add(light)
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line = DashedLine(dot.get_center(), circle.get_bottom())
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lines.add(line)
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self.add(circle)
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self.add(lights)
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self.add(product)
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self.add(new_proof)
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self.add(bottom_dot, observer)
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@ -72,8 +72,8 @@ class ImageMobject(Mobject):
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DOWN + LEFT,
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])
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self.center()
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self.scale_to_fit_height(self.height)
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h, w = self.pixel_array.shape[:2]
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self.stretch_to_fit_height(self.height)
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self.stretch_to_fit_width(self.height * w / h)
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def set_opacity(self, alpha):
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Add table
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