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Retired sphere_area and for_flammy
This commit is contained in:
Grant Sanderson
339
old_projects/for_flammy.py
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339
old_projects/for_flammy.py
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from big_ol_pile_of_manim_imports import *
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from old_projects.sphere_area import *
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class MadAtMathologer(PiCreatureScene):
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def create_pi_creature(self):
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return Mortimer().to_corner(DR)
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def construct(self):
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morty = self.pi_creature
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self.play(morty.change, "angry")
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self.wait(3)
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self.play(morty.change, "heistant")
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self.wait(2)
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self.play(morty.change, "shruggie")
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self.wait(3)
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class JustTheIntegral(Scene):
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def construct(self):
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tex = TexMobject("\\int_0^{\\pi / 2} \\cos(\\theta)d\\theta")
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tex.scale(2)
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self.add(tex)
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class SphereVideoWrapper(Scene):
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def construct(self):
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title = TextMobject("Surface area of a sphere")
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title.scale(1.5)
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title.to_edge(UP)
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rect = ScreenRectangle(height=6)
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rect.next_to(title, DOWN)
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self.add(title)
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self.play(ShowCreation(rect))
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self.wait()
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class SphereRings(SecondProof):
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CONFIG = {
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"sphere_config": {
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"resolution": (60, 60),
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},
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}
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def construct(self):
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self.setup_shapes()
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self.grow_rings()
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self.show_one_ring()
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self.show_radial_line()
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self.show_thickness()
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self.flash_through_rings()
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def grow_rings(self):
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sphere = self.sphere
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rings = self.rings
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north_rings = rings[:len(rings) // 2]
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sphere.set_fill(opacity=0)
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sphere.set_stroke(WHITE, 0.5, opacity=0.5)
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southern_mesh = VGroup(*[
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face.copy() for face in sphere
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if face.get_center()[2] < 0
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])
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southern_mesh.set_stroke(WHITE, 0.1, 0.5)
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self.play(Write(sphere))
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self.wait()
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self.play(
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FadeOut(sphere),
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FadeIn(southern_mesh),
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FadeIn(north_rings),
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)
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self.wait(4)
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self.north_rings = north_rings
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self.southern_mesh = southern_mesh
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def show_one_ring(self):
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north_rings = self.north_rings
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index = len(north_rings) // 2
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ring = north_rings[index]
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to_fade = VGroup(*[
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nr for nr in north_rings
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if nr is not ring
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])
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north_rings.save_state()
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circle = Circle()
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circle.set_stroke(PINK, 5)
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circle.set_width(ring.get_width())
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circle.move_to(ring, IN)
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thickness = ring.get_depth() * np.sqrt(2)
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brace = Brace(Line(ORIGIN, 0.2 * RIGHT), UP)
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brace.set_width(thickness)
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brace.rotate(90 * DEGREES, RIGHT)
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brace.rotate(45 * DEGREES, UP)
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brace.move_to(1.5 * (RIGHT + OUT))
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brace.set_stroke(WHITE, 1)
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word = TextMobject("Thickness")
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word.rotate(90 * DEGREES, RIGHT)
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word.next_to(brace, RIGHT + OUT, buff=0)
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self.play(
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to_fade.set_fill, {"opacity": 0.2},
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to_fade.set_stroke, {"opacity": 0.0},
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)
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self.move_camera(
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phi=0, theta=-90 * DEGREES,
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run_time=2,
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)
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self.stop_ambient_camera_rotation()
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self.play(ShowCreation(circle))
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self.play(FadeOut(circle))
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self.move_camera(
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phi=70 * DEGREES,
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theta=-100 * DEGREES,
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run_time=2,
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)
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self.begin_ambient_camera_rotation(0.02)
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self.play(
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GrowFromCenter(brace),
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Write(word),
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)
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self.wait(2)
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self.play(FadeOut(VGroup(brace, word)))
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self.circum_circle = circle
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self.thickness_label = VGroup(brace, word)
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self.ring = ring
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def show_radial_line(self):
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ring = self.ring
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point = ring.get_corner(RIGHT + IN)
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R_line = Line(ORIGIN, point)
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xy_line = Line(ORIGIN, self.sphere.get_right())
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theta = np.arccos(np.dot(
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normalize(R_line.get_vector()),
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normalize(xy_line.get_vector())
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))
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arc = Arc(angle=theta, radius=0.5)
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arc.rotate(90 * DEGREES, RIGHT, about_point=ORIGIN)
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theta = TexMobject("\\theta")
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theta.rotate(90 * DEGREES, RIGHT)
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theta.next_to(arc, RIGHT)
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theta.shift(SMALL_BUFF * (LEFT + OUT))
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R_label = TexMobject("R")
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R_label.rotate(90 * DEGREES, RIGHT)
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R_label.next_to(
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R_line.get_center(), OUT + LEFT,
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buff=SMALL_BUFF
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)
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VGroup(R_label, R_line).set_color(YELLOW)
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z_axis_point = np.array(point)
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z_axis_point[:2] = 0
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r_line = DashedLine(z_axis_point, point)
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r_line.set_color(RED)
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r_label = TexMobject("R\\cos(\\theta)")
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r_label.rotate(90 * DEGREES, RIGHT)
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r_label.scale(0.7)
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r_label.match_color(r_line)
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r_label.set_stroke(width=0, background=True)
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r_label.next_to(r_line, OUT, 0.5 * SMALL_BUFF)
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VGroup(
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R_label, xy_line, arc, R_label,
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r_line, r_label,
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).set_shade_in_3d(True)
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# self.stop_ambient_camera_rotation()
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self.move_camera(
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phi=85 * DEGREES,
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theta=-100 * DEGREES,
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added_anims=[
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ring.set_fill, {"opacity": 0.5},
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ring.set_stroke, {"opacity": 0.1},
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ShowCreation(R_line),
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FadeInFrom(R_label, IN),
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]
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)
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self.wait()
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self.play(
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FadeIn(xy_line),
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ShowCreation(arc),
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Write(theta),
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)
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self.wait()
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self.play(
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ShowCreation(r_line),
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FadeInFrom(r_label, IN),
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)
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self.wait()
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self.move_camera(
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phi=70 * DEGREES,
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theta=-110 * DEGREES,
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run_time=3
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)
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self.wait(2)
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def show_thickness(self):
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brace, word = self.thickness_label
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R_dtheta = TexMobject("R \\, d\\theta")
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R_dtheta.rotate(90 * DEGREES, RIGHT)
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R_dtheta.move_to(word, LEFT)
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self.play(
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GrowFromCenter(brace),
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Write(R_dtheta)
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)
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self.wait(3)
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def flash_through_rings(self):
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rings = self.north_rings.copy()
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rings.fade(1)
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rings.sort_submobjects(lambda p: p[2])
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for x in range(8):
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self.play(LaggedStart(
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ApplyMethod, rings,
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lambda m: (m.set_fill, PINK, 0.5),
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rate_func=there_and_back,
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lag_ratio=0.1,
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run_time=2,
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))
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class IntegralSymbols(Scene):
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def construct(self):
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int_sign = TexMobject("\\displaystyle \\int")
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int_sign.set_height(1.5)
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int_sign.move_to(5 * LEFT)
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circumference, times, thickness = ctt = TextMobject(
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"circumference", "$\\times$", "thickness"
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)
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circumference.set_color(MAROON_B)
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ctt.next_to(int_sign, RIGHT, SMALL_BUFF)
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area_brace = Brace(ctt, DOWN)
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area_text = area_brace.get_text("Area of a ring")
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all_rings = TextMobject("All rings")
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all_rings.scale(0.5)
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all_rings.next_to(int_sign, DOWN, SMALL_BUFF)
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all_rings.shift(SMALL_BUFF * LEFT)
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circum_formula = TexMobject(
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"2\\pi", "R\\cos(\\theta)",
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)
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circum_formula[1].set_color(RED)
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circum_formula.move_to(circumference)
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circum_brace = Brace(circum_formula, UP)
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R_dtheta = TexMobject("R \\, d\\theta")
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R_dtheta.move_to(thickness, LEFT)
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R_dtheta_brace = Brace(R_dtheta, UP)
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zero, pi_halves = bounds = TexMobject("0", "\\pi / 2")
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bounds.scale(0.5)
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zero.move_to(all_rings)
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pi_halves.next_to(int_sign, UP, SMALL_BUFF)
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pi_halves.shift(SMALL_BUFF * RIGHT)
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self.add(int_sign)
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self.play(
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GrowFromCenter(area_brace),
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FadeInFrom(area_text, UP),
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)
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self.wait()
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self.play(FadeInFromDown(circumference))
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self.play(
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FadeInFromDown(thickness),
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Write(times)
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)
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self.play(Write(all_rings))
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self.wait()
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self.play(
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circumference.next_to, circum_brace, UP, MED_SMALL_BUFF,
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circumference.shift, SMALL_BUFF * UR,
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GrowFromCenter(circum_brace),
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)
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self.play(FadeInFrom(circum_formula, UP))
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self.wait()
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self.play(
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thickness.next_to, circumference, RIGHT, MED_SMALL_BUFF,
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GrowFromCenter(R_dtheta_brace),
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area_brace.stretch, 0.84, 0, {"about_edge": LEFT},
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MaintainPositionRelativeTo(area_text, area_brace),
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)
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self.play(FadeInFrom(R_dtheta, UP))
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self.wait()
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self.play(ReplacementTransform(all_rings, bounds))
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self.wait()
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# RHS
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rhs = TexMobject(
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"\\displaystyle =", "2\\pi R^2", "\\int_0^{\\pi / 2}",
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"\\cos(\\theta)", "d\\theta",
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)
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rhs.set_color_by_tex("cos", RED)
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rhs.next_to(R_dtheta, RIGHT)
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int_brace = Brace(rhs[2:], DOWN)
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q_marks = int_brace.get_text("???")
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one = TexMobject("1")
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one.move_to(q_marks)
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self.play(FadeInFrom(rhs, 4 * LEFT))
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self.wait()
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self.play(CircleThenFadeAround(rhs[1]))
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self.wait()
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self.play(CircleThenFadeAround(rhs[2:]))
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self.wait()
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self.play(
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GrowFromCenter(int_brace),
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LaggedStart(
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FadeInFrom, q_marks,
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lambda m: (m, UP),
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)
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)
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self.wait()
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self.play(ReplacementTransform(q_marks, one))
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self.wait()
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class ShamelessPlug(TeacherStudentsScene):
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def construct(self):
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self.student_says(
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"But why $4\\pi R^2$?",
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target_mode="maybe"
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)
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self.change_student_modes(
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"erm", "maybe", "happy",
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added_anims=[self.teacher.change, "happy"]
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)
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self.wait(3)
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