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Finished ApproximateOneRing scene of eoc1
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Grant Sanderson
parent
ce93d88944
commit
8b12ec879e
1 changed files with 191 additions and 33 deletions
224
eoc/chapter1.py
224
eoc/chapter1.py
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@ -20,6 +20,7 @@ from topics.three_dimensions import *
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from topics.objects import *
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from scene import Scene
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from scene.zoomed_scene import ZoomedScene
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from scene.reconfigurable_scene import ReconfigurableScene
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from camera import Camera
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from mobject.svg_mobject import *
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from mobject.tex_mobject import *
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@ -178,7 +179,7 @@ class CircleScene(PiCreatureScene):
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rings.rotate, np.pi/2,
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rings.next_to, unwrapped.get_bottom(), UP,
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run_time = 2,
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path_arc = np.pi/2
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path_arc = np.pi/2,
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)
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self.play(
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Transform(rings, unwrapped, run_time = 3),
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@ -655,22 +656,24 @@ class IntroduceCircle(CircleScene):
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self.play(Write(VGroup(*ftc[-2:])))
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self.dither(2)
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class ApproximateOneRing(CircleScene):
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class ApproximateOneRing(CircleScene, ReconfigurableScene):
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CONFIG = {
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"num_lines" : 24,
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"ring_index_proportion" : 0.75,
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"ring_index_proportion" : 0.6,
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"ring_shift_val" : 6*RIGHT,
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"ring_colors" : [BLUE, GREEN_E],
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"unwrapped_tip" : 2*RIGHT+0.5*UP,
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}
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def construct(self):
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self.force_skipping()
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def setup(self):
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CircleScene.setup(self)
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ReconfigurableScene.setup(self)
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def construct(self):
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self.write_radius_three()
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self.try_to_understand_area()
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self.slice_into_rings()
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self.isolate_one_ring()
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self.straighten_ring_out()
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self.ask_about_precise_shape()
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self.approximate_as_rectangle()
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def write_radius_three(self):
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@ -738,14 +741,10 @@ class ApproximateOneRing(CircleScene):
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self.pi_creature.look_at, self.circle
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)
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self.dither(2)
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group = VGroup(self.circle, rings, self.radius_group)
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for x in range(2):
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self.play(
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ApplyMethod(
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group.rotate_in_place, np.pi,
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path_arc = np.pi,
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rate_func = there_and_back,
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),
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Rotate(rings, np.pi, in_place = True, run_time = 2),
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Animation(self.radius_group),
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self.pi_creature.change_mode, "happy"
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)
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self.dither(2)
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@ -753,51 +752,210 @@ class ApproximateOneRing(CircleScene):
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self.rings = rings
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def isolate_one_ring(self):
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index = int(self.ring_index_proportion*len(self.rings))
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ring = self.rings[index]
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rings = self.rings
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index = int(self.ring_index_proportion*len(rings))
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original_ring = rings[index]
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ring = original_ring.copy()
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radius = Line(ORIGIN, ring.R*RIGHT, color = WHITE)
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radius.rotate(np.pi/4)
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r_label = TexMobject("r")
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r_label.next_to(radius.get_center(), UP+LEFT, SMALL_BUFF)
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area_q = TextMobject("Area?")
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area_q = TextMobject("Area", "?", arg_separator = "")
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area_q.highlight(YELLOW)
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self.revert_to_original_skipping_status()
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self.play(ring.shift, self.ring_shift_val)
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self.play(
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ring.shift, self.ring_shift_val,
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original_ring.set_fill, None, 0.25,
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Animation(self.radius_group),
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)
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VGroup(radius, r_label).shift(ring.get_center())
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area_q.next_to(ring, DOWN)
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area_q.next_to(ring, RIGHT)
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self.play(ShowCreation(radius))
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self.play(Write(r_label))
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self.dither()
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self.play(Write(area_q))
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self.dither()
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self.play(
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Indicate(
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self.rings,
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scale_factor = 1.01,
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submobject_mode = "lagged_start",
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run_time = 3,
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),
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self.play(*[
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ApplyMethod(
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r.set_fill, YELLOW,
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rate_func = squish_rate_func(there_and_back, alpha, alpha+0.15),
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run_time = 3
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)
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for r, alpha in zip(rings, np.linspace(0, 0.85, len(rings)))
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]+[
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Animation(self.radius_group)
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)
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])
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self.dither()
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self.change_mode("thinking")
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self.dither()
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self.original_ring = original_ring
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self.ring = ring
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self.ring_radius_group = VGroup(radius, r_label)
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self.area_q = area_q
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def straighten_ring_out(self):
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pass
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ring = self.ring.copy()
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trapazoid = TextMobject("Trapazoid?")
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rectangle_ish = TextMobject("Rectangle-ish")
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for text in trapazoid, rectangle_ish:
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text.next_to(
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self.pi_creature.get_corner(UP+RIGHT),
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DOWN+RIGHT, buff = MED_LARGE_BUFF
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)
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def ask_about_precise_shape(self):
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pass
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self.unwrap_ring(ring, to_edge = RIGHT)
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self.change_mode("pondering")
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self.dither()
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self.play(Write(trapazoid))
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self.dither()
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self.play(trapazoid.shift, DOWN)
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strike = Line(
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trapazoid.get_left(), trapazoid.get_right(),
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stroke_color = RED,
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stroke_width = 8
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)
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self.play(
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Write(rectangle_ish),
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ShowCreation(strike),
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self.pi_creature.change_mode, "happy"
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)
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self.dither()
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self.play(*map(FadeOut, [trapazoid, strike]))
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self.unwrapped_ring = ring
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def approximate_as_rectangle(self):
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pass
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top_brace, side_brace = [
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Brace(
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self.unwrapped_ring, vect, buff = SMALL_BUFF,
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min_num_quads = 2,
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)
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for vect in UP, LEFT
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]
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top_brace.scale_in_place(self.ring.R/(self.ring.R+self.dR))
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side_brace.set_stroke(WHITE, 0.5)
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width_label = TexMobject("2\\pi", "r")
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width_label.next_to(top_brace, UP, SMALL_BUFF)
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dr_label = TexMobject("dr")
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q_marks = TexMobject("???")
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concrete_dr = TexMobject("=0.1")
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concrete_dr.submobjects.reverse()
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for mob in dr_label, q_marks, concrete_dr:
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mob.next_to(side_brace, LEFT, SMALL_BUFF)
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dr_label.save_state()
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alt_side_brace = side_brace.copy()
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alt_side_brace.move_to(ORIGIN, UP+RIGHT)
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alt_side_brace.rotate(-np.pi/2)
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alt_side_brace.shift(
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self.original_ring.get_boundary_point(RIGHT)
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)
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alt_dr_label = dr_label.copy()
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alt_dr_label.next_to(alt_side_brace, UP, SMALL_BUFF)
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approx = TexMobject("\\approx")
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approx.next_to(
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self.area_q.get_part_by_tex("Area"),
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RIGHT,
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align_using_submobjects = True,
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)
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two_pi_r_dr = VGroup(width_label, dr_label).copy()
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two_pi_r_dr.generate_target()
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two_pi_r_dr.target.arrange_submobjects(
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RIGHT, buff = SMALL_BUFF, aligned_edge = DOWN
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)
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two_pi_r_dr.target.next_to(approx, RIGHT, aligned_edge = DOWN)
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self.play(GrowFromCenter(top_brace))
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self.play(
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Write(width_label.get_part_by_tex("pi")),
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ReplacementTransform(
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self.ring_radius_group[1].copy(),
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width_label.get_part_by_tex("r")
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)
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)
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self.dither()
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self.play(
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GrowFromCenter(side_brace),
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Write(q_marks)
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)
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self.change_mode("confused")
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self.dither()
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for num_rings in 20, 7:
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self.show_alternate_width(num_rings)
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self.play(ReplacementTransform(q_marks, dr_label))
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self.play(
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ReplacementTransform(side_brace.copy(), alt_side_brace),
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ReplacementTransform(dr_label.copy(), alt_dr_label),
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run_time = 2
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)
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self.dither()
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self.play(
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dr_label.next_to, concrete_dr.copy(), LEFT, SMALL_BUFF, DOWN,
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Write(concrete_dr, run_time = 2),
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self.pi_creature.change_mode, "pondering"
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)
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self.dither(2)
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self.play(
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MoveToTarget(two_pi_r_dr),
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FadeIn(approx),
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self.area_q.get_part_by_tex("?").fade, 1,
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)
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self.dither()
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self.play(
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FadeOut(concrete_dr),
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dr_label.restore
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)
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self.show_alternate_width(
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40,
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transformation_kwargs = {"run_time" : 4},
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return_to_original_configuration = False,
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)
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self.dither(2)
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self.look_at(self.circle)
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self.play(
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ApplyWave(self.rings, amplitude = 0.1),
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Animation(self.radius_group),
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Animation(alt_side_brace),
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Animation(alt_dr_label),
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run_time = 3,
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submobject_mode = "lagged_start"
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)
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self.dither(2)
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def show_alternate_width(self, num_rings, **kwargs):
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self.transition_to_alt_config(
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dR = self.radius/num_rings, **kwargs
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)
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class GraphRectangles(CircleScene, GraphScene):
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CONFIG = {
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"x_min" : -1,
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"x_max" : 4,
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"x_axis_width" : 8,
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"x_labeled_nums" : range(1, 5),
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"x_axis_label" : "$r$",
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"y_min" : 0,
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"y_max" : 20,
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"y_tick_frequency" : 2.5,
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"y_labeled_nums" : range(5, 25, 5),
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"y+axis_label" : ""
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}
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def setup(self):
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CircleScene.setup(self)
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self.graph_origin = (self.circle.get_right()[0]+LARGE_BUFF)*RIGHT
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self.graph_origin += 3*DOWN
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GraphScene.setup(self)
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def construct(self):
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self.setup_axes()
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