mirror of
https://github.com/3b1b/videos.git
synced 2025-09-18 21:38:53 +00:00
Final inscribed rectangle animations
This commit is contained in:
Grant Sanderson
parent
8f54648b19
commit
00edbe600b
3 changed files with 254 additions and 18 deletions
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@ -96,7 +96,7 @@ class StateThePuzzle(LoopScene):
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loop = get_example_loop(4)
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loop.set_height(7)
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loop.move_to(2 * RIGHT)
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curve_words = Text("Closed\nContinus\nCurve", alignment="LEFT", font_size=72)
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curve_words = Text("Closed\nContinuous\nCurve", alignment="LEFT", font_size=72)
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curve_words.to_edge(LEFT)
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self.play(
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@ -162,14 +162,17 @@ class StateThePuzzle(LoopScene):
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self.wait()
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# Ambiently animate to various different loops
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def true_find_square(loop_func, trg_angle=90 * DEG, cost_tol=1e-2, max_tries=10):
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def true_find_square(loop_func, trg_angle=90 * DEG, cost_tol=1e-2, max_tries=8):
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ic = np.arange(0, 1, 0.25)
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min_params = ic
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min_cost = np.inf
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for x in range(max_tries):
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params, cost = find_rectangle(loop_func, target_angle=trg_angle, n_refinements=3, return_cost=True)
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if cost < cost_tol:
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break
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if cost < min_cost:
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min_params = params
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min_cost = cost
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ic = np.random.random(4)
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return params
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return min_params
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new_loops = [
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get_example_loop(1),
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@ -188,15 +191,19 @@ class StateThePuzzle(LoopScene):
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dots.resume_updating()
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self.add(dots, polygon)
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for new_loop in new_loops:
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self.remove(dots, polygon)
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self.play(
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Transform(loop, new_loop),
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UpdateFromFunc(
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quad_tracker,
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lambda m: m.set_value(true_find_square(loop_func))
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),
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run_time=5
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# UpdateFromFunc(
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# quad_tracker,
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# lambda m: m.set_value(true_find_square(loop_func))
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# ),
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run_time=1
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)
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self.wait()
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self.add(dots, polygon)
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for _ in range(5):
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quad_tracker.set_value(find_rectangle(loop_func, np.random.random(4), target_angle=90 * DEG))
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self.wait(0.5)
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# Change question to rectangle
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square_word = question["square"]
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@ -427,17 +434,18 @@ class ShowTheSurface(LoopScene):
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# Pair of points
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uv_tracker = ValueTracker([0, 0.5])
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dots = self.get_movable_pair(uv_tracker, loop_func, radius=0.05)
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dots = self.get_movable_pair(uv_tracker, loop_func, radius=0.075)
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connecting_line = self.get_connecting_line(dots)
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midpoint_dot = self.get_midpoint_dot(dots)
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self.add(uv_tracker)
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self.add(dots)
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self.add(connecting_line)
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self.play(
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UpdateFromFunc(uv_tracker, lambda m: m.set_value(np.random.random(2))),
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)
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self.add(dots)
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self.add(dots, connecting_line)
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self.play(uv_tracker.animate.set_value([0.8, 0.5]), run_time=3)
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# Add coordinates
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@ -2033,6 +2041,63 @@ class MapTheStripOntoTheSurface(ShowTheSurface):
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)
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class AmbientRectangleSearch(ShowTheSurface):
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def construct(self):
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# Setup loop
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frame = self.frame
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axes, plane = self.get_axes_and_plane()
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self.add(plane)
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loop = get_example_loop(2)
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loop.insert_n_curves(50)
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loop.set_height(5)
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loop.set_stroke(WHITE, 3)
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loop.set_fill(opacity=0)
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loop_func = get_quick_loop_func(loop)
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self.add(loop)
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# Dots
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abcd_tracker = ValueTracker(np.random.random(4))
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dots = self.get_movable_quad(abcd_tracker, loop_func, radius=0.1)
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polygon = self.get_dot_polygon(dots)
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polygon.set_stroke(YELLOW, 2)
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self.add(dots, polygon)
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# Various rectangles
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for _ in range(20):
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rect_params = find_rectangle(
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loop_func,
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initial_condition=np.random.random(4),
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target_angle=np.random.uniform(0, 90 * DEG),
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)
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self.play(abcd_tracker.animate.set_value(rect_params), run_time=2)
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self.wait()
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class GenericLoopPair(ShowTheSurface):
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def construct(self):
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loop = Circle(radius=2.5)
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loop.set_stroke(WHITE, 3)
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loop.set_fill(opacity=0)
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loop_func = get_quick_loop_func(loop)
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self.add(loop)
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uv_tracker = ValueTracker([0, 0.5])
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# self.set_uv_tracker_in_motion(uv_tracker, velocity=(0.1 * PI / 2, -0.1))
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dots = self.get_movable_pair(uv_tracker, loop_func, radius=0.075, colors=[YELLOW, YELLOW])
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connecting_line = self.get_connecting_line(dots)
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connecting_line.set_stroke(YELLOW)
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pair_group = Group(dots, connecting_line)
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self.add(uv_tracker, pair_group)
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# Wait
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for _ in range(20):
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self.play(uv_tracker.animate.set_value(np.random.random(2)), run_time=2)
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self.wait(0.5)
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class SudaneseBand(InteractiveScene):
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def construct(self):
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# Tranform mobius to Sudanese
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@ -2044,7 +2109,10 @@ class SudaneseBand(InteractiveScene):
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sudanese_band.set_height(6)
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frame.reorient(28, 75, 0, ORIGIN, 8)
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self.add(strip)
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# self.add(strip)
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self.add(sudanese_band)
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frame.add_ambient_rotation(6 * DEG)
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self.wait(60)
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self.play(frame.animate.increment_theta(180 * DEG), run_time=12)
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self.play(
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frame.animate.reorient(99, 102, 0),
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@ -2448,7 +2516,6 @@ class PuzzleOverMobiusDiagram(ConstructKleinBottle):
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)
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class ShowAngleInformation(ShowTheSurface):
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def construct(self):
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# Setup (fairly heavily copied from above)
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@ -167,6 +167,28 @@ class WhatIsTopology(InteractiveScene):
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self.wait()
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class ThreeShapes(InteractiveScene):
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def construct(self):
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# Test
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v_lines = Line(DOWN, UP).replicate(2)
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v_lines.set_height(FRAME_HEIGHT)
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v_lines.arrange(RIGHT, buff=FRAME_WIDTH / 3)
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v_lines.set_stroke(WHITE, 3)
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titles = VGroup(
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Text("Möbius Strip"),
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Text("Torus"),
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Text("Klein Bottle"),
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)
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for title, x in zip(titles, [-1, 0, 1]):
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title.scale(60 / 48)
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title.set_x(x * FRAME_WIDTH / 3)
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title.to_edge(UP)
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self.add(v_lines)
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self.add(titles)
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class ThisIsTheSame(InteractiveScene):
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def construct(self):
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# Test
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@ -264,6 +286,36 @@ class AskAboutProvingCollision(InteractiveScene):
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self.wait()
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class GraphOfBellCurve(InteractiveScene):
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def construct(self):
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# Test
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axes = ThreeDAxes((-3, 3), (-3, 3), (0, 1))
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axes.set_depth(2, stretch=True)
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surface = axes.get_graph(lambda x, y: np.exp(-x**2 - y**2))
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surface.set_opacity(0.7)
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surface.always_sort_to_camera(self.camera)
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mesh = SurfaceMesh(surface, resolution=(21, 21))
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mesh.set_stroke(WHITE, 0.5, 0.5)
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self.frame.reorient(42, 67, 0, (0.42, 0.43, 0.1), 6.03)
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self.frame.add_ambient_rotation(3 * DEG)
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self.add(axes)
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self.add(surface, mesh)
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self.wait(30)
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class GraphLabel(InteractiveScene):
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def construct(self):
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group = VGroup(
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Text("Graph of"),
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Tex(R"f(x, y) = e^{-x^2 - y^2}"),
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)
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group.arrange(DOWN)
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group.to_edge(UP)
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self.play(Write(group))
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self.wait()
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class ChekhovsGun(InteractiveScene):
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def construct(self):
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# Add image
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@ -519,7 +571,7 @@ class AskAboutUnsolved(InteractiveScene):
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def construct(self):
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randy = Randolph()
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randy.to_corner(DL)
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self.play(randy.says("What about the\nunsolvd problem?", "maybe"))
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self.play(randy.says("What about the\nunsolved problem?", "maybe"))
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self.play(Blink(randy))
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self.wait(2)
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@ -602,7 +654,7 @@ class GreeneLobbTheorem(InteractiveScene):
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Theorem by Greene and Lobb (2020):
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Every smooth closed curve contains
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inscribed rectangles of all possible
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aspect ratio.
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aspect ratios.
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""", t2s={"smooth": ITALIC}, alignment="LEFT")
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text.to_corner(UL)
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@ -640,3 +692,121 @@ class SmoothImplication(InteractiveScene):
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FadeIn(tangent, 0.5 * DOWN),
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)
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self.wait()
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class ProblemSolvingToRecreation(InteractiveScene):
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def construct(self):
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# Test
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words = VGroup(
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Text("Solving\nproblems"),
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Text("Helpful\nconstructs"),
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Text("Recreational\nmath"),
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)
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words.arrange(RIGHT, buff=2.5)
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words.set_y(-1.5)
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mind_bending = Text("(Sometimes Mind-bending)", font_size=24)
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mind_bending.next_to(words[1], DOWN)
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arrows = VGroup(
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Arrow(w1, w2, thickness=4, buff=0.45)
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for w1, w2 in zip(words, words[1:])
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)
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arrows.space_out_submobjects(1.1)
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self.play(FadeIn(words[0], lag_ratio=0.1))
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self.wait()
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self.play(
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FadeIn(words[1], lag_ratio=0.1),
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GrowArrow(arrows[0]),
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)
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self.wait()
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self.play(FadeIn(mind_bending, 0.25 * DOWN))
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self.wait()
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# Move mind-bending
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mb = mind_bending["Mind-bending"]
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helpful = words[1]["Helpful"]
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self.play(
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mb.animate.scale(2).move_to(helpful),
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FadeOut(helpful, 0.25 * UP),
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FadeOut(mind_bending["(Sometimes"][0]),
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FadeOut(mind_bending[")"][0]),
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)
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self.play(
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FadeIn(words[2], lag_ratio=0.1),
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GrowArrow(arrows[1]),
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)
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self.wait()
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self.play(
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words[0].animate.set_opacity(0.1),
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arrows[0].animate.set_opacity(0.1),
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)
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self.wait()
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class WriteTopologicalSpace(InteractiveScene):
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def construct(self):
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# Test
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text = Text("Topological Space", font_size=72)
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text.to_edge(UP)
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self.play(Write(text))
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self.wait()
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class AskAboutTopology(TeacherStudentsScene):
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def construct(self):
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morty = self.teacher
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stds = self.students
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self.play(
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stds[0].says("What is a\ntopological space?", "raise_left_hand"),
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stds[1].change("pondering", stds[0].eyes),
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stds[2].change("pondering", stds[0].eyes),
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morty.change("tease"),
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)
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self.wait(2)
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self.play(
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stds[1].animate.look_at(stds[2].eyes),
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stds[2].says("What is\ntopology?", "maybe", look_at=morty.eyes, bubble_direction=LEFT)
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)
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self.wait()
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self.play(morty.change("guilty"))
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self.play(stds[0].change('confused'))
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self.play(morty.change("hesitant"))
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self.wait(4)
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class PlaylistMention(InteractiveScene):
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def construct(self):
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# Test
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rects = ScreenRectangle().replicate(8)
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rects.set_fill(GREY_E, 1)
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rects.set_stroke(WHITE, 1)
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group = Group()
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for x, rect in zip(np.linspace(1, 0, len(rects)), rects):
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rect.shift(x * 0.75 * UR)
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group.add(rect)
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group.add(Point())
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thumbnail = ImageMobject("https://img.youtube.com/vi/OkmNXy7er84/maxresdefault.jpg")
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thumbnail.replace(rects[-1])
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group.add(thumbnail)
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group.set_height(2)
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group.to_edge(UP, buff=1.0)
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words = Text("More neat proofs\nand puzzle solutions")
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words.next_to(group, DOWN, buff=2.5)
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arrow = Arrow(words, group)
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self.play(
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FadeIn(group, UP),
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Write(words),
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GrowArrow(arrow)
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)
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self.wait()
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self.play(FadeOut(words), FadeOut(arrow))
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class EndScreen(PatreonEndScreen):
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title_text = ""
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@ -53,7 +53,6 @@ def get_full_surface(band_func, x_range):
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bound.apply_depth_test()
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meshes.set_stroke(WHITE, 0.5, 0.5)
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return Group(surface, m1, m2, bound)
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return Group(surface, bound)
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def get_sudanese_band(circle_on_xy_plane=False):
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