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xt-plane to heat graph animations
This commit is contained in:
Grant Sanderson
@ -2,6 +2,7 @@ from active_projects.ode.part2.staging import *
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from active_projects.ode.part2.fourier_series import *
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from active_projects.ode.part2.heat_equation import *
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from active_projects.ode.part2.pi_scenes import *
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from active_projects.ode.part2.wordy_scenes import *
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OUTPUT_DIRECTORY = "ode/part2"
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ALL_SCENE_CLASSES = [
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@ -30,7 +31,14 @@ ALL_SCENE_CLASSES = [
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TwoDBodyWithManyTemperaturesContour,
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BringTwoRodsTogether,
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ShowEvolvingTempGraphWithArrows,
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TodaysTargetWrapper,
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WriteHeatEquation,
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ReactionsToInitialHeatEquation,
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TalkThrough1DHeatGraph,
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ShowCubeFormation,
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CompareInputsOfGeneralCaseTo1D,
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TransitionToTempVsTime,
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ShowNewton,
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ShowCupOfWater,
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ShowNewtonsLawGraph,
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]
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@ -603,12 +603,12 @@ class TalkThrough1DHeatGraph(ShowEvolvingTempGraphWithArrows, SpecialThreeDScene
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graph = self.graph
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x_axis = axes.x_axis
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x_numbers = x_axis.get_number_mobjects(*range(1, 11))
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x_label = TexMobject("x")
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x_label.next_to(x_axis.get_right(), UP)
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x_axis_label = TexMobject("x")
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x_axis_label.next_to(x_axis.get_right(), UP)
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self.play(
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rod.set_opacity, 0.5,
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FadeInFrom(x_label, UL),
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FadeInFrom(x_axis_label, UL),
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LaggedStartMap(
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FadeInFrom, x_numbers,
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lambda m: (m, UP),
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@ -714,6 +714,7 @@ class TalkThrough1DHeatGraph(ShowEvolvingTempGraphWithArrows, SpecialThreeDScene
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graph_dot, t_label,
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)
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self.set_variables_as_attrs(*self.graph_label_group)
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self.set_variables_as_attrs(x_numbers, x_axis_label)
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def show_changes_over_time(self):
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graph = self.graph
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@ -772,12 +773,22 @@ class TalkThrough1DHeatGraph(ShowEvolvingTempGraphWithArrows, SpecialThreeDScene
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def show_surface(self):
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axes = self.axes
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graph = self.graph
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axes_copy = axes.deepcopy()
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# Time axis
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t_min = 0
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t_max = 10
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axes_copy = axes.deepcopy()
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original_axes = self.axes
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# Set rod final state
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final_graph = self.get_graph(t_max)
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curr_graph = self.graph
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self.graph = final_graph
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final_rod = self.rod.copy()
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final_rod.set_opacity(1)
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self.color_rod_by_graph(final_rod)
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self.graph = curr_graph
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# Time axis
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t_axis = NumberLine(
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x_min=t_min,
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x_max=t_max,
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@ -791,6 +802,7 @@ class TalkThrough1DHeatGraph(ShowEvolvingTempGraphWithArrows, SpecialThreeDScene
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time_label = TextMobject("Time")
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time_label.scale(1.5)
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time_label.next_to(t_axis, UP)
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t_axis.time_label = time_label
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t_axis.add(time_label)
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# t_axis.rotate(90 * DEGREES, LEFT, about_point=origin)
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t_axis.rotate(90 * DEGREES, UP, about_point=origin)
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@ -804,6 +816,7 @@ class TalkThrough1DHeatGraph(ShowEvolvingTempGraphWithArrows, SpecialThreeDScene
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for t in np.arange(0, t_max + step, step)
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])
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graph_slices.set_stroke(width=1)
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graph_slices.set_shade_in_3d(True)
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# Input plane
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x_axis = self.axes.x_axis
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@ -885,12 +898,23 @@ class TalkThrough1DHeatGraph(ShowEvolvingTempGraphWithArrows, SpecialThreeDScene
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LaggedStart(*[
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TransformFromCopy(graph, graph_slice)
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for graph_slice in graph_slices
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])
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], lag_ratio=0.02)
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)
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self.wait(4)
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# Show slices
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self.axes = axes_copy # So get_graph works...
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slicing_plane = Rectangle(
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stroke_width=0,
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fill_color=WHITE,
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fill_opacity=0.2,
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)
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slicing_plane.set_shade_in_3d(True)
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slicing_plane.replace(
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Line(axes_copy.c2p(0, 0), axes_copy.c2p(10, 100)),
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stretch=True
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)
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self.orient_mobject_for_3d(slicing_plane)
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def get_time_slice(t):
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new_slice = self.get_graph(t)
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@ -905,18 +929,26 @@ class TalkThrough1DHeatGraph(ShowEvolvingTempGraphWithArrows, SpecialThreeDScene
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get_time_slice(t_tracker.get_value())
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))
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self.orient_mobject_for_3d(final_rod)
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final_rod.shift(10 * UP)
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kw = {"run_time": 10, "rate_func": linear}
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self.play(
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t_tracker.set_value, 10,
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self.rod.shift, 10 * UP,
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ApplyMethod(
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graph_slices.set_stroke, {"opacity": 0.5},
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rate_func=squish_rate_func(smooth, 0, 0.2),
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),
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run_time=10,
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rate_func=linear,
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ApplyMethod(t_tracker.set_value, 10, **kw),
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Transform(self.rod, final_rod, **kw),
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ApplyMethod(slicing_plane.shift, 10 * UP, **kw),
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)
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graph.clear_updaters()
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self.wait()
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self.set_variables_as_attrs(
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t_axis,
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input_plane,
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surface,
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graph_slices,
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slicing_plane,
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)
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self.axes = original_axes
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#
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def get_graph(self, time=0):
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graph = self.axes.get_graph(
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@ -954,5 +986,177 @@ class TalkThrough1DHeatGraph(ShowEvolvingTempGraphWithArrows, SpecialThreeDScene
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axis=RIGHT,
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about_point=ORIGIN
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)
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mob.shift(1 * DOWN)
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return mob
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class TransitionToTempVsTime(TalkThrough1DHeatGraph):
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def construct(self):
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self.force_skipping()
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# super().construct()
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self.add_axes()
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self.add_graph()
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self.add_rod()
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# self.emphasize_graph()
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# self.emphasize_rod()
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self.rod_word = Point()
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self.show_x_axis()
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# self.show_changes_over_time()
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self.show_surface()
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self.revert_to_original_skipping_status()
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axes = self.axes
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t_axis = self.t_axis
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y_axis = axes.y_axis
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x_axis = axes.x_axis
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self.stop_ambient_camera_rotation()
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self.move_camera(
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phi=90 * DEGREES,
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theta=0 * DEGREES,
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added_anims=[
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Rotate(
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y_axis, 90 * DEGREES,
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axis=OUT,
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about_point=y_axis.n2p(0),
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),
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FadeOut(VGroup(
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self.graph_slices,
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self.surface,
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self.slicing_plane,
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self.rod,
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self.graph,
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self.x_numbers,
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self.x_axis_label,
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)),
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self.camera.frame_center.shift, 5 * LEFT,
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]
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)
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self.play(
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VGroup(x_axis, self.input_plane).stretch,
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0, 0, {"about_point": y_axis.n2p(0)},
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)
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self.play(
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t_axis.time_label.scale, 1 / 1.5,
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t_axis.time_label.next_to, t_axis, IN, MED_LARGE_BUFF,
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t_axis.numbers.shift, 0.7 * IN,
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)
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self.wait()
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class ShowNewtonsLawGraph(Scene):
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CONFIG = {
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"k": 0.2,
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"initial_water_temp": 80,
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"room_temp": 20,
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}
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def construct(self):
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self.setup_axes()
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self.show_temperatures()
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self.show_graph()
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self.show_equation()
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self.talk_through_examples()
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def setup_axes(self):
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axes = Axes(
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x_min=0,
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x_max=10,
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y_min=0,
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y_max=100,
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y_axis_config={
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"unit_size": 0.06,
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"tick_frequency": 10,
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},
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center_point=5 * LEFT + 2.5 * DOWN
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)
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x_axis = axes.x_axis
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y_axis = axes.y_axis
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y_axis.add_numbers(*range(20, 100, 20))
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x_axis.add_numbers(*range(1, 11))
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x_axis.label = TextMobject("Time")
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x_axis.label.next_to(x_axis, DOWN, MED_SMALL_BUFF)
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y_axis.label = TexMobject("\\text{Temperature}")
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y_axis.label.next_to(y_axis, RIGHT, buff=SMALL_BUFF)
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y_axis.label.align_to(axes, UP)
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for axis in [x_axis, y_axis]:
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axis.add(axis.label)
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self.add(axes)
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self.axes = axes
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def show_temperatures(self):
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axes = self.axes
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water_dot = Dot()
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water_dot.color_using_background_image("VerticalTempGradient")
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water_dot.move_to(axes.c2p(0, self.initial_water_temp))
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room_line = DashedLine(
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axes.c2p(0, self.room_temp),
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axes.c2p(10, self.room_temp),
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)
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room_line.set_color(BLUE)
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room_line.color_using_background_image("VerticalTempGradient")
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water_arrow = Vector(LEFT, color=WHITE)
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water_arrow.next_to(water_dot, RIGHT, SMALL_BUFF)
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water_words = TextMobject(
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"Initial water temperature"
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)
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water_words.next_to(water_arrow, RIGHT)
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room_words = TextMobject("Room temperature")
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room_words.next_to(room_line, DOWN, SMALL_BUFF)
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self.play(
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FadeInFrom(water_dot, RIGHT),
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GrowArrow(water_arrow),
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Write(water_words),
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)
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self.play(ShowCreation(room_line))
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self.play(FadeInFromDown(room_words))
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self.wait()
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self.set_variables_as_attrs(
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water_dot,
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water_arrow,
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water_words,
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room_line,
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room_words,
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)
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def show_graph(self):
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axes = self.axes
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water_dot = self.water_dot
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k = self.k
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rt = self.room_temp
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t0 = self.initial_water_temp
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graph = axes.get_graph(
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lambda t: rt + (t0 - rt) * np.exp(-k * t)
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)
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graph.color_using_background_image("VerticalTempGradient")
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def get_x():
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return axes.x_axis.p2n(water_dot.get_center())
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brace_line = always_redraw(lambda: Line(
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axes.c2p(get_x(), rt),
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water_dot.get_center(),
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stroke_width=0,
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))
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brace = Brace(brace_line, RIGHT, SMALL_BUFF)
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brace.add_updater(lambda b: b.match_height(brace_line))
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brace.add_updater(lambda b: b.next_to(brace_line, RIGHT, SMALL_BUFF))
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self.add(graph)
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def show_equation(self):
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pass
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def talk_through_examples(self):
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pass
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@ -83,73 +83,52 @@ class PartTwoOfTour(TourOfDifferentialEquations):
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}
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class CompareODEToPDE(Scene):
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class ShowCubeFormation(ThreeDScene):
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CONFIG = {
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"camera_config": {
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"shading_factor": 1.0,
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}
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}
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def construct(self):
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light_source = self.camera.light_source
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light_source.move_to(np.array([-6, -3, 6]))
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cube = Cube(
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side_length=4,
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fill_color=GREY,
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stroke_color=WHITE,
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stroke_width=0.5,
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)
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cube.set_fill(opacity=1)
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# light_source.next_to(cube, np.array([1, -1, 1]), buff=2)
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cube_3d = cube.copy()
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cube_2d = cube_3d.copy().stretch(0, 2)
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cube_1d = cube_2d.copy().stretch(0, 1)
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cube_0d = cube_1d.copy().stretch(0, 0)
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cube.become(cube_0d)
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self.set_camera_orientation(
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phi=70 * DEGREES,
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theta=-145 * DEGREES,
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)
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self.begin_ambient_camera_rotation(rate=0.05)
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for target in [cube_1d, cube_2d, cube_3d]:
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self.play(
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Transform(cube, target, run_time=1.5)
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)
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self.wait(3)
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class ShowNewton(Scene):
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def construct(self):
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pass
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class WriteHeatEquation(Scene):
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class ShowCupOfWater(Scene):
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def construct(self):
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d1_words = TextMobject("Heat equation\\\\", "(1 dimension)")
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d3_words = TextMobject("Heat equation\\\\", "(3 dimensions)")
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kwargs = {
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"tex_to_color_map": {
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"{T}": YELLOW,
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"{t}": WHITE,
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"{x}": GREEN,
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"{y}": RED,
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"{z}": BLUE,
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}
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}
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d1_equation = TexMobject(
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"{\\partial {T} \\over \\partial {t}}({x}, {t})="
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"{\\partial^2 {T} \\over \\partial {x}^2} ({x}, {t})",
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**kwargs
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)
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d3_equation = TexMobject(
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"{\\partial {T} \\over \\partial {t}} = ",
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"{\\partial^2 {T} \\over \\partial {x}^2} + ",
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"{\\partial^2 {T} \\over \\partial {y}^2} + ",
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"{\\partial^2 {T} \\over \\partial {z}^2}",
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**kwargs
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)
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d1_group = VGroup(d1_words, d1_equation)
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d3_group = VGroup(d3_words, d3_equation)
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groups = VGroup(d1_group, d3_group)
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for group in groups:
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group.arrange(DOWN, buff=MED_LARGE_BUFF)
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groups.arrange(RIGHT, buff=2)
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groups.to_edge(UP)
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d3_rhs = d3_equation[6:]
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d3_brace = Brace(d3_rhs, DOWN)
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nabla_words = TextMobject("Sometimes written as")
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nabla_words.match_width(d3_brace)
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nabla_words.next_to(d3_brace, DOWN)
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nabla_exp = TexMobject("\\nabla^2 {T}", **kwargs)
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nabla_exp.next_to(nabla_words, DOWN)
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# nabla_group = VGroup(nabla_words, nabla_exp)
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d1_group.save_state()
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d1_group.center().to_edge(UP)
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self.play(
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Write(d1_words),
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FadeInFrom(d1_equation, UP),
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run_time=1,
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)
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self.wait(2)
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self.play(
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Restore(d1_group),
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FadeInFrom(d3_group, LEFT)
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)
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self.wait()
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self.play(
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GrowFromCenter(d3_brace),
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Write(nabla_words),
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TransformFromCopy(d3_rhs, nabla_exp),
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run_time=1,
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)
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self.wait()
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pass
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155
active_projects/ode/part2/wordy_scenes.py
Normal file
155
active_projects/ode/part2/wordy_scenes.py
Normal file
@ -0,0 +1,155 @@
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from big_ol_pile_of_manim_imports import *
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class CompareODEToPDE(Scene):
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def construct(self):
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||||
pass
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class TodaysTargetWrapper(Scene):
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def construct(self):
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pass
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class WriteHeatEquation(Scene):
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CONFIG = {
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"tex_mobject_config": {
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"tex_to_color_map": {
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"{T}": YELLOW,
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"{t}": WHITE,
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"{x}": GREEN,
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||||
"{y}": RED,
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"{z}": BLUE,
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},
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||||
},
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||||
}
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||||
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def construct(self):
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d1_group = self.get_d1_group()
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||||
d3_group = self.get_d3_group()
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||||
d1_words, d1_equation = d1_group
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d3_words, d3_equation = d3_group
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||||
|
||||
groups = VGroup(d1_group, d3_group)
|
||||
for group in groups:
|
||||
group.arrange(DOWN, buff=MED_LARGE_BUFF)
|
||||
groups.arrange(RIGHT, buff=2)
|
||||
groups.to_edge(UP)
|
||||
|
||||
d3_rhs = d3_equation[6:]
|
||||
d3_brace = Brace(d3_rhs, DOWN)
|
||||
nabla_words = TextMobject("Sometimes written as")
|
||||
nabla_words.match_width(d3_brace)
|
||||
nabla_words.next_to(d3_brace, DOWN)
|
||||
nabla_exp = TexMobject(
|
||||
"\\nabla^2 {T}",
|
||||
**self.tex_mobject_config,
|
||||
)
|
||||
nabla_exp.next_to(nabla_words, DOWN)
|
||||
# nabla_group = VGroup(nabla_words, nabla_exp)
|
||||
|
||||
d1_group.save_state()
|
||||
d1_group.center().to_edge(UP)
|
||||
|
||||
self.play(
|
||||
Write(d1_words),
|
||||
FadeInFrom(d1_equation, UP),
|
||||
run_time=1,
|
||||
)
|
||||
self.wait(2)
|
||||
self.play(
|
||||
Restore(d1_group),
|
||||
FadeInFrom(d3_group, LEFT)
|
||||
)
|
||||
self.wait()
|
||||
self.play(
|
||||
GrowFromCenter(d3_brace),
|
||||
Write(nabla_words),
|
||||
TransformFromCopy(d3_rhs, nabla_exp),
|
||||
run_time=1,
|
||||
)
|
||||
self.wait()
|
||||
|
||||
def get_d1_equation(self):
|
||||
return TexMobject(
|
||||
"{\\partial {T} \\over \\partial {t}}({x}, {t})="
|
||||
"{\\partial^2 {T} \\over \\partial {x}^2} ({x}, {t})",
|
||||
**self.tex_mobject_config
|
||||
)
|
||||
|
||||
def get_d3_equation(self):
|
||||
return TexMobject(
|
||||
"{\\partial {T} \\over \\partial {t}} = ",
|
||||
"{\\partial^2 {T} \\over \\partial {x}^2} + ",
|
||||
"{\\partial^2 {T} \\over \\partial {y}^2} + ",
|
||||
"{\\partial^2 {T} \\over \\partial {z}^2}",
|
||||
**self.tex_mobject_config
|
||||
)
|
||||
|
||||
def get_d3_equation_with_inputs(self):
|
||||
return TexMobject(
|
||||
"{\\partial {T} \\over \\partial {t}} = ",
|
||||
"{\\partial^2 {T} \\over \\partial {x}^2}",
|
||||
"(x, y, z, t) + ",
|
||||
"{\\partial^2 {T} \\over \\partial {y}^2}",
|
||||
"(x, y, z, t) + ",
|
||||
"{\\partial^2 {T} \\over \\partial {z}^2}",
|
||||
"(x, y, z, t)",
|
||||
**self.tex_mobject_config
|
||||
)
|
||||
|
||||
def get_d1_words(self):
|
||||
return TextMobject("Heat equation\\\\", "(1 dimension)")
|
||||
|
||||
def get_d3_words(self):
|
||||
return TextMobject("Heat equation\\\\", "(3 dimensions)")
|
||||
|
||||
def get_d1_group(self):
|
||||
group = VGroup(
|
||||
self.get_d1_words(),
|
||||
self.get_d1_equation(),
|
||||
)
|
||||
group.arrange(DOWN, buff=MED_LARGE_BUFF)
|
||||
return group
|
||||
|
||||
def get_d3_group(self):
|
||||
group = VGroup(
|
||||
self.get_d3_words(),
|
||||
self.get_d3_equation(),
|
||||
)
|
||||
group.arrange(DOWN, buff=MED_LARGE_BUFF)
|
||||
return group
|
||||
|
||||
|
||||
class CompareInputsOfGeneralCaseTo1D(WriteHeatEquation):
|
||||
def construct(self):
|
||||
three_d_expr, one_d_expr = [
|
||||
TexMobject(
|
||||
"{T}(" + inputs + ", {t})",
|
||||
**self.tex_mobject_config,
|
||||
)
|
||||
for inputs in ["{x}, {y}, {z}", "{x}"]
|
||||
]
|
||||
for expr in three_d_expr, one_d_expr:
|
||||
expr.scale(2)
|
||||
expr.to_edge(UP)
|
||||
|
||||
x, y, z = [
|
||||
three_d_expr.get_part_by_tex(letter)
|
||||
for letter in ["x", "y", "z"]
|
||||
]
|
||||
|
||||
self.play(FadeInFromDown(three_d_expr))
|
||||
self.play(LaggedStartMap(
|
||||
ShowCreationThenFadeAround,
|
||||
VGroup(x, y, z)
|
||||
))
|
||||
self.wait()
|
||||
low = 3
|
||||
high = -3
|
||||
self.play(
|
||||
ReplacementTransform(three_d_expr[:low], one_d_expr[:low]),
|
||||
ReplacementTransform(three_d_expr[high:], one_d_expr[high:]),
|
||||
three_d_expr[low:high].scale, 0,
|
||||
)
|
||||
self.wait()
|
||||
Reference in New Issue
Block a user