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Up to StandardDerivativeVisual in alt_calc
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Grant Sanderson
parent
8e71db4f69
commit
38d3916654
1 changed files with 337 additions and 4 deletions
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@ -3,16 +3,78 @@ from big_ol_pile_of_manim_imports import *
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class NumberlineTransformationScene(Scene):
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CONFIG = {
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"input_line_center": 2 * UP,
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"output_line_center": 2 * DOWN,
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"number_line_config": {
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"include_numbers": True,
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"x_min": -3.5,
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"x_max": 3.5,
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"unit_size": 2,
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},
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# These would override number_line_config
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"input_line_config": {
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"color": BLUE,
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},
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"output_line_config": {},
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"num_inserted_number_line_anchors": 20,
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}
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def setup(self):
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pass
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self.setup_number_lines()
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self.setup_titles()
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def setup_number_lines(self):
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number_lines = self.number_lines = VGroup()
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added_configs = (self.input_line_config, self.output_line_config)
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centers = (self.input_line_center, self.output_line_center)
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for added_config, center in zip(added_configs, centers):
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full_config = dict(self.number_line_config)
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full_config.update(added_config)
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number_line = NumberLine(**full_config)
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number_line.main_line.insert_n_anchor_points(
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self.num_inserted_number_line_anchors
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)
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number_line.move_to(center)
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number_lines.add(number_line)
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self.input_line, self.output_line = number_lines
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self.add(number_lines)
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def setup_titles(self):
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input_title, output_title = self.titles = VGroup(*[
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TextMobject()
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for word in "Inputs", "Outputs"
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])
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for title, line in zip(self.titles, self.number_lines):
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title.next_to(line, UP)
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title.shift_onto_screen()
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self.add(self.titles)
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def get_line_mapping_animation(self, func, run_time=3, path_arc=30 * DEGREES):
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input_line, output_line = self.number_lines
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input_line_copy = input_line.deepcopy()
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input_line_copy.remove(input_line_copy.numbers)
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input_line_copy.set_stroke(width=2)
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def point_func(point):
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input_number = input_line.point_to_number(point)
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output_number = func(input_number)
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return output_line.number_to_point(output_number)
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return ApplyPointwiseFunction(
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point_func, input_line_copy,
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run_time=run_time,
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path_arc=path_arc,
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)
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class ExampleNumberlineTransformationScene(NumberlineTransformationScene):
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def construct(self):
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pass
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func = lambda x: x**2
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anim = self.get_line_mapping_animation(func)
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self.play(anim)
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self.wait()
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# Scenes
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@ -52,7 +114,7 @@ class StartingCalc101(PiCreatureScene):
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def construct(self):
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randy = self.pi_creature
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deriv_equation = TexMobject(
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"\\frac{df}{dx}(x) = \\lim(\\Delta x \\to \\infty)" +
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"\\frac{df}{dx}(x) = \\lim_{\\Delta x \\to \\infty}" +
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"{f(x + \\Delta x) - f(x) \\over \\Delta x}",
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tex_to_color_map={"\\Delta x": BLUE}
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)
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@ -70,3 +132,274 @@ class StartingCalc101(PiCreatureScene):
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self.wait()
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class StandardDerivativeVisual(GraphScene):
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CONFIG = {
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# "y_axis_label": "$f(x)$",
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"y_max": 8,
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"y_axis_height": 5,
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}
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def construct(self):
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self.add_title()
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self.show_function_graph()
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self.show_slope_of_graph()
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self.encourage_not_to_think_of_slope_as_definition()
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self.show_sensitivity()
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def add_title(self):
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title = self.title = TextMobject("Standard derivative visual")
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title.to_edge(UP)
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h_line = Line(LEFT, RIGHT)
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h_line.scale_to_fit_width(FRAME_WIDTH - 2 * LARGE_BUFF)
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h_line.next_to(title, DOWN)
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self.add(title, h_line)
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def show_function_graph(self):
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self.setup_axes()
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def func(x):
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x -= 5
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return 0.1 * (x + 3) * (x - 3) * x + 3
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graph = self.get_graph(func)
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graph_label = self.get_graph_label(graph, x_val=9.5)
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input_tracker = ValueTracker(4)
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def get_x_value():
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return input_tracker.get_value()
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def get_y_value():
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return graph.underlying_function(get_x_value())
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def get_x_point():
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return self.coords_to_point(get_x_value(), 0)
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def get_y_point():
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return self.coords_to_point(0, get_y_value())
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def get_graph_point():
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return self.coords_to_point(get_x_value(), get_y_value())
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def get_v_line():
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return DashedLine(get_x_point(), get_graph_point(), stroke_width=2)
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def get_h_line():
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return DashedLine(get_graph_point(), get_y_point(), stroke_width=2)
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input_triangle = RegularPolygon(n=3, start_angle=TAU / 4)
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output_triangle = RegularPolygon(n=3, start_angle=0)
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for triangle in input_triangle, output_triangle:
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triangle.set_fill(WHITE, 1)
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triangle.set_stroke(width=0)
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triangle.scale(0.1)
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input_triangle_update = ContinualUpdateFromFunc(
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input_triangle, lambda m: m.move_to(get_x_point(), UP)
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)
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output_triangle_update = ContinualUpdateFromFunc(
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output_triangle, lambda m: m.move_to(get_y_point(), RIGHT)
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)
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x_label = TexMobject("x")
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x_label_update = ContinualUpdateFromFunc(
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x_label, lambda m: m.next_to(input_triangle, DOWN, SMALL_BUFF)
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)
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output_label = TexMobject("f(x)")
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output_label_update = ContinualUpdateFromFunc(
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output_label, lambda m: m.next_to(
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output_triangle, LEFT, SMALL_BUFF)
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)
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v_line = get_v_line()
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v_line_update = ContinualUpdateFromFunc(
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v_line, lambda vl: Transform(vl, get_v_line()).update(1)
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)
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h_line = get_h_line()
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h_line_update = ContinualUpdateFromFunc(
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h_line, lambda hl: Transform(hl, get_h_line()).update(1)
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)
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graph_dot = Dot(color=YELLOW)
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graph_dot_update = ContinualUpdateFromFunc(
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graph_dot, lambda m: m.move_to(get_graph_point())
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)
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self.play(
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ShowCreation(graph),
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Write(graph_label),
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)
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self.play(
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DrawBorderThenFill(input_triangle, run_time=1),
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Write(x_label),
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ShowCreation(v_line),
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GrowFromCenter(graph_dot),
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)
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self.add_foreground_mobject(graph_dot)
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self.play(
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ShowCreation(h_line),
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Write(output_label),
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DrawBorderThenFill(output_triangle, run_time=1)
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)
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self.add(
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input_triangle_update,
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x_label_update,
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graph_dot_update,
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v_line_update,
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h_line_update,
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output_triangle_update,
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output_label_update,
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)
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self.play(
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input_tracker.set_value, 8,
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run_time=6,
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rate_func=there_and_back
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)
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self.input_tracker = input_tracker
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self.graph = graph
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def show_slope_of_graph(self):
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input_tracker = self.input_tracker
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deriv_input_tracker = ValueTracker(input_tracker.get_value())
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# Slope line
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def get_slope_line():
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return self.get_secant_slope_group(
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x=deriv_input_tracker.get_value(),
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graph=self.graph,
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dx=0.01,
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secant_line_length=4
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).secant_line
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slope_line = get_slope_line()
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slope_line_update = ContinualUpdateFromFunc(
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slope_line, lambda sg: Transform(sg, get_slope_line()).update(1)
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)
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def position_deriv_label(deriv_label):
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deriv_label.next_to(slope_line, UP)
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return deriv_label
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deriv_label = TexMobject(
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"\\frac{df}{dx}(x) =", "\\text{Slope}", "="
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)
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deriv_label.get_part_by_tex("Slope").match_color(slope_line)
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deriv_label_update = ContinualUpdateFromFunc(
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deriv_label, position_deriv_label
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)
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slope_decimal = DecimalNumber(slope_line.get_slope())
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slope_decimal.match_color(slope_line)
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slope_decimal_update = ContinualChangingDecimal(
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slope_decimal, lambda dt: slope_line.get_slope(),
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position_update_func=lambda m: m.next_to(
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deriv_label, RIGHT, SMALL_BUFF
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).shift(0.2 * SMALL_BUFF * DOWN)
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)
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self.play(
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ShowCreation(slope_line),
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Write(deriv_label),
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Write(slope_decimal),
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run_time=1
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)
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self.wait()
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self.add(
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slope_line_update,
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# deriv_label_update,
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slope_decimal_update,
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)
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for x in 9, 2, 4:
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self.play(
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input_tracker.set_value, x,
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deriv_input_tracker.set_value, x,
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run_time=3
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)
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self.wait()
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self.deriv_input_tracker = deriv_input_tracker
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def encourage_not_to_think_of_slope_as_definition(self):
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morty = Mortimer(height=2)
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morty.to_corner(DR)
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self.play(FadeIn(morty))
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self.play(PiCreatureSays(
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morty, "Don't think of \\\\ this as the definition",
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bubble_kwargs={"height": 2, "width": 4}
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))
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self.play(Blink(morty))
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self.wait()
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self.play(
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RemovePiCreatureBubble(morty),
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UpdateFromAlphaFunc(
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morty, lambda m, a: m.set_fill(opacity=1 - a),
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remover=True
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)
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)
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def show_sensitivity(self):
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input_tracker = self.input_tracker
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deriv_input_tracker = self.deriv_input_tracker
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self.wiggle_input()
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for x in 9, 7, 2:
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self.play(
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input_tracker.set_value, x,
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deriv_input_tracker.set_value, x,
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run_time=3
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)
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self.wiggle_input()
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###
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def wiggle_input(self, dx=0.5, run_time=3):
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input_tracker = self.input_tracker
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x = input_tracker.get_value()
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x_min = x - dx
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x_max = x + dx
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y, y_min, y_max = map(
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self.graph.underlying_function,
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[x, x_min, x_max]
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)
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x_line = Line(
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self.coords_to_point(x_min, 0),
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self.coords_to_point(x_max, 0),
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)
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y_line = Line(
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self.coords_to_point(0, y_min),
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self.coords_to_point(0, y_max),
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)
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x_rect, y_rect = rects = VGroup(Rectangle(), Rectangle())
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rects.set_stroke(width=0)
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rects.set_fill(YELLOW, 0.5)
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x_rect.match_width(x_line)
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x_rect.stretch_to_fit_height(0.25)
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x_rect.move_to(x_line)
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y_rect.match_height(y_line)
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y_rect.stretch_to_fit_width(0.25)
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y_rect.move_to(y_line)
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self.play(
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ApplyMethod(
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input_tracker.set_value, input_tracker.get_value() + dx,
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rate_func=lambda t: wiggle(t, 6)
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),
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FadeIn(
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rects,
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rate_func=squish_rate_func(smooth, 0, 0.33),
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remover=True,
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),
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run_time=run_time,
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)
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self.play(FadeOut(rects))
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class EoCWrapper(Scene):
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def construct(self):
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title = Title("Essence of calculus")
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self.play(Write(title))
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self.wait()
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