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Up to GraphCarTrajectory of eoc chapter 2
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Grant Sanderson
parent
740eba856d
commit
a7720f308d
2 changed files with 210 additions and 15 deletions
176
eoc/chapter2.py
176
eoc/chapter2.py
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@ -377,16 +377,22 @@ class GraphCarTrajectory(GraphScene):
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graph = self.graph_function(lambda t : 100*smooth(t/10.))
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origin = self.coords_to_point(0, 0)
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self.introduce_graph(graph, origin)
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self.comment_on_slope(graph, origin)
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self.show_velocity_graph()
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self.ask_critically_about_velocity()
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def introduce_graph(self, graph, origin):
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h_line, v_line = [
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Line(origin, origin, color = color, stroke_width = 2)
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for color in MAROON_B, YELLOW
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]
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def h_update(h_line):
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end = graph.points[-1]
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def h_update(h_line, proportion = 1):
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end = graph.point_from_proportion(proportion)
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t_axis_point = end[0]*RIGHT + origin[1]*UP
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h_line.put_start_and_end_on(t_axis_point, end)
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def v_update(v_line):
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end = graph.points[-1]
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def v_update(v_line, proportion = 1):
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end = graph.point_from_proportion(proportion)
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d_axis_point = origin[0]*RIGHT + end[1]*UP
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v_line.put_start_and_end_on(d_axis_point, end)
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@ -407,6 +413,168 @@ class GraphCarTrajectory(GraphScene):
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run_time = 10,
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)
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self.dither()
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self.play(*map(FadeOut, [h_line, v_line, car]))
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#Show example vertical distance
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h_update(h_line, 0.6)
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t_dot = Dot(h_line.get_start(), color = h_line.get_color())
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t_dot.save_state()
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t_dot.move_to(self.x_axis_label_mob)
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t_dot.set_fill(opacity = 0)
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dashed_h = DashedLine(*h_line.get_start_and_end())
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dashed_h.highlight(h_line.get_color())
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brace = Brace(dashed_h, RIGHT)
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brace_text = brace.get_text("Distance traveled")
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self.play(t_dot.restore)
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self.dither()
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self.play(ShowCreation(dashed_h))
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self.play(
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GrowFromCenter(brace),
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Write(brace_text)
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)
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self.dither(2)
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self.play(*map(FadeOut, [t_dot, dashed_h, brace, brace_text]))
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#Name graph
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s_of_t = TexMobject("s(t)")
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s_of_t.next_to(
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graph.point_from_proportion(1),
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DOWN+RIGHT,
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buff = SMALL_BUFF
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)
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s = s_of_t[0]
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d = TexMobject("d")
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d.move_to(s, DOWN)
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d.highlight(YELLOW)
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self.play(Write(s_of_t))
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self.dither()
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s.save_state()
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self.play(Transform(s, d))
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self.dither()
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self.play(s.restore)
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def comment_on_slope(self, graph, origin):
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delta_t = 1
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curr_time = 0
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ghost_line = Line(
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origin,
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self.coords_to_point(delta_t, self.y_max)
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)
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rect = Rectangle().replace(ghost_line, stretch = True)
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rect.set_stroke(width = 0)
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rect.set_fill(BLUE, opacity = 0.3)
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def get_change_lines():
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p1 = self.input_to_graph_point(curr_time)
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p2 = self.input_to_graph_point(curr_time+delta_t)
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interim_point = p2[0]*RIGHT + p1[1]*UP
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delta_t_line = Line(p1, interim_point, color = YELLOW)
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delta_s_line = Line(interim_point, p2, color = MAROON_B)
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brace = Brace(delta_s_line, RIGHT, buff = SMALL_BUFF)
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return VGroup(delta_t_line, delta_s_line, brace)
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change_lines = get_change_lines()
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self.play(FadeIn(rect))
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self.dither()
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self.play(Write(change_lines))
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self.dither()
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for x in range(1, 10):
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curr_time = x
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new_change_lines = get_change_lines()
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self.play(
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rect.move_to, self.coords_to_point(curr_time, 0), DOWN+LEFT,
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Transform(change_lines, new_change_lines)
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)
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if curr_time == 5:
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text = change_lines[-1].get_text(
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"$\\frac{\\text{meters}}{\\text{second}}$"
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)
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self.play(Write(text))
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self.dither()
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self.play(FadeOut(text))
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else:
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self.dither()
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self.play(*map(FadeOut, [rect, change_lines]))
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self.rect = rect
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def show_velocity_graph(self):
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velocity_graph = self.get_derivative_graph()
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self.play(ShowCreation(velocity_graph))
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def get_velocity_label(v_graph):
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result = self.label_graph(
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v_graph,
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label = "v(t)",
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direction = UP+RIGHT,
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proportion = 0.5,
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buff = SMALL_BUFF,
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animate = False,
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)
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self.remove(result)
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return result
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label = get_velocity_label(velocity_graph)
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self.play(Write(label))
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self.dither()
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self.rect.move_to(self.coords_to_point(0, 0), DOWN+LEFT)
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self.play(FadeIn(self.rect))
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self.dither()
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for time in 4.5, 9:
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self.play(
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self.rect.move_to, self.coords_to_point(time, 0), DOWN+LEFT
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)
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self.dither()
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self.play(FadeOut(self.rect))
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#Change distance and velocity graphs
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self.graph.save_state()
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velocity_graph.save_state()
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label.save_state()
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def shallow_slope(t):
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return 100*smooth(t/10., inflection = 4)
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def steep_slope(t):
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return 100*smooth(t/10., inflection = 25)
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def double_smooth_graph_function(t):
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if t < 5:
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return 50*smooth(t/5.)
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else:
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return 50*(1+smooth((t-5)/5.))
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graph_funcs = [
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shallow_slope,
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steep_slope,
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double_smooth_graph_function,
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]
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for graph_func in graph_funcs:
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new_graph = self.graph_function(
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graph_func,
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is_main_graph = False
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)
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self.remove(new_graph)
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new_velocity_graph = self.get_derivative_graph(graph = new_graph)
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new_velocity_label = get_velocity_label(new_velocity_graph)
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self.play(Transform(self.graph, new_graph))
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self.play(
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Transform(velocity_graph, new_velocity_graph),
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Transform(label, new_velocity_label),
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)
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self.dither(2)
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self.play(self.graph.restore)
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self.play(
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velocity_graph.restore,
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label.restore,
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)
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self.dither(2)
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def ask_critically_about_velocity(self):
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morty = Mortimer().flip()
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morty.to_corner(DOWN+LEFT)
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self.play(PiCreatureSays(morty,
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"Think critically about \\\\",
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"what velocity means."
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))
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self.play(Blink(morty))
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self.dither()
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@ -28,13 +28,15 @@ class GraphScene(Scene):
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"axes_color" : GREY,
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"graph_origin" : 2.5*DOWN + 4*LEFT,
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"y_axis_numbers_nudge" : 0.4*UP+0.5*LEFT,
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"num_graph_anchor_points" : 25,
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}
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def setup_axes(self, animate = True):
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x_num_range = float(self.x_max - self.x_min)
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self.space_unit_to_x = self.x_axis_width/x_num_range
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x_axis = NumberLine(
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x_min = self.x_min,
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x_max = self.x_max,
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space_unit_to_num = self.x_axis_width/x_num_range,
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space_unit_to_num = self.space_unit_to_x,
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tick_frequency = self.x_tick_frequency,
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leftmost_tick = self.x_leftmost_tick or self.x_min,
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numbers_with_elongated_ticks = self.x_labeled_nums,
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@ -50,10 +52,11 @@ class GraphScene(Scene):
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self.x_axis_label_mob = x_label
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y_num_range = float(self.y_max - self.y_min)
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self.space_unit_to_y = self.y_axis_height/y_num_range
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y_axis = NumberLine(
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x_min = self.y_min,
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x_max = self.y_max,
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space_unit_to_num = self.y_axis_height/y_num_range,
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space_unit_to_num = self.space_unit_to_y,
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tick_frequency = self.y_tick_frequency,
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leftmost_tick = self.y_bottom_tick or self.y_min,
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numbers_with_elongated_ticks = self.y_labeled_nums,
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@ -88,11 +91,16 @@ class GraphScene(Scene):
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is_main_graph = True,
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):
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def parameterized_graph(alpha):
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def parameterized_function(alpha):
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x = interpolate(self.x_min, self.x_max, alpha)
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return self.coords_to_point(x, func(x))
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graph = ParametricFunction(parameterized_graph, color = color)
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graph = ParametricFunction(
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parameterized_function,
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color = color,
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num_anchor_points = self.num_graph_anchor_points,
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)
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graph.underlying_function = func
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if is_main_graph:
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self.graph = graph
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@ -102,16 +110,35 @@ class GraphScene(Scene):
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self.add(graph)
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return graph
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def input_to_graph_point(self, x):
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assert(hasattr(self, "graph"))
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alpha = (x - self.x_min)/(self.x_max - self.x_min)
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return self.graph.point_from_proportion(alpha)
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def angle_of_tangent(self, x, dx = 0.01):
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def input_to_graph_point(self, x, graph = None):
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if graph is None:
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assert(hasattr(self, "graph"))
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vect = self.graph_point(x + dx) - self.graph_point(x)
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graph = self.graph
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return self.coords_to_point(
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x, graph.underlying_function(x)
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)
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# alpha = (x - self.x_min)/(self.x_max - self.x_min)
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# return graph.point_from_proportion(alpha)
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def angle_of_tangent(self, x, graph = None, dx = 0.01):
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vect = self.input_to_graph_point(x + dx, graph) - self.input_to_graph_point(x, graph)
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return angle_of_vector(vect)
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def slope_of_tangent(self, *args):
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return np.tan(self.angle_of_tangent(*args))
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def get_derivative_graph(self, graph = None, dx = 0.01, color = RED):
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derivative_graph = self.graph_function(
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lambda x : self.slope_of_tangent(x, graph, dx) / self.space_unit_to_y,
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color = color,
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animate = False,
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is_main_graph = False
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)
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self.remove(derivative_graph)
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return derivative_graph
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def label_graph(self, graph, label = "f(x)",
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proportion = 0.7,
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direction = LEFT,
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