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Preliminary end to eoc8
This commit is contained in:
Grant Sanderson
@ -99,10 +99,15 @@ class Car(SVGMobject):
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return VGroup(self[1][1], self[1][3])
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class MoveCar(ApplyMethod):
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CONFIG = {
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"moving_forward" : True,
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}
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def __init__(self, car, target_point, **kwargs):
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ApplyMethod.__init__(self, car.move_to, target_point, **kwargs)
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displacement = self.target_mobject.get_right()-self.starting_mobject.get_right()
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distance = np.linalg.norm(displacement)
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if not self.moving_forward:
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distance *= -1
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tire_radius = car.get_tires()[0].get_width()/2
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self.total_tire_radians = -distance/tire_radius
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249
eoc/chapter8.py
249
eoc/chapter8.py
@ -1429,6 +1429,15 @@ class LessWrongCarJourneyApproximation(CarJourneyApproximation):
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"n_jumps" : 20,
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}
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class TellMeThatsNotSurprising(TeacherStudentsScene):
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def construct(self):
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self.teacher_says(
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"Tell me that's \\\\ not surprising!",
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target_mode = "hooray",
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run_time = 1
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)
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self.dither(3)
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class HowDoesThisHelp(TeacherStudentsScene):
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def construct(self):
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self.student_says(
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@ -1763,7 +1772,6 @@ class AreaIsDerivative(PlotVelocity, ReconfigurableScene):
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**kwargs
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)
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class DirectInterpretationOfDsDt(TeacherStudentsScene):
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def construct(self):
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equation = TexMobject("{ds", "\\over\\,", "dT}", "(T)", "=", "v(T)")
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@ -2473,12 +2481,239 @@ class FundamentalTheorem(GraphScene):
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self.play(self.integral.set_fill, None, 1)
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self.dither(3)
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class LetsRecap(TeacherStudentsScene):
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def construct(self):
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self.teacher_says(
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"Let's recap",
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target_mode = "hesitant",
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)
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self.change_student_modes(*["happy"]*3)
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self.dither(3)
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class NegativeArea(GraphScene):
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CONFIG = {
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"x_axis_label" : "Time",
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"y_axis_label" : "Velocity",
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"graph_origin" : 1.5*DOWN + 5*LEFT,
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"y_min" : -3,
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"y_max" : 7,
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"small_dx" : 0.01,
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"sample_input" : 5,
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}
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def construct(self):
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self.setup_axes()
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self.add_graph_and_area()
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self.write_negative_area()
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self.show_negative_point()
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self.show_car_going_backwards()
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self.write_v_dt()
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self.show_rectangle()
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self.write_signed_area()
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def add_graph_and_area(self):
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graph = self.get_graph(
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lambda x : -0.02*(x+1)*(x-3)*(x-7)*(x-10),
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x_min = 0,
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x_max = 8,
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color = VELOCITY_COLOR
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)
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area = self.get_riemann_rectangles(
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graph,
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x_min = 0,
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x_max = 8,
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dx = self.small_dx,
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start_color = BLUE_D,
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end_color = BLUE_D,
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fill_opacity = 0.75,
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stroke_width = 0,
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)
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self .play(
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ShowCreation(graph),
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FadeIn(
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area,
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run_time = 2,
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submobject_mode = "lagged_start",
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)
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)
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self.graph = graph
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self.area = area
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def write_negative_area(self):
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words = TextMobject("Negative area")
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words.highlight(RED)
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words.next_to(
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self.coords_to_point(7, -2),
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RIGHT,
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)
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arrow = Arrow(words, self.coords_to_point(
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self.sample_input, -1,
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))
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self.play(
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Write(words, run_time = 2),
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ShowCreation(arrow)
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)
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self.dither(2)
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self.play(*map(FadeOut, [self.area, arrow]))
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self.negative_area_words = words
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def show_negative_point(self):
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v_line = self.get_vertical_line_to_graph(
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self.sample_input, self.graph,
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color = RED
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)
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self.play(ShowCreation(v_line))
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self.dither()
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self.v_line = v_line
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def show_car_going_backwards(self):
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car = Car()
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start_point = 3*RIGHT + 2*UP
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end_point = start_point + LEFT
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nudged_end_point = end_point + MED_SMALL_BUFF*LEFT
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car.move_to(start_point)
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arrow = Arrow(RIGHT, LEFT, color = RED)
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arrow.next_to(car, UP+LEFT)
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arrow.shift(MED_LARGE_BUFF*RIGHT)
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self.play(FadeIn(car))
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self.play(ShowCreation(arrow))
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self.play(MoveCar(
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car, end_point,
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moving_forward = False,
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run_time = 3
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))
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self.dither()
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ghost_car = car.copy().fade()
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right_nose_line = self.get_car_nose_line(car)
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self.play(ShowCreation(right_nose_line))
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self.add(ghost_car)
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self.play(MoveCar(
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car, nudged_end_point,
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moving_forward = False
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))
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left_nose_line = self.get_car_nose_line(car)
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self.play(ShowCreation(left_nose_line))
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self.nose_lines = VGroup(left_nose_line, right_nose_line)
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self.car = car
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self.ghost_car = ghost_car
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def write_v_dt(self):
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brace = Brace(self.nose_lines, DOWN, buff = 0)
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equation = TexMobject("ds", "=", "v(t)", "dt")
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equation.next_to(brace, DOWN, SMALL_BUFF, LEFT)
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equation.highlight_by_tex("ds", DISTANCE_COLOR)
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equation.highlight_by_tex("dt", TIME_COLOR)
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negative = TextMobject("Negative")
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negative.highlight(RED)
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negative.next_to(equation.get_corner(UP+RIGHT), UP, LARGE_BUFF)
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ds_arrow, v_arrow = arrows = VGroup(*[
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Arrow(
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negative.get_bottom(),
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equation.get_part_by_tex(tex).get_top(),
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color = RED,
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)
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for tex in "ds", "v(t)"
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])
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self.play(
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GrowFromCenter(brace),
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Write(equation)
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)
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self.dither()
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self.play(FadeIn(negative))
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self.play(ShowCreation(v_arrow))
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self.dither(2)
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self.play(ReplacementTransform(
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v_arrow.copy(),
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ds_arrow
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))
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self.dither(2)
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self.ds_equation = equation
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self.negative_word = negative
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self.negative_word_arrows = arrows
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def show_rectangle(self):
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rect_list = self.get_riemann_rectangles_list(
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self.graph, x_min = 0, x_max = 8,
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n_iterations = 6,
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start_color = BLUE_D,
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end_color = BLUE_D,
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fill_opacity = 0.75,
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)
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rects = rect_list[0]
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rect = rects[len(rects)*self.sample_input//8]
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dt_brace = Brace(rect, UP, buff = 0)
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v_brace = Brace(rect, LEFT, buff = 0)
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dt_label = dt_brace.get_text("$dt$", buff = SMALL_BUFF)
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dt_label.highlight(YELLOW)
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v_label = v_brace.get_text("$v(t)$", buff = SMALL_BUFF)
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v_label.add_background_rectangle()
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self.play(FadeOut(self.v_line), FadeIn(rect))
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self.play(
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GrowFromCenter(dt_brace),
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GrowFromCenter(v_brace),
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Write(dt_label),
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Write(v_label),
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)
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self.dither(2)
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self.play(*it.chain(
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[FadeIn(r) for r in rects if r is not rect],
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map(FadeOut, [
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dt_brace, v_brace, dt_label, v_label
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])
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))
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self.dither()
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for new_rects in rect_list[1:]:
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self.transform_between_riemann_rects(rects, new_rects)
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self.dither()
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def write_signed_area(self):
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words = TextMobject("``Signed area''")
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words.next_to(self.coords_to_point(self.sample_input, 0), UP)
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symbols = VGroup(*[
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TexMobject(sym).move_to(self.coords_to_point(*coords))
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for sym, coords in [
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("+", (1, 2)),
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("-", (5, -1)),
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("+", (7.6, 0.5)),
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]
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])
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self.play(Write(words))
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self.play(Write(symbols))
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self.dither()
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####
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def get_car_nose_line(self, car):
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line = DashedLine(car.get_top(), car.get_bottom())
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line.move_to(car.get_right())
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return line
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class NextVideo(TeacherStudentsScene):
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def construct(self):
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series = VideoSeries()
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series.to_edge(UP)
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next_video = series[8]
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integral = TexMobject("\\int")
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integral.next_to(next_video, DOWN, LARGE_BUFF)
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self.play(FadeIn(series, submobject_mode = "lagged_start"))
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self.play(
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next_video.highlight, YELLOW,
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next_video.shift, next_video.get_height()*DOWN/2,
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self.teacher.change_mode, "raise_right_hand"
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)
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self.play(Write(integral))
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self.dither(5)
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@ -196,11 +196,15 @@ class GraphScene(Scene):
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stroke_width = 1,
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fill_opacity = 1,
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start_color = BLUE,
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end_color = GREEN):
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end_color = GREEN,
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show_signed_area = True,
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):
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x_min = x_min if x_min is not None else self.x_min
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x_max = x_max if x_max is not None else self.x_max
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rectangles = VGroup()
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for x in np.arange(x_min, x_max, dx):
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x_range = np.arange(x_min, x_max, dx)
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colors = color_gradient([start_color, end_color], len(x_range))
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for x, color in zip(x_range, colors):
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if input_sample_type == "left":
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sample_input = x
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elif input_sample_type == "right":
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@ -216,10 +220,13 @@ class GraphScene(Scene):
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rect = Rectangle()
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rect.replace(points, stretch = True)
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rect.set_fill(opacity = fill_opacity)
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if graph_point[1] < self.graph_origin[1] and show_signed_area:
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fill_color = invert_color(color)
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else:
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fill_color = color
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rect.set_fill(fill_color, opacity = fill_opacity)
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rect.set_stroke(BLACK, width = stroke_width)
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rectangles.add(rect)
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rectangles.gradient_highlight(start_color, end_color)
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rectangles.set_stroke(BLACK, width = stroke_width)
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return rectangles
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def get_riemann_rectangles_list(
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@ -118,6 +118,9 @@ def rgb_to_color(rgb):
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except:
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return Color(WHITE)
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def invert_color(color):
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return rgb_to_color(1.0 - color_to_rgb(color))
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def color_to_int_rgb(color):
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return (255*color_to_rgb(color)).astype('uint8')
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