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Halfway through TCubedExample
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Grant Sanderson
parent
978a52e60f
commit
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1 changed files with 196 additions and 7 deletions
203
eoc/chapter2.py
203
eoc/chapter2.py
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@ -1545,30 +1545,39 @@ class LeadIntoASpecificExample(TeacherStudentsScene, SecantLineToTangentLine):
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# )
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# self.dither(2)
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class TCubedExample(GraphCarTrajectory):
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class TCubedExample(SecantLineToTangentLine):
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CONFIG = {
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"y_axis_label" : "Distance",
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"y_min" : 0,
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"y_max" : 10,
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"y_max" : 16,
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"y_tick_frequency" : 1,
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"y_labeled_nums" : range(10),
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"y_labeled_nums" : range(0, 17, 2),
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"x_min" : 0,
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"x_max" : 4,
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"x_labeled_nums" : range(1, 5),
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"graph_origin" : 2.5*DOWN + 6*LEFT,
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"start_time" : 2,
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"start_dt" : 0.25,
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"secant_line_length" : 0,
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}
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def construct(self):
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self.draw_graph()
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self.show_vertical_lines()
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self.bear_with_me()
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self.add_ds_dt_group()
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self.brace_for_details()
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self.show_expansion()
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def draw_graph(self):
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self.setup_axes(animate = False)
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self.x_axis_label_mob.shift(0.*DOWN)
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self.x_axis_label_mob.shift(0.5*DOWN)
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# self.y_axis_label_mob.next_to(self.y_axis, UP)
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graph = self.graph_function(lambda t : t**3, animate = True)
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self.label_graph(
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graph,
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label = "s(t) = t^3",
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proportion = 0.525,
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direction = RIGHT,
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proportion = 0.62,
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direction = LEFT,
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buff = SMALL_BUFF
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)
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self.dither()
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@ -1593,7 +1602,187 @@ class TCubedExample(GraphCarTrajectory):
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else:
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self.play(Transform(last_group, group))
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self.dither()
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self.play(FadeOut(group))
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self.play(FadeOut(last_group))
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def bear_with_me(self):
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morty = Mortimer()
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morty.to_corner(DOWN+RIGHT)
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self.play(FadeIn(morty))
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self.play(PiCreatureSays(
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morty, "Bear with \\\\ me here",
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target_mode = "sassy"
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))
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self.play(Blink(morty))
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self.dither()
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self.play(*map(
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FadeOut,
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[morty, morty.bubble, morty.bubble.content]
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))
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def add_ds_dt_group(self):
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self.curr_time = self.start_time
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self.curr_dt = self.start_dt
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ds_dt_group = self.get_ds_dt_group(dt = self.start_dt)
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v_lines = self.get_vertical_lines()
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lhs = TexMobject("\\frac{ds}{dt}(2) = ")
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lhs.next_to(ds_dt_group, UP+RIGHT, buff = 2*MED_BUFF)
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ds = VGroup(*lhs[:2])
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dt = VGroup(*lhs[3:5])
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ds.highlight(DISTANCE_COLOR)
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dt.highlight(TIME_COLOR)
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ds.target, dt.target = ds_dt_group[3:5]
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for mob in ds, dt:
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mob.save_state()
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mob.move_to(mob.target)
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rhs = TexMobject(
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"\\frac{s(2+dt) - s(2)}{dt}"
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)
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rhs.next_to(lhs[-1])
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VGroup(*rhs[4:6]).highlight(TIME_COLOR)
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VGroup(*rhs[-2:]).highlight(TIME_COLOR)
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numerator = VGroup(*rhs[:-3])
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non_numerator = VGroup(*rhs[-3:])
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numerator_non_minus = VGroup(*numerator)
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numerator_non_minus.remove(rhs[7])
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s_pair = rhs[0], rhs[8]
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lp_pair = rhs[6], rhs[11]
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for s, lp in zip(s_pair, lp_pair):
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s.target = TexMobject("3").scale(0.7)
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s.target.move_to(lp.get_corner(UP+RIGHT), LEFT)
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self.play(Write(ds_dt_group, run_time = 2))
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self.play(
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FadeIn(lhs),
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*[mob.restore for mob in ds, dt]
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)
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self.play(ShowCreation(v_lines[0]))
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self.dither()
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self.play(
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dt.target.scale_in_place, 1.2,
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rate_func = there_and_back
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)
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self.dither(2)
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self.play(Write(numerator))
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self.play(ShowCreation(v_lines[1]))
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self.dither()
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self.play(Write(non_numerator))
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self.dither(2)
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self.play(
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*map(MoveToTarget, s_pair),
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**{
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"path_arc" : -np.pi/2
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}
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)
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self.play(numerator_non_minus.shift, 0.2*LEFT)
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self.dither()
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self.vertical_lines = v_lines
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self.ds_dt_group = ds_dt_group
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self.lhs = lhs
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self.rhs = rhs
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def get_vertical_lines(self):
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return VGroup(*[
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self.get_vertical_line_to_graph(
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time,
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line_class = DashedLine,
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line_kwargs = {
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"color" : WHITE,
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"dashed_segment_length" : 0.05,
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}
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)
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for time in self.start_time, self.start_time+self.start_dt
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])
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def brace_for_details(self):
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brace_yourself = TextMobject(
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"(Brace yourself for details)"
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)
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brace_yourself.next_to(
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self.lhs, DOWN,
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buff = LARGE_BUFF,
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aligned_edge = LEFT
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)
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self.play(FadeIn(brace_yourself))
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self.dither()
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self.play(FadeOut(brace_yourself))
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def show_expansion(self):
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expression = TexMobject("""
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\\frac{
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2^3 +
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3 (2)^2 dt +
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3 (2)(dt)^2 +
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(dt)^3
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- 2^3
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}{dt}
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""")
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expression.scale_to_fit_width(
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VGroup(self.lhs, self.rhs).get_width()
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)
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expression.next_to(
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self.lhs, DOWN,
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aligned_edge = LEFT,
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buff = LARGE_BUFF
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)
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term_lens = [
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len("23+"),
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len("3(2)2dt+"),
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len("3(2)(dt)2+"),
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len("(dt)3"),
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len("-23"),
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len("_"),#frac bar
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len("dt"),
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]
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terms = [
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VGroup(*expression[i1:i2])
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for i1, i2 in zip(
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[0]+list(np.cumsum(term_lens)),
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np.cumsum(term_lens)
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)
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]
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dts = [
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VGroup(*terms[1][-3:-1]),
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VGroup(*terms[2][5:7]),
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VGroup(*terms[3][1:3]),
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terms[-1]
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]
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VGroup(*dts).highlight(TIME_COLOR)
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two_cubed_terms = terms[0], terms[4]
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for term in terms:
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self.play(FadeIn(term))
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self.dither()
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#Cancel out two_cubed terms
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self.play(*it.chain(*[
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[
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tc.scale, 1.3, tc.get_corner(vect),
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tc.highlight, RED
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]
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for tc, vect in zip(
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two_cubed_terms,
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[DOWN+RIGHT, DOWN+LEFT]
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)
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]))
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self.play(*map(FadeOut, two_cubed_terms))
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numerator = VGroup(*terms[1:4])
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self.play(
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numerator.scale, 1.3, numerator.get_bottom(),
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terms[-1].scale, 1.3, terms[-1].get_top()
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)
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#Cancel out dt
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#TODO
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