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Up to multiplicative group of reals in efvgt
This commit is contained in:
Grant Sanderson
parent
3eac6bcaf9
commit
163ad545a8
4 changed files with 429 additions and 57 deletions
373
efvgt.py
373
efvgt.py
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@ -1232,6 +1232,8 @@ class AdditiveGroupOfReals(Scene):
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"number_line_center" : UP,
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"shadow_line_center" : DOWN,
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"zero_color" : GREEN_B,
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"x_min" : -2*SPACE_WIDTH,
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"x_max" : 2*SPACE_WIDTH,
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}
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def construct(self):
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self.add_number_line()
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@ -1248,8 +1250,8 @@ class AdditiveGroupOfReals(Scene):
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def add_number_line(self):
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number_line = NumberLine(
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x_min = -2*SPACE_WIDTH,
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x_max = 2*SPACE_WIDTH
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x_min = self.x_min,
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x_max = self.x_max,
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)
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number_line.shift(self.number_line_center)
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@ -1535,7 +1537,7 @@ class AdditiveGroupOfComplexNumbers(ComplexTransformationScene):
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self.foreground_mobjects.remove(imag_arrow)
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self.play(*map(FadeOut, [real_arrow, imag_arrow, self.plane]))
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self.plane.restore()
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self.plane.set_stroke(0)
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self.plane.set_stroke(width = 0)
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self.play(self.plane.restore)
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self.z1 = z
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@ -1690,6 +1692,371 @@ class AdditiveGroupOfComplexNumbers(ComplexTransformationScene):
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*added_anims
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)
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class SchizophrenicNumbers(Scene):
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def construct(self):
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v_line = DashedLine(
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SPACE_HEIGHT*UP,
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SPACE_HEIGHT*DOWN
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)
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left_title = TextMobject("Additive group")
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left_title.shift(SPACE_WIDTH*LEFT/2)
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right_title = TextMobject("Multiplicative group")
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right_title.shift(SPACE_WIDTH*RIGHT/2)
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VGroup(left_title, right_title).to_edge(UP)
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self.add(v_line, left_title, right_title)
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numbers = VGroup(
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Randolph(mode = "happy").scale(0.2),
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TexMobject("3").shift(UP+LEFT),
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TexMobject("5.83").shift(UP+RIGHT),
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TexMobject("\\sqrt{2}").shift(DOWN+LEFT),
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TexMobject("2-i").shift(DOWN+RIGHT),
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)
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for number in numbers:
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number.highlight(ADDER_COLOR)
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number.scale(1.5)
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if isinstance(number, PiCreature):
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continue
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number.eyes = Eyes(number[0], height = 0.1)
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number.add(number.eyes)
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numbers[3].eyes.next_to(numbers[3][1], UP, buff = 0)
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numbers.shift(SPACE_WIDTH*LEFT/2)
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self.play(FadeIn(numbers))
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self.blink_numbers(numbers)
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self.dither()
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self.add(numbers.copy())
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for number in numbers:
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number.generate_target()
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number.target.shift(SPACE_WIDTH*RIGHT)
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number.target.eyes.save_state()
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number.target.highlight(MULTIPLIER_COLOR)
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number.target.eyes.restore()
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self.play(*[
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MoveToTarget(
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number,
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rate_func = squish_rate_func(
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smooth, alpha, alpha+0.5
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),
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run_time = 2,
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)
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for number, alpha in zip(numbers, np.linspace(0, 0.5, len(numbers)))
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])
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self.dither()
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self.blink_numbers(numbers)
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self.dither()
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def blink_numbers(self, numbers):
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self.play(*[
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num.eyes.blink_anim(
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rate_func = squish_rate_func(
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there_and_back, alpha, alpha+0.2
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)
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)
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for num, alpha in zip(
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numbers[1:], 0.8*np.random.random(len(numbers))
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)
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])
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class MultiplicativeGroupOfReals(AdditiveGroupOfReals):
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CONFIG = {
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"number_line_center" : 0.5*UP,
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"shadow_line_center" : 1.5*DOWN,
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"x_min" : -3*SPACE_WIDTH,
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"x_max" : 3*SPACE_WIDTH,
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}
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def setup(self):
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self.foreground_mobjects = VGroup()
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def construct(self):
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self.add_title()
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self.add_number_line()
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self.introduce_stretch_and_squish()
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self.show_zero_fixed_in_place()
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self.follow_one()
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self.every_positive_number_association()
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self.compose_actions(3, 2)
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self.compose_actions(4, 0.5)
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self.write_group_name()
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self.compose_actions(1.5, 1.5)
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def add_title(self):
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self.title = TextMobject("Group of stretching/squishing actions")
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self.title.to_edge(UP)
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self.add(self.title)
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def add_number_line(self):
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AdditiveGroupOfReals.add_number_line(self)
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self.zero_point = self.number_line.number_to_point(0)
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self.one = filter(
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lambda m : m.get_tex_string() is "1",
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self.number_line.numbers
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)[0]
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self.one.add_background_rectangle()
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self.one.background_rectangle.scale_in_place(1.3)
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self.number_line.save_state()
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def introduce_stretch_and_squish(self):
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for num in [3, 0.25]:
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self.stretch(num)
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self.dither()
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self.play(self.number_line.restore)
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self.dither()
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def show_zero_fixed_in_place(self):
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arrow = Arrow(self.zero_point + UP, self.zero_point, buff = 0)
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arrow.highlight(ADDER_COLOR)
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words = TextMobject("Fix zero")
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words.highlight(ADDER_COLOR)
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words.next_to(arrow, UP)
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self.play(
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ShowCreation(arrow),
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Write(words)
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)
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self.foreground_mobjects.add(arrow)
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self.stretch(4)
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self.stretch(0.1)
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self.dither()
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self.play(self.number_line.restore)
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self.play(FadeOut(words))
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self.dither()
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self.zero_arrow = arrow
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def follow_one(self):
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dot = Dot(self.number_line.number_to_point(1))
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arrow = Arrow(dot.get_center()+UP+RIGHT, dot)
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words = TextMobject("Follow one")
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words.next_to(arrow.get_start(), UP)
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for mob in dot, arrow, words:
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mob.highlight(MULTIPLIER_COLOR)
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three_line, half_line = [
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DashedLine(
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self.number_line.number_to_point(num),
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self.shadow_line.number_to_point(num)
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)
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for num in 3, 0.5
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]
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three_mob = filter(
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lambda m : m.get_tex_string() == "3",
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self.shadow_line.numbers
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)[0]
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half_point = self.shadow_line.number_to_point(0.5)
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half_arrow = Arrow(
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half_point+UP+LEFT, half_point, buff = SMALL_BUFF,
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tip_length = 0.15,
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)
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half_label = TexMobject("1/2")
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half_label.scale(0.7)
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half_label.highlight(MULTIPLIER_COLOR)
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half_label.next_to(half_arrow.get_start(), LEFT, buff = SMALL_BUFF)
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self.play(
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ShowCreation(arrow),
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DrawBorderThenFill(dot),
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Write(words)
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)
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self.number_line.add(dot)
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self.number_line.numbers.add(dot)
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self.number_line.save_state()
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self.dither()
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self.play(*map(FadeOut, [arrow, words]))
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self.stretch(3)
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self.play(
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ShowCreation(three_line),
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Animation(self.one)
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)
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dot_copy = dot.copy()
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self.play(
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dot_copy.move_to, three_line.get_bottom()
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)
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self.play(Indicate(three_mob, run_time = 2))
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self.dither()
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self.play(
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self.number_line.restore,
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*map(FadeOut, [three_line, dot_copy])
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)
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self.dither()
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self.stretch(0.5)
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self.play(
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ShowCreation(half_line),
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Animation(self.one)
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)
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dot_copy = dot.copy()
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self.play(
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dot_copy.move_to, half_line.get_bottom()
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)
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self.play(
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Write(half_label),
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ShowCreation(half_arrow)
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)
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self.dither()
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self.play(
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self.number_line.restore,
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*map(FadeOut, [
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half_label, half_arrow,
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half_line, dot_copy
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])
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)
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self.dither()
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self.one_dot = dot
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def every_positive_number_association(self):
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positive_reals_line = Line(
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self.shadow_line.number_to_point(0),
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self.shadow_line.number_to_point(SPACE_WIDTH),
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color = MULTIPLIER_COLOR
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)
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positive_reals_words = TextMobject("All positive reals")
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positive_reals_words.highlight(MULTIPLIER_COLOR)
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positive_reals_words.next_to(positive_reals_line, UP)
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positive_reals_words.add_background_rectangle()
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half_line, one_line = [
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DashedLine(
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self.number_line.number_to_point(num),
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self.shadow_line.number_to_point(num)
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)
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for num in 0.5, 1
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]
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self.play(
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self.zero_arrow.shift, 0.5*UP,
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rate_func = there_and_back
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)
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self.dither()
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self.play(
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self.one_dot.shift, 0.25*UP,
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rate_func = wiggle
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)
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self.stretch(3)
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self.stretch(0.33/3, run_time = 3)
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self.dither()
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self.play(ShowCreation(half_line), Animation(self.one))
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self.play(
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ShowCreation(positive_reals_line),
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Write(positive_reals_words),
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)
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self.dither()
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self.play(
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ReplacementTransform(half_line, one_line),
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self.number_line.restore,
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Animation(positive_reals_words),
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run_time = 2
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)
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self.number_line.add_to_back(one_line)
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self.number_line.save_state()
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self.stretch(
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7, run_time = 10, rate_func = there_and_back,
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added_anims = [Animation(positive_reals_words)]
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)
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self.dither()
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def compose_actions(self, num1, num2):
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words = VGroup(*[
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TextMobject("(%s by %s)"%(word, str(num)))
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for num in num1, num2, num1*num2
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for word in ["Stretch" if num > 1 else "Squish"]
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])
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words.submobjects.insert(2, TexMobject("="))
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words.arrange_submobjects(RIGHT)
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top_words = VGroup(*words[:2])
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top_words.highlight(MULTIPLIER_COLOR)
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bottom_words = VGroup(*words[2:])
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bottom_words.next_to(top_words, DOWN)
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words.scale(0.8)
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words.next_to(self.number_line, UP)
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words.to_edge(RIGHT)
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for num, word in zip([num1, num2], top_words):
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self.stretch(
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num,
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added_anims = [FadeIn(word)],
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run_time = 3
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)
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self.dither()
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self.play(FadeOut(self.number_line))
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self.number_line.restore()
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self.play(FadeIn(self.number_line))
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self.stretch(
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num1*num2,
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added_anims = [FadeIn(bottom_words)],
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run_time = 3
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)
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self.dither(2)
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self.play(
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ApplyMethod(self.number_line.restore, run_time = 2),
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FadeOut(words),
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)
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self.dither()
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def write_group_name(self):
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new_title = TextMobject(
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"Multiplicative group of positive real numbers"
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)
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new_title.to_edge(UP)
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VGroup(*new_title[:len("Multiplicative")]).highlight(MULTIPLIER_COLOR)
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VGroup(*new_title[-len("positiverealnumbers"):]).highlight(MULTIPLIER_COLOR)
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self.play(Transform(self.title, new_title))
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self.dither()
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###
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def stretch(self, factor, run_time = 2, **kwargs):
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kwargs["run_time"] = run_time
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target = self.number_line.copy()
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target.stretch_about_point(factor, 0, self.zero_point)
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total_factor = (target.number_to_point(1)-self.zero_point)[0]
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for number in target.numbers:
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number.stretch_in_place(1./factor, dim = 0)
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if total_factor < 0.7:
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number.stretch_in_place(total_factor, dim = 0)
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self.play(
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Transform(self.number_line, target, **kwargs),
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*kwargs.get("added_anims", [])
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)
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def play(self, *anims, **kwargs):
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anims = list(anims) + [Animation(self.foreground_mobjects)]
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Scene.play(self, *anims, **kwargs)
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class MultiplicativeGroupOfComplexNumbers(AdditiveGroupOfComplexNumbers):
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def construct(self):
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self.add_plane()
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@ -126,10 +126,6 @@ class Mobject(object):
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self.shift(about_point)
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return self
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def scale_about_point(self, scale_factor, point):
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self.do_about_point(point, self.scale, scale_factor)
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return self
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def rotate_about_origin(self, angle, axis = OUT, axes = []):
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if len(axes) == 0:
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axes = [axis]
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@ -214,6 +210,10 @@ class Mobject(object):
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self.do_in_place(self.scale, scale_factor)
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return self
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def scale_about_point(self, scale_factor, point):
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self.do_about_point(point, self.scale, scale_factor)
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return self
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def pose_at_angle(self):
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self.rotate_in_place(np.pi / 7, RIGHT+UP)
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return self
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@ -284,6 +284,10 @@ class Mobject(object):
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return True
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return False
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def stretch_about_point(self, factor, dim, point):
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self.do_about_point(point, self.stretch, factor, dim)
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return self
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def stretch_in_place(self, factor, dim):
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self.do_in_place(self.stretch, factor, dim)
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return self
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|
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@ -1454,56 +1454,6 @@ class RecursionTime(Scene):
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self.play(Blink(morty))
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self.dither()
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class Eyes(VMobject):
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CONFIG = {
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"height" : 0.3,
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"thing_looked_at" : None,
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"mode" : "plain",
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}
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def __init__(self, mobject, **kwargs):
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VMobject.__init__(self, **kwargs)
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self.mobject = mobject
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self.submobjects = self.get_eyes().submobjects
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def get_eyes(self, mode = None, thing_to_look_at = None):
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mode = mode or self.mode
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if thing_to_look_at is None:
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thing_to_look_at = self.thing_looked_at
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pi = Randolph(mode = mode)
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eyes = VGroup(pi.eyes, pi.pupils)
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eyes.scale_to_fit_height(self.height)
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if self.submobjects:
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eyes.move_to(self, DOWN)
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else:
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eyes.move_to(self.mobject.get_top(), DOWN)
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if thing_to_look_at is not None:
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pi.look_at(thing_to_look_at)
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return eyes
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def change_mode_anim(self, mode, **kwargs):
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self.mode = mode
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return Transform(self, self.get_eyes(mode = mode), **kwargs)
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def look_at_anim(self, point_or_mobject, **kwargs):
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self.thing_looked_at = point_or_mobject
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return Transform(
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self, self.get_eyes(thing_to_look_at = point_or_mobject),
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**kwargs
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)
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def blink_anim(self):
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target = self.copy()
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bottom_y = self.get_bottom()[1]
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for submob in target:
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submob.apply_function(
|
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lambda p : [p[0], bottom_y, p[2]]
|
||||
)
|
||||
return Transform(
|
||||
self, target,
|
||||
rate_func = squish_rate_func(there_and_back)
|
||||
)
|
||||
|
||||
class RecursiveSolution(TowersOfHanoiScene):
|
||||
CONFIG = {
|
||||
"num_disks" : 4,
|
||||
|
|
|
|||
|
|
@ -229,6 +229,57 @@ class Blink(ApplyMethod):
|
|||
def __init__(self, pi_creature, **kwargs):
|
||||
ApplyMethod.__init__(self, pi_creature.blink, **kwargs)
|
||||
|
||||
class Eyes(VMobject):
|
||||
CONFIG = {
|
||||
"height" : 0.3,
|
||||
"thing_looked_at" : None,
|
||||
"mode" : "plain",
|
||||
}
|
||||
def __init__(self, mobject, **kwargs):
|
||||
VMobject.__init__(self, **kwargs)
|
||||
self.mobject = mobject
|
||||
self.submobjects = self.get_eyes().submobjects
|
||||
|
||||
def get_eyes(self, mode = None, thing_to_look_at = None):
|
||||
mode = mode or self.mode
|
||||
if thing_to_look_at is None:
|
||||
thing_to_look_at = self.thing_looked_at
|
||||
|
||||
pi = Randolph(mode = mode)
|
||||
eyes = VGroup(pi.eyes, pi.pupils)
|
||||
eyes.scale_to_fit_height(self.height)
|
||||
if self.submobjects:
|
||||
eyes.move_to(self, DOWN)
|
||||
else:
|
||||
eyes.move_to(self.mobject.get_top(), DOWN)
|
||||
if thing_to_look_at is not None:
|
||||
pi.look_at(thing_to_look_at)
|
||||
return eyes
|
||||
|
||||
def change_mode_anim(self, mode, **kwargs):
|
||||
self.mode = mode
|
||||
return Transform(self, self.get_eyes(mode = mode), **kwargs)
|
||||
|
||||
def look_at_anim(self, point_or_mobject, **kwargs):
|
||||
self.thing_looked_at = point_or_mobject
|
||||
return Transform(
|
||||
self, self.get_eyes(thing_to_look_at = point_or_mobject),
|
||||
**kwargs
|
||||
)
|
||||
|
||||
def blink_anim(self, **kwargs):
|
||||
target = self.copy()
|
||||
bottom_y = self.get_bottom()[1]
|
||||
for submob in target:
|
||||
submob.apply_function(
|
||||
lambda p : [p[0], bottom_y, p[2]]
|
||||
)
|
||||
if "rate_func" not in kwargs:
|
||||
kwargs["rate_func"] = squish_rate_func(there_and_back)
|
||||
return Transform(self, target, **kwargs)
|
||||
|
||||
|
||||
#######################
|
||||
|
||||
class PiCreatureBubbleIntroduction(AnimationGroup):
|
||||
CONFIG = {
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue