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Symmetries of a square
This commit is contained in:
Grant Sanderson
parent
1b0b54a393
commit
be56ffa687
1 changed files with 138 additions and 30 deletions
168
efvgt.py
168
efvgt.py
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@ -307,16 +307,10 @@ class SymmetriesOfSquare(ThreeDScene):
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},
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}
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def construct(self):
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##REMOVE##
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should_skip_animations = self.skip_animations
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self.skip_animations = True
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##
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self.add_title()
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self.ask_about_square_symmetry()
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self.talk_through_90_degree_rotation()
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self.talk_through_vertical_flip()
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self.skip_animations = should_skip_animations
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self.confused_by_lack_of_labels()
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self.add_labels()
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self.show_full_group()
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@ -353,18 +347,7 @@ class SymmetriesOfSquare(ThreeDScene):
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self.play(*map(FadeOut, [brace, q_marks]))
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def talk_through_90_degree_rotation(self):
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square_radius = np.linalg.norm(self.square.get_corner(UP+RIGHT))
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arc = Arc(
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radius = square_radius + SMALL_BUFF,
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start_angle = np.pi/4 + SMALL_BUFF,
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angle = np.pi/2 - 2*SMALL_BUFF,
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color = YELLOW
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)
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arc.add_tip()
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arcs = VGroup(arc, *[
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arc.copy().rotate(i*np.pi/2)
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for i in range(1, 4)
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])
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arcs = self.get_rotation_arcs(self.square, np.pi/2)
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self.play(*map(ShowCreation, arcs))
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self.dither()
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@ -379,8 +362,8 @@ class SymmetriesOfSquare(ThreeDScene):
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def confused_by_lack_of_labels(self):
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randy = Randolph(mode = "confused")
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randy.next_to(self.square, DOWN+LEFT)
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randy.shift_onto_screen()
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randy.next_to(self.square, LEFT, buff = LARGE_BUFF)
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randy.to_edge(DOWN)
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self.play(FadeIn(randy))
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for axis in OUT, RIGHT, UP:
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self.rotate_square(
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@ -393,19 +376,117 @@ class SymmetriesOfSquare(ThreeDScene):
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self.randy = randy
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def add_labels(self):
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pass
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labels = VGroup()
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dots = VGroup()
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for tex, vertex in zip("ABCD", self.square.get_anchors()):
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label = TexMobject(tex)
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label.next_to(vertex, vertex, SMALL_BUFF)
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labels.add(label)
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dot = Dot(vertex, color = WHITE)
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dots.add(dot)
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self.square.add(labels, dots)
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self.square.labels = labels
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self.square.dots = dots
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self.play(
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Write(labels),
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Write(dots),
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self.randy.change_mode, "happy",
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self.randy.look_at, labels[0]
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)
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self.play(Blink(self.randy))
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self.play(FadeOut(self.randy))
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self.rotate_square(run_time = 2)
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self.dither()
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def show_full_group(self):
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pass
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new_title = TextMobject("Group", "of", "symmetries")
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new_title.move_to(self.title)
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all_squares = VGroup(*[
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self.square.copy().scale(0.5)
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for x in range(8)
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])
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all_squares.arrange_submobjects(RIGHT, buff = LARGE_BUFF)
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top_squares = VGroup(*all_squares[:4])
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bottom_squares = VGroup(*all_squares[4:])
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bottom_squares.next_to(top_squares, DOWN, buff = LARGE_BUFF)
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all_squares.scale_to_fit_width(2*SPACE_WIDTH-2*LARGE_BUFF)
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all_squares.center()
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all_squares.to_edge(DOWN, buff = LARGE_BUFF)
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self.play(ReplacementTransform(self.square, all_squares[0]))
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self.play(ReplacementTransform(self.title, new_title))
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self.title = new_title
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self.play(*[
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ApplyMethod(mob.highlight, GREY)
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for mob in self.title[1:]
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])
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for square, angle in zip(all_squares[1:4], [np.pi/2, np.pi, -np.pi/2]):
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arcs = self.get_rotation_arcs(square, angle, MED_SMALL_BUFF)
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if angle == np.pi:
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arcs = VGroup(arcs[0], arcs[2])
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self.play(*map(FadeIn, [square, arcs]))
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square.rotation_kwargs = {"angle" : angle}
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self.rotate_square(square = square, **square.rotation_kwargs)
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square.add(arcs)
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for square, axis in zip(bottom_squares, [RIGHT, RIGHT+UP, UP, UP+LEFT]):
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axis_line = self.get_axis_line(square, axis)
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self.play(FadeIn(square))
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self.play(ShowCreation(axis_line))
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square.rotation_kwargs = {"angle" : np.pi, "axis" : axis}
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self.rotate_square(square = square, **square.rotation_kwargs)
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square.add(axis_line)
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self.dither()
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self.all_squares = all_squares
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def show_top_actions(self):
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pass
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all_squares = self.all_squares
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self.play(Indicate(all_squares[0]))
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self.dither()
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rotations = [
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Rotate(
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square,
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rate_func = lambda t : -there_and_back(t),
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run_time = 3,
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about_point = square.get_center(),
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**square.rotation_kwargs
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)
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for square in all_squares[1:4]
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]
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for rotation in rotations:
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for label in rotation.target_mobject.labels:
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label.rotate_in_place(-rotation.angle)
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self.play(*rotations)
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self.dither()
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def show_bottom_actions(self):
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pass
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for square in self.all_squares[4:]:
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self.rotate_square(
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square = square,
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rate_func = there_and_back,
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run_time = 2,
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**square.rotation_kwargs
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)
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self.dither()
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def name_dihedral_group(self):
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pass
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new_title = TextMobject(
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"``Dihedral group'' of order 8"
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)
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new_title.to_edge(UP)
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self.play(FadeOut(self.title))
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self.play(FadeIn(new_title))
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self.dither()
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##########
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@ -422,13 +503,19 @@ class SymmetriesOfSquare(ThreeDScene):
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assert hasattr(self, "square")
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square = self.square
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added_anims = added_anims or []
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rotation = Rotate(square, angle = angle, axis = axis, **kwargs)
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rotation = Rotate(
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square,
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angle = angle,
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axis = axis,
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about_point = square.get_center(),
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**kwargs
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)
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if hasattr(square, "labels"):
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for label in rotation.target_mobject.labels:
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label.rotate_in_place(-angle, axis)
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if show_axis:
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axis_line = DashedLine(2*axis, -2*axis)
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axis_line = self.get_axis_line(square, axis)
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self.play(
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ShowCreation(axis_line),
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Animation(square)
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@ -448,9 +535,30 @@ class SymmetriesOfSquare(ThreeDScene):
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**kwargs
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)
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def get_rotation_arcs(self, square, angle, angle_buff = SMALL_BUFF):
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square_radius = np.linalg.norm(
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square.points[0] - square.get_center()
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)
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arc = Arc(
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radius = square_radius + SMALL_BUFF,
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start_angle = np.pi/4 + np.sign(angle)*angle_buff,
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angle = angle - np.sign(angle)*2*angle_buff,
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color = YELLOW
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)
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arc.add_tip()
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arcs = VGroup(arc, *[
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arc.copy().rotate(i*np.pi/2)
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for i in range(1, 4)
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])
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arcs.move_to(square[0])
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return arcs
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def get_axis_line(self, square, axis):
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axis_line = DashedLine(2*axis, -2*axis)
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axis_line.replace(square, dim_to_match = np.argmax(np.abs(axis)))
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axis_line.scale_in_place(1.2)
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return axis_line
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