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Starting into symmetry description for efvgt
This commit is contained in:
Grant Sanderson
285
efvgt.py
285
efvgt.py
@ -18,6 +18,7 @@ from topics.combinatorics import *
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from topics.numerals import *
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from topics.three_dimensions import *
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from topics.objects import *
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from topics.complex_numbers import *
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from scene import Scene
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from scene.zoomed_scene import ZoomedScene
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from scene.reconfigurable_scene import ReconfigurableScene
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@ -124,12 +125,12 @@ class Anniversary(TeacherStudentsScene):
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def complain(self):
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self.student_says(
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"Why are you \\\\ talking so fast?",
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"Why were you \\\\ talking so fast?",
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student_index = 0,
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target_mode = "sassy",
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)
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self.change_student_modes(*["sassy"]*3)
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self.play(self.get_teacher().change_mode, "guilty")
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self.play(self.get_teacher().change_mode, "shruggie")
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self.dither(2)
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def get_party_hats(self):
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@ -172,12 +173,280 @@ class Anniversary(TeacherStudentsScene):
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]
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return confetti_spirils
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class WatchingScreen(PiCreatureScene):
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CONFIG = {
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"screen_height" : 5.5
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}
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def create_pi_creatures(self):
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randy = Randolph().to_corner(DOWN+LEFT)
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return VGroup(randy)
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def construct(self):
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screen = Rectangle(height = 9, width = 16)
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screen.scale_to_fit_height(self.screen_height)
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screen.to_corner(UP+RIGHT)
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self.add(screen)
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for mode in "erm", "pondering", "confused":
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self.dither()
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self.change_mode(mode)
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self.play(Animation(screen))
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self.dither()
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class LetsStudyTheBasics(TeacherStudentsScene):
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def construct(self):
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self.teacher_says("Let's learn some \\\\ group theory.")
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self.change_student_modes(*["happy"]*3)
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self.dither(2)
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class QuickExplanation(ComplexTransformationScene):
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CONFIG = {
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"plane_config" : {
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"x_line_frequency" : 1,
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"y_line_frequency" : 1,
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"secondary_line_ratio" : 1,
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"space_unit_to_x_unit" : 1.5,
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"space_unit_to_y_unit" : 1.5,
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},
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"background_fade_factor" : 0.2,
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"background_label_scale_val" : 0.7,
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"velocity_color" : RED,
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"position_color" : YELLOW,
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}
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def construct(self):
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# self.add_transformable_plane()
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self.add_equation()
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self.add_explanation()
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self.add_vectors()
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def add_equation(self):
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equation = TexMobject(
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"\\frac{d(e^{it})}{dt}",
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"=",
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"i", "e^{it}"
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)
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equation[0].highlight(self.velocity_color)
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equation[-1].highlight(self.position_color)
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equation.add_background_rectangle()
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brace = Brace(equation, UP)
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equation.add(brace)
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brace_text = TextMobject(
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"Velocity vector", "is a",
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"$90^\\circ$ \\\\ rotation",
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"of", "position vector"
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)
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brace_text[0].highlight(self.velocity_color)
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brace_text[-1].highlight(self.position_color)
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brace_text.add_background_rectangle()
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brace_text.scale(0.8)
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brace_text.to_corner(UP+LEFT, buff = MED_SMALL_BUFF)
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equation.next_to(brace_text, DOWN)
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self.add_foreground_mobjects(brace_text, equation)
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self.brace_text = brace_text
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def add_explanation(self):
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words = TextMobject("""
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Only a walk around the unit
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circle at rate 1 satisfies both
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this property and e^0 = 1.
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""")
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words.scale(0.8)
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words.add_background_rectangle()
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words.to_corner(UP+RIGHT, buff = MED_SMALL_BUFF)
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arrow = Arrow(RIGHT, 1.5*LEFT, color = WHITE)
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arrow.to_edge(UP)
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self.add(words, arrow)
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def add_vectors(self):
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right = self.z_to_point(1)
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s_vector = Arrow(
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ORIGIN, right,
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tip_length = 0.2,
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buff = 0,
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color = self.position_color,
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)
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v_vector = s_vector.copy().rotate(np.pi/2)
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v_vector.highlight(self.velocity_color)
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circle = Circle(
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radius = self.z_to_point(1)[0],
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color = self.position_color
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)
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self.dither(2)
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self.play(ShowCreation(s_vector))
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self.play(ReplacementTransform(
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s_vector.copy(), v_vector, path_arc = np.pi/2
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))
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self.dither()
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self.play(v_vector.shift, right)
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self.dither()
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self.vectors = VGroup(s_vector, v_vector)
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kwargs = {
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"rate_func" : None,
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"run_time" : 5,
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}
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rotation = Rotating(self.vectors, about_point = ORIGIN, **kwargs)
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self.play(
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ShowCreation(circle, **kwargs),
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rotation
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)
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self.play(rotation)
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self.play(rotation)
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class SymmetriesOfSquare(ThreeDScene):
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CONFIG = {
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"square_config" : {
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"side_length" : 2,
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"stroke_width" : 0,
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"fill_color" : BLUE,
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"fill_opacity" : 0.75,
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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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self.show_top_actions()
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self.show_bottom_actions()
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self.name_dihedral_group()
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def add_title(self):
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title = TextMobject("Groups", "$\\leftrightarrow$", "Symmetry")
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title.to_edge(UP)
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for index in 0, 2:
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self.play(Write(title[index], run_time = 1))
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self.play(GrowFromCenter(title[1]))
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self.dither()
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self.title = title
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def ask_about_square_symmetry(self):
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brace = Brace(self.title[-1])
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q_marks = brace.get_text("???")
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self.square = Square(**self.square_config)
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self.play(DrawBorderThenFill(self.square))
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self.play(GrowFromCenter(brace), Write(q_marks))
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self.rotate_square()
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self.dither()
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for axis in UP, UP+RIGHT:
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self.flip_square(axis)
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self.dither()
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self.rotate_square(-np.pi)
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self.dither()
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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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self.play(*map(ShowCreation, arcs))
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self.dither()
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self.rotate_square(np.pi/2, run_time = 2)
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self.dither()
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self.play(FadeOut(arcs))
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self.dither()
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def talk_through_vertical_flip(self):
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self.flip_square(UP, run_time = 2)
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self.dither()
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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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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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angle = np.pi, axis = axis,
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added_anims = [randy.look_at, self.square.points[0]]
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)
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self.play(Blink(randy))
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self.dither()
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self.randy = randy
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def add_labels(self):
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pass
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def show_full_group(self):
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pass
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def show_top_actions(self):
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pass
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def show_bottom_actions(self):
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pass
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def name_dihedral_group(self):
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pass
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##########
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def rotate_square(
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self,
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angle = np.pi/2,
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axis = OUT,
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square = None,
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show_axis = False,
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added_anims = None,
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**kwargs
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):
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if square is None:
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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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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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self.play(
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ShowCreation(axis_line),
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Animation(square)
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)
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self.play(rotation, *added_anims)
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if show_axis:
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self.play(
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FadeOut(axis_line),
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Animation(square)
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)
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def flip_square(self, axis = UP, **kwargs):
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self.rotate_square(
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angle = np.pi,
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axis = axis,
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show_axis = True,
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**kwargs
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)
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@ -20,9 +20,9 @@ class PartyHat(SVGMobject):
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"stroke_width" : 0,
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"fill_opacity" : 1,
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"propogate_style_to_family" : True,
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"frills_color" : MAROON_B,
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"frills_colors" : [MAROON_B, PURPLE],
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"cone_color" : RED,
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"dots_color" : YELLOW,
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"dots_colors" : [YELLOW],
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}
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NUM_FRILLS = 7
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NUM_DOTS = 6
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@ -36,9 +36,9 @@ class PartyHat(SVGMobject):
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self.cone = self[self.NUM_FRILLS]
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self.dots = VGroup(*self[self.NUM_FRILLS+1:])
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self.frills.highlight(self.frills_color)
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self.frills.gradient_highlight(*self.frills_colors)
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self.cone.highlight(self.cone_color)
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self.dots.highlight(self.dots_color)
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self.dots.gradient_highlight(*self.dots_colors)
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