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Partial progress to ShowVectorEquation in waves
This commit is contained in:
Grant Sanderson
parent
b3fdf20767
commit
41e715718b
4 changed files with 312 additions and 27 deletions
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@ -1,5 +1,6 @@
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from helpers import *
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from mobject import Mobject, Group
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from simple_animations import MaintainPositionRelativeTo
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import copy
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class ContinualAnimation(object):
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@ -63,7 +64,6 @@ class ContinualAnimationGroup(ContinualAnimation):
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for continual_animation in self.continual_animations:
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continual_animation.update(dt)
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class AmbientRotation(ContinualAnimation):
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CONFIG = {
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"axis" : OUT,
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@ -73,8 +73,6 @@ class AmbientRotation(ContinualAnimation):
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def update_mobject(self, dt):
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self.mobject.rotate(dt*self.rate, axis = self.axis)
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class AmbientMovement(ContinualAnimation):
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CONFIG = {
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"direction" : RIGHT,
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@ -84,9 +82,21 @@ class AmbientMovement(ContinualAnimation):
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def update_mobject(self, dt):
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self.mobject.shift(dt*self.rate*self.direction)
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class ContinualUpdateFromFunc(ContinualAnimation):
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def __init__(self, mobject, func, **kwargs):
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self.func = func
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ContinualAnimation.__init__(self, mobject, **kwargs)
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def update_mobject(self, dt):
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self.func(self.mobject)
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class ContinualMaintainPositionRelativeTo(ContinualAnimation):
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def __init__(self, mobject, tracked_mobject, **kwargs):
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self.anim = MaintainPositionRelativeTo(mobject, tracked_mobject, **kwargs)
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ContinualAnimation.__init__(self, mobject, **kwargs)
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def update_mobject(self, dt):
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self.anim.update(0)
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@ -122,9 +122,11 @@ class Scene(object):
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self.clear()
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###
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def continual_update(self):
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def continual_update(self, dt = None):
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if dt is None:
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dt = self.frame_duration
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for continual_animation in self.continual_animations:
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continual_animation.update(self.frame_duration)
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continual_animation.update(dt)
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def wind_down(self, *continual_animations, **kwargs):
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wind_down_time = kwargs.get("wind_down_time", 1)
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@ -384,6 +386,7 @@ class Scene(object):
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self.add(*moving_mobjects)
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self.mobjects_from_last_animation = moving_mobjects
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self.clean_up_animations(*animations)
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self.continual_update(0)
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return self
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def clean_up_animations(self, *animations):
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@ -141,28 +141,31 @@ class Axes(VGroup):
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"color" : LIGHT_GREY,
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"include_tip" : True,
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},
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"x_axis_radius" : SPACE_WIDTH,
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"y_axis_radius" : SPACE_HEIGHT,
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"z_axis_radius" : 3.5,
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"x_min" : -SPACE_WIDTH,
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"x_max" : SPACE_WIDTH,
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"y_min" : -SPACE_HEIGHT,
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"y_max" : SPACE_HEIGHT,
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"z_min" : -3.5,
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"z_max" : 3.5,
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}
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def __init__(self, **kwargs):
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VGroup.__init__(self, **kwargs)
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self.x_axis = NumberLine(
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x_min = -self.x_axis_radius,
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x_max = self.x_axis_radius,
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x_min = self.x_min,
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x_max = self.x_max,
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**self.number_line_config
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)
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self.y_axis = NumberLine(
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x_min = -self.y_axis_radius,
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x_max = self.y_axis_radius,
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x_min = self.y_min,
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x_max = self.y_max,
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**self.number_line_config
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)
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self.y_axis.rotate(np.pi/2)
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self.add(self.x_axis, self.y_axis)
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if self.three_d:
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self.z_axis = NumberLine(
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x_min = -self.z_axis_radius,
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x_max = self.z_axis_radius,
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x_min = self.min,
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x_max = self.max,
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**self.number_line_config
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)
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self.z_axis.rotate(-np.pi/2, UP)
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@ -171,8 +174,10 @@ class Axes(VGroup):
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class ThreeDAxes(Axes):
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CONFIG = {
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"x_axis_radius" : 5.5,
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"y_axis_radius" : 4.5,
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"x_min" : -5.5,
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"x_max" : 5.5,
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"y_min" : -4.5,
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"y_max" : -4.5,
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"three_d" : True,
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}
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283
waves.py
283
waves.py
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@ -762,7 +762,7 @@ class ListRelevantWaveIdeas(TeacherStudentsScene):
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topics = VGroup(*map(TextMobject, [
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"- Superposition",
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"- Amplitudes",
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"- Phase influences addition",
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"- How phase influences addition",
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]))
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topics.scale(0.8)
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topics.arrange_submobjects(DOWN, aligned_edge = LEFT)
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@ -848,6 +848,11 @@ class DirectWaveOutOfScreen(IntroduceEMWave):
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self.dither(4)
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class ShowVectorEquation(Scene):
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CONFIG = {
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"f_color" : RED,
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"phi_color" : MAROON_B,
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"A_color" : GREEN,
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}
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def construct(self):
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self.force_skipping()
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@ -869,26 +874,288 @@ class ShowVectorEquation(Scene):
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frequency = 0.25,
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)
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self.add(self.oscillating_vector)
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self.revert_to_original_skipping_status()
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self.dither(3)
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def add_plane(self):
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pass
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xy_plane = NumberPlane(
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axes_color = LIGHT_GREY,
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color = DARK_GREY,
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secondary_color = DARK_GREY,
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x_unit_size = 2,
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y_unit_size = 2,
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)
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xy_plane.add_coordinates()
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xy_plane.add(xy_plane.get_axis_labels())
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self.play(
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Write(xy_plane),
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Animation(self.vector)
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)
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self.dither(2)
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def write_horizontally_polarized(self):
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pass
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words = TextMobject("``Horizontally polarized''")
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words.next_to(ORIGIN, LEFT)
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words.to_edge(UP)
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words.add_background_rectangle()
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self.play(Write(words, run_time = 3))
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self.dither()
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self.horizontally_polarized_words = words
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def write_components(self):
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pass
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x, y = components = VGroup(
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TexMobject("\\cos(", "2\\pi", "f_x", "t", "+ ", "\\phi_x", ")"),
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TexMobject("0")
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)
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components.arrange_submobjects(DOWN)
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lb, rb = brackets = TexMobject("[]")
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brackets.scale_to_fit_height(components.get_height() + SMALL_BUFF)
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lb.next_to(components, LEFT, buff = 0.3)
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rb.next_to(components, RIGHT, buff = 0.3)
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E, equals = E_equals = TexMobject(
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"\\vec{\\textbf{E}}", "="
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)
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E.highlight(E_COLOR)
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E_equals.next_to(brackets, LEFT)
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E_equals.add_background_rectangle()
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brackets.add_background_rectangle()
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group = VGroup(E_equals, brackets, components)
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group.next_to(
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self.horizontally_polarized_words,
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DOWN, MED_LARGE_BUFF, RIGHT
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)
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x_without_phi = TexMobject("\\cos(", "2\\pi", "f_x", "t", ")")
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x_without_phi.move_to(x)
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for mob in x, x_without_phi:
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mob.highlight_by_tex_to_color_map({
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"f_x" : self.f_color,
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"phi_x" : self.phi_color,
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})
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def update_brace(brace):
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brace.stretch_to_fit_width(
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max(self.vector.get_width(), 0.001)
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)
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brace.next_to(self.vector.get_center(), DOWN, SMALL_BUFF)
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return brace
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moving_brace = ContinualUpdateFromFunc(
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Brace(Line(LEFT, RIGHT), DOWN), update_brace
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)
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moving_x_without_phi = ContinualUpdateFromFunc(
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x_without_phi.copy().add_background_rectangle(),
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lambda m : m.next_to(moving_brace.mobject, DOWN, SMALL_BUFF)
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)
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self.play(Write(E_equals), Write(brackets))
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y.save_state()
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y.move_to(self.horizontally_polarized_words)
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y.set_fill(opacity = 0)
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self.play(y.restore)
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self.dither()
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self.add(moving_brace, moving_x_without_phi)
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self.play(
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FadeIn(moving_brace.mobject),
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FadeIn(x_without_phi),
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FadeIn(moving_x_without_phi.mobject),
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submobject_mode = "lagged_start",
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run_time = 2,
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)
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self.dither(3)
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self.play(
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FadeOut(moving_brace.mobject),
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FadeOut(moving_x_without_phi.mobject),
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)
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self.remove(moving_brace, moving_x_without_phi)
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self.E_equals = E_equals
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self.brackets = brackets
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self.x_without_phi = x_without_phi
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self.components = components
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def show_graph(self):
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pass
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axes = Axes(
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x_min = -0.5,
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x_max = 5.2,
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y_min = -1.5,
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y_max = 1.5,
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)
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axes.x_axis.add_numbers(*range(1, 6))
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t = TexMobject("t")
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t.next_to(axes.x_axis, UP, SMALL_BUFF, RIGHT)
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cos = self.x_without_phi.copy()
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cos.next_to(axes.y_axis, RIGHT, SMALL_BUFF, UP)
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cos_arg = VGroup(*cos[1:-1])
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fx_equals_1 = TexMobject("f_x", "= 1")
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fx_equals_fourth = TexMobject("f_x", "= 0.25")
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fx_group = VGroup(fx_equals_1, fx_equals_fourth)
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for fx in fx_group:
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fx[0].highlight(self.f_color)
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fx.move_to(axes, UP+RIGHT)
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high_f_graph, low_f_graph = graphs = VGroup(*[
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FunctionGraph(
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lambda x : np.cos(2*np.pi*f*x),
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color = E_COLOR,
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x_min = 0,
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x_max = 4/f,
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num_steps = 20/f,
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)
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for f in 1, 0.25,
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])
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group = VGroup(axes, t, cos, high_f_graph, *fx_group)
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rect = SurroundingRectangle(
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group,
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buff = MED_LARGE_BUFF,
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stroke_color = WHITE,
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stroke_width = 3,
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fill_color = BLACK,
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fill_opacity = 0.9
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)
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group.add_to_back(rect)
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group.scale(0.8)
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group.to_corner(UP+RIGHT, buff = -SMALL_BUFF)
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group.remove(*it.chain(fx_group, graphs))
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low_f_graph.scale(0.8)
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low_f_graph.move_to(high_f_graph, LEFT)
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cos_arg_rect = SurroundingRectangle(cos_arg)
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new_ov = OscillatingVector(
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Vector(RIGHT, color = E_COLOR),
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A_vect = [2, 0, 0],
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frequency = 1,
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start_up_time = 0,
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)
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self.play(FadeIn(group))
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self.play(
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ReplacementTransform(
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self.components[0].get_part_by_tex("f_x").copy(),
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fx_equals_1
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),
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)
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self.dither(4 - (self.oscillating_vector.internal_time%4))
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self.remove(self.oscillating_vector)
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self.add(new_ov)
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self.play(ShowCreation(
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high_f_graph, run_time = 4,
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rate_func = None,
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))
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self.dither()
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self.play(FadeOut(new_ov.vector))
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self.remove(new_ov)
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self.add(self.oscillating_vector)
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self.play(
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ReplacementTransform(*fx_group),
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ReplacementTransform(*graphs),
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FadeOut(new_ov.vector),
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FadeIn(self.vector)
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)
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self.dither(4)
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self.play(ShowCreation(cos_arg_rect))
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self.play(FadeOut(cos_arg_rect))
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self.dither(5)
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self.corner_group = group
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self.fx_equals_fourth = fx_equals_fourth
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self.corner_cos = cos
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self.low_f_graph = low_f_graph
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self.graph_axes = axes
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def add_phi(self):
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pass
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corner_cos = self.corner_cos
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corner_phi = TexMobject("+", "\\phi_x")
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corner_phi.highlight_by_tex("phi", self.phi_color)
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corner_phi.scale(0.8)
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corner_phi.next_to(corner_cos[-2], RIGHT, SMALL_BUFF)
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x, y = self.components
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x_without_phi = self.x_without_phi
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words = TextMobject("``Phase shift''")
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words.next_to(ORIGIN, UP+LEFT)
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words.highlight(self.phi_color)
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words.add_background_rectangle()
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arrow = Arrow(words.get_top(), x[-2])
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arrow.highlight(WHITE)
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self.play(
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ReplacementTransform(
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VGroup(*x_without_phi[:-1]),
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VGroup(*x[:-3]),
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),
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ReplacementTransform(x_without_phi[-1], x[-1]),
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Write(VGroup(*x[-3:-1])),
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corner_cos[-1].next_to, corner_phi.copy(), RIGHT, SMALL_BUFF,
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Write(corner_phi),
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FadeOut(self.fx_equals_fourth),
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)
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self.play(self.low_f_graph.shift, MED_LARGE_BUFF*LEFT)
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self.play(
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Write(words, run_time = 1),
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ShowCreation(arrow)
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)
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self.dither(3)
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self.play(*map(FadeOut, [words, arrow]))
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self.corner_cos.add(corner_phi)
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def add_amplitude(self):
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pass
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x, y = self.components
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corner_cos = self.corner_cos
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graph = self.low_f_graph
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graph_y_axis = self.graph_axes.y_axis
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A = TexMobject("A_x")
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A.highlight(self.A_color)
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A.move_to(x.get_left())
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corner_A = A.copy()
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corner_A.scale(0.8)
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corner_A.move_to(corner_cos, LEFT)
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h_brace = Brace(Line(ORIGIN, 2*RIGHT), UP)
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v_brace = Brace(Line(
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graph_y_axis.number_to_point(0),
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graph_y_axis.number_to_point(1),
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), LEFT, buff = SMALL_BUFF)
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for brace in h_brace, v_brace:
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brace.A = brace.get_tex("A_x")
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brace.A.highlight(self.A_color)
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v_brace.A.scale(0.5, about_point = v_brace.get_center())
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all_As = VGroup(A, corner_A, h_brace.A, v_brace.A)
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def update_vect(vect):
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self.oscillating_vector.A_vect[0] = h_brace.get_width()
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return vect
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self.revert_to_original_skipping_status()
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self.play(
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GrowFromCenter(h_brace),
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GrowFromCenter(v_brace),
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)
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self.dither(2)
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self.play(
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x.next_to, A, RIGHT, SMALL_BUFF,
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corner_cos.next_to, corner_A, RIGHT, SMALL_BUFF,
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FadeIn(all_As)
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)
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self.dither()
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factor = 0.5
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self.play(
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v_brace.stretch_in_place, factor, 1,
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v_brace.move_to, v_brace.copy(), DOWN,
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MaintainPositionRelativeTo(v_brace.A, v_brace),
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h_brace.stretch_in_place, factor, 0,
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h_brace.move_to, h_brace.copy(), LEFT,
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MaintainPositionRelativeTo(h_brace.A, h_brace),
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UpdateFromFunc(self.vector, update_vect),
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graph.stretch_in_place, factor, 1,
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)
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self.dither(4)
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def add_kets(self):
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pass
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