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Added ManipulateLightsourceSetups
This commit is contained in:
Grant Sanderson
parent
0bf9f0b644
commit
3a59795330
1 changed files with 108 additions and 249 deletions
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@ -56,7 +56,6 @@ inverse_power_law = lambda maxint,scale,cutoff,exponent: \
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(lambda r: maxint * (cutoff/(r/scale+cutoff))**exponent)
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inverse_quadratic = lambda maxint,scale,cutoff: inverse_power_law(maxint,scale,cutoff,2)
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A = np.array([5.,-3.,0.])
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B = np.array([-5.,3.,0.])
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C = np.array([-5.,-3.,0.])
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@ -74,9 +73,6 @@ prelim_vector = np.array([xB * yA - xA * yB, xC * (xA - xB) + yC * (yA - yB)])
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H2 = np.linalg.solve(prelim_matrix,prelim_vector)
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H = np.append(H2, 0.)
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class AngleUpdater(ContinualAnimation):
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def __init__(self, angle_arc, spotlight, **kwargs):
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self.angle_arc = angle_arc
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@ -1713,6 +1709,10 @@ class InverseSquareLaw(ThreeDScene):
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self.play(
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screen_group.scale, 2, {"about_edge" : IN + DOWN},
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screen_group.shift, unit_distance*RIGHT,
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UpdateFromAlphaFunc(
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four_copies,
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lambda nc, a : nc.set_stroke(width = a).set_fill(opacity = 0.5*a)
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),
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four_copies_update_anim,
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screen_copy.shift, 0.25*OUT, #WHY?
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run_time = 2,
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@ -1737,8 +1737,7 @@ class InverseSquareLaw(ThreeDScene):
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Write(three, rate_func = squish_rate_func(smooth, 0.5, 1)),
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run_time = 2,
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)
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self.wait()
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self.wait(10)
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###
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@ -1751,261 +1750,121 @@ class InverseSquareLaw(ThreeDScene):
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anims += added_anims
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self.play(*anims, run_time = 2)
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class IndicatorScalingScene(Scene):
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class ScreensIntroWrapper(TeacherStudentsScene):
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def construct(self):
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point = VectorizedPoint(SPACE_WIDTH*LEFT/2 + SPACE_HEIGHT*UP/2)
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self.play(self.teacher.change, "raise_right_hand")
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self.change_student_modes(
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"pondering", "erm", "confused",
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look_at_arg = point,
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)
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self.play(self.teacher.look_at, point)
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self.wait(5)
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unit_intensity = 0.6
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indicator1 = LightIndicator(show_reading = False, color = LIGHT_COLOR)
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indicator1.set_intensity(unit_intensity)
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reading1 = TexMobject("1")
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reading1.move_to(indicator1)
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indicator2 = LightIndicator(show_reading = False, color = LIGHT_COLOR)
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indicator2.shift(2*RIGHT)
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indicator2.set_intensity(unit_intensity/4)
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reading2 = TexMobject("{1\over 4}").scale(0.8)
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reading2.move_to(indicator2)
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indicator3 = LightIndicator(show_reading = False, color = LIGHT_COLOR)
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indicator3.shift(4*RIGHT)
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indicator3.set_intensity(unit_intensity/9)
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reading3 = TexMobject("{1\over 9}").scale(0.8)
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reading3.move_to(indicator3)
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self.play(FadeIn(indicator1))
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self.play(FadeIn(reading1))
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self.wait()
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self.play(FadeOut(reading1))
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self.play(Transform(indicator1, indicator2))
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self.play(FadeIn(reading2))
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self.wait()
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self.play(FadeOut(reading2))
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self.play(Transform(indicator1, indicator3))
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self.play(FadeIn(reading3))
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self.wait()
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class BackToEulerSumScene(PiCreatureScene):
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class ManipulateLightsourceSetups(PiCreatureScene):
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CONFIG = {
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"num_levels" : 100,
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"radius" : 10,
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}
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def construct(self):
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self.remove(self.get_primary_pi_creature())
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unit_distance = 3
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NUM_CONES = 7
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NUM_VISIBLE_CONES = 6
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INDICATOR_RADIUS = 0.5
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OPACITY_FOR_UNIT_INTENSITY = 1.0
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# Morty
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morty = self.pi_creature
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morty.flip()
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morty.scale(0.5)
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morty.move_to(2*LEFT + SPACE_HEIGHT*DOWN/2)
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observer_point = morty.eyes[1].get_center()
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self.number_line = NumberLine(
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x_min = 0,
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color = WHITE,
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number_at_center = 1.6,
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stroke_width = 1,
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numbers_with_elongated_ticks = range(1,5),
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numbers_to_show = range(1,5),
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unit_size = 2,
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tick_frequency = 0.2,
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line_to_number_buff = LARGE_BUFF,
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label_direction = UP,
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bubble = ThoughtBubble(height = 3, width = 4, direction = RIGHT)
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bubble.set_fill(BLACK, 1)
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bubble.pin_to(morty)
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# Indicator
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light_indicator = LightIndicator(
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opacity_for_unit_intensity = 0.5,
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fill_color = YELLOW,
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radius = 0.4,
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reading_height = 0.2,
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)
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light_indicator.move_to(bubble.get_bubble_center())
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def update_light_indicator(light_indicator):
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distance = np.linalg.norm(light_source.get_source_point()-observer_point)
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light_indicator.set_intensity((unit_distance/distance)**2)
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self.number_line.label_direction = DOWN
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#self.number_line.shift(3*UP)
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#Light source
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light_source = LightSource(
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opacity_function = inverse_quadratic(1,2,1),
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num_levels = self.num_levels,
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radius = self.radius,
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max_opacity_ambient = AMBIENT_FULL,
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)
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light_source.move_to(observer_point + unit_distance*RIGHT)
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self.number_line_labels = self.number_line.get_number_mobjects()
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self.add(self.number_line,self.number_line_labels)
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#Light source copies
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light_source_copies = VGroup(*[light_source.copy() for x in range(2)])
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for lsc, vect in zip(light_source_copies, [RIGHT, UP]):
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lsc.move_to(observer_point + np.sqrt(2)*unit_distance*vect)
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self.add(light_source)
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self.add_foreground_mobjects(morty, bubble, light_indicator)
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self.add(ContinualUpdateFromFunc(light_indicator, update_light_indicator))
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self.play(
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ApplyMethod(
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light_source.shift, 0.66*unit_distance*LEFT,
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rate_func = wiggle,
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run_time = 5,
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),
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morty.change, "erm",
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)
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self.play(
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UpdateFromAlphaFunc(
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light_source,
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lambda ls, a : ls.move_to(
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observer_point + rotate_vector(
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unit_distance*RIGHT, (1+1./8)*a*TAU
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)
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),
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run_time = 6,
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rate_func = bezier([0, 0, 1, 1])
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),
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morty.change, "pondering",
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UpdateFromFunc(morty, lambda m : m.look_at(light_source))
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)
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self.wait()
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origin_point = self.number_line.number_to_point(0)
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self.default_pi_creature_class = Randolph
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randy = self.get_primary_pi_creature()
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randy.scale(0.5)
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randy.flip()
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right_pupil = randy.pupils[1]
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randy.next_to(origin_point, LEFT, buff = 0, submobject_to_align = right_pupil)
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randy_copy = randy.copy()
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randy_copy.target = randy.copy().shift(DOWN)
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bubble = ThoughtBubble(direction = RIGHT,
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width = 4, height = 3,
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file_name = "Bubbles_thought.svg")
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bubble.next_to(randy,LEFT+UP)
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bubble.set_fill(color = BLACK, opacity = 1)
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plus = TexMobject("+")
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point = light_indicator.get_center()
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plus.move_to(point)
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light_indicator_copy = light_indicator.copy()
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self.add_foreground_mobjects(plus, light_indicator_copy)
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self.play(
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randy.change, "wave_2",
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ShowCreation(bubble),
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ReplacementTransform(
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light_source, light_source_copies[0]
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),
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ReplacementTransform(
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light_source.copy().fade(1),
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light_source_copies[1]
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),
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FadeIn(plus),
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UpdateFromFunc(
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light_indicator_copy,
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lambda li : update_light_indicator(li),
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),
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UpdateFromAlphaFunc(
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light_indicator, lambda m, a : m.move_to(
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point + a*0.75*RIGHT,
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)
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),
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UpdateFromAlphaFunc(
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light_indicator_copy, lambda m, a : m.move_to(
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point + a*0.75*LEFT,
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)
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),
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run_time = 2
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)
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euler_sum = TexMobject("1", "+", "{1\over 4}",
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"+", "{1\over 9}", "+", "{1\over 16}", "+", "{1\over 25}", "+", "\cdots", " ")
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# the last entry is a dummy element which makes looping easier
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# used just for putting the fractions into the light indicators
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intensities = np.array([1./(n+1)**2 for n in range(NUM_CONES)])
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opacities = intensities * OPACITY_FOR_UNIT_INTENSITY
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# repeat:
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# fade in lighthouse
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# switch on / fade in ambient light
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# show creation / write light indicator
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# move indicator onto origin
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# while morphing and dimming
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# move indicator into thought bubble
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# while indicators already inside shift to the back
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# and while term appears in the series below
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point = self.number_line.number_to_point(1)
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v = point - self.number_line.number_to_point(0)
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light_source = LightSource()
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light_source.move_source_to(point)
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#light_source.ambient_light.move_source_to(point)
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#light_source.lighthouse.move_to(point)
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self.play(FadeIn(light_source.lighthouse))
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self.play(SwitchOn(light_source.ambient_light))
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# create an indicator that will move along the number line
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indicator = LightIndicator(color = LIGHT_COLOR,
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radius = INDICATOR_RADIUS,
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opacity_for_unit_intensity = OPACITY_FOR_UNIT_INTENSITY,
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show_reading = False
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)
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indicator_reading = euler_sum[0]
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indicator_reading.scale_to_fit_height(0.5 * indicator.get_height())
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indicator_reading.move_to(indicator.get_center())
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indicator.add(indicator_reading)
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indicator.tex_reading = indicator_reading
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# the TeX reading is too bright at full intensity
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indicator.tex_reading.set_fill(color = BLACK)
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indicator.foreground.set_fill(None,opacities[0])
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indicator.move_to(point)
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indicator.set_intensity(intensities[0])
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self.play(FadeIn(indicator))
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self.add_foreground_mobject(indicator)
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collection_point = np.array([-6.,2.,0.])
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left_shift = 0.2*LEFT
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collected_indicators = Mobject()
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for i in range(2, NUM_VISIBLE_CONES + 1):
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previous_point = self.number_line.number_to_point(i - 1)
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point = self.number_line.number_to_point(i)
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v = point - previous_point
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#print v
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# Create and position the target indicator (next on number line).
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indicator_target = indicator.deepcopy()
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indicator_target.shift(v)
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# Here we make a copy that will move into the thought bubble.
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bubble_indicator = indicator.deepcopy()
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# And its target
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bubble_indicator_target = bubble_indicator.deepcopy()
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bubble_indicator_target.set_intensity(intensities[i - 2])
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# give the target the appropriate reading
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euler_sum[2*i-4].move_to(bubble_indicator_target)
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bubble_indicator_target.remove(bubble_indicator_target.tex_reading)
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bubble_indicator_target.tex_reading = euler_sum[2*i-4].copy()
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bubble_indicator_target.add(bubble_indicator_target.tex_reading)
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# center it in the indicator
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if bubble_indicator_target.tex_reading.get_tex_string() != "1":
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bubble_indicator_target.tex_reading.scale_to_fit_height(0.8*indicator.get_height())
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# the target is less bright, possibly switch to a white text color
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if bubble_indicator_target.intensity < 0.7:
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bubble_indicator.tex_reading.set_fill(color = WHITE)
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# position the target in the thought bubble
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bubble_indicator_target.move_to(collection_point)
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self.add_foreground_mobject(bubble_indicator)
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self.wait()
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self.play(
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Transform(bubble_indicator,bubble_indicator_target),
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collected_indicators.shift,left_shift,
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)
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collected_indicators.add(bubble_indicator)
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new_light = light_source.deepcopy()
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w = new_light.get_source_point()
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new_light.move_source_to(w + (i-2)*v)
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w2 = new_light.get_source_point()
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self.add(new_light.lighthouse)
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self.play(
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Transform(indicator,indicator_target),
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new_light.lighthouse.shift,v,
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)
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new_light.move_source_to(w + (i-1)*v)
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new_light.lighthouse.move_to(w + (i-1)*v)
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self.play(SwitchOn(new_light.ambient_light),
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)
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# quickly switch on off-screen light cones
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for i in range(NUM_VISIBLE_CONES,NUM_CONES):
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indicator_start_time = 0.5 * (i+1) * FAST_SWITCH_ON_RUN_TIME/light_source.ambient_light.radius * self.number_line.unit_size
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indicator_stop_time = indicator_start_time + FAST_INDICATOR_UPDATE_TIME
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indicator_rate_func = squish_rate_func(#smooth, 0.8, 0.9)
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smooth,indicator_start_time,indicator_stop_time)
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ls = LightSource()
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point = point = self.number_line.number_to_point(i)
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ls.move_source_to(point)
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self.play(
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SwitchOn(ls.ambient_light, run_time = FAST_SWITCH_ON_RUN_TIME),
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)
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# and morph indicator stack into limit value
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sum_indicator = LightIndicator(color = LIGHT_COLOR,
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radius = INDICATOR_RADIUS,
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opacity_for_unit_intensity = OPACITY_FOR_UNIT_INTENSITY,
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show_reading = False
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)
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sum_indicator.set_intensity(intensities[0] * np.pi**2/6)
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sum_indicator_reading = TexMobject("{\pi^2 \over 6}")
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sum_indicator_reading.set_fill(color = BLACK)
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sum_indicator_reading.scale_to_fit_height(0.8 * sum_indicator.get_height())
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sum_indicator.add(sum_indicator_reading)
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sum_indicator.move_to(collection_point)
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self.play(
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FadeOut(collected_indicators),
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FadeIn(sum_indicator)
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)
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self.wait()
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self.play(morty.change, "hooray")
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self.wait(2)
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class TwoLightSourcesScene(PiCreatureScene):
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