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https://github.com/3b1b/manim.git
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Finished TwoLightSourcesScene
This commit is contained in:
Grant Sanderson
@@ -56,22 +56,22 @@ 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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xA = A[0]
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yA = A[1]
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xB = B[0]
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yB = B[1]
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xC = C[0]
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yC = C[1]
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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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# xA = A[0]
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# yA = A[1]
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# xB = B[0]
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# yB = B[1]
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# xC = C[0]
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# yC = C[1]
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# find the coords of the altitude point H
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# as the solution of a certain LSE
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prelim_matrix = np.array([[yA - yB, xB - xA], [xA - xB, yA - yB]]) # sic
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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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# prelim_matrix = np.array([[yA - yB, xB - xA], [xA - xB, yA - yB]]) # sic
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# 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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@@ -136,7 +136,7 @@ class LightIndicator(Mobject):
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return self
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def get_measurement_point(self):
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if self.measurement_point != None:
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if self.measurement_point is not None:
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return self.measurement_point
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else:
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return self.get_center()
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@@ -1765,15 +1765,13 @@ 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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"pi_creature_point" : 2*LEFT + 2*DOWN,
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}
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def construct(self):
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unit_distance = 3
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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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bubble = ThoughtBubble(height = 3, width = 4, direction = RIGHT)
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@@ -1866,182 +1864,287 @@ class ManipulateLightsourceSetups(PiCreatureScene):
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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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##
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def create_pi_creature(self):
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morty = Mortimer()
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morty.flip()
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morty.scale(0.5)
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morty.move_to(self.pi_creature_point)
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return morty
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class TwoLightSourcesScene(ManipulateLightsourceSetups):
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CONFIG = {
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"num_levels" : 200,
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"radius" : 15,
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"a" : 9,
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"b" : 5,
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}
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def construct(self):
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MAX_OPACITY = 0.4
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INDICATOR_RADIUS = 0.6
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OPACITY_FOR_UNIT_INTENSITY = 0.5
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origin_point = 5*LEFT + 2.5*DOWN
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morty = self.get_primary_pi_creature()
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morty.scale(0.3).flip()
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right_pupil = morty.pupils[1]
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morty.next_to(C, LEFT, buff = 0, submobject_to_align = right_pupil)
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horizontal = VMobject(stroke_width = 1)
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horizontal.set_points_as_corners([C,A])
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vertical = VMobject(stroke_width = 1)
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vertical.set_points_as_corners([C,B])
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self.play(
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ShowCreation(horizontal),
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ShowCreation(vertical)
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#Morty
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morty = self.pi_creature
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morty.change("hooray") # From last scen
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morty.generate_target()
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morty.target.change("plain")
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morty.target.scale(0.6)
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morty.target.next_to(
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origin_point, LEFT, buff = 0,
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submobject_to_align = morty.target.eyes[1]
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)
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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 = True,
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precision = 2
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#Axes
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axes = Axes(
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x_min = -1, x_max = 10.5,
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y_min = -1, y_max = 6.5,
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)
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axes.shift(origin_point)
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indicator.next_to(morty,LEFT)
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self.play(
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Write(indicator)
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#Important reference points
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A = axes.coords_to_point(self.a, 0)
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B = axes.coords_to_point(0, self.b)
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C = axes.coords_to_point(0, 0)
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xA = A[0]
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yA = A[1]
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xB = B[0]
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yB = B[1]
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xC = C[0]
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yC = C[1]
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# find the coords of the altitude point H
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# as the solution of a certain LSE
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prelim_matrix = np.array([
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[yA - yB, xB - xA],
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[xA - xB, yA - yB]
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]) # sic
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prelim_vector = np.array(
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[xB * yA - xA * yB, xC * (xA - xB) + yC * (yA - yB)]
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)
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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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ls1 = LightSource(radius = 20, num_levels = 50)
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ls2 = ls1.deepcopy()
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ls1.move_source_to(A)
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ls2.move_source_to(B)
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self.play(
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FadeIn(ls1.lighthouse),
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FadeIn(ls2.lighthouse),
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SwitchOn(ls1.ambient_light),
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SwitchOn(ls2.ambient_light)
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#Lightsources
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lsA = LightSource(
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radius = self.radius,
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num_levels = self.num_levels,
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opacity_function = inverse_power_law(2, 1, 1, 1.5),
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)
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lsB = lsA.deepcopy()
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lsA.move_source_to(A)
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lsB.move_source_to(B)
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lsC = lsA.deepcopy()
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lsC.move_source_to(H)
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distance1 = np.linalg.norm(C - ls1.get_source_point())
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intensity = ls1.ambient_light.opacity_function(distance1) / indicator.opacity_for_unit_intensity
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distance2 = np.linalg.norm(C - ls2.get_source_point())
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intensity += ls2.ambient_light.opacity_function(distance2) / indicator.opacity_for_unit_intensity
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#Lighthouse labels
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A_label = TextMobject("A")
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A_label.next_to(lsA.lighthouse, RIGHT)
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B_label = TextMobject("B")
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B_label.next_to(lsB.lighthouse, LEFT)
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self.play(
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UpdateLightIndicator(indicator,intensity)
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)
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#Identical lighthouse labels
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identical_lighthouses_words = TextMobject("All identical \\\\ lighthouses")
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identical_lighthouses_words.to_corner(UP+RIGHT)
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identical_lighthouses_words.shift(LEFT)
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identical_lighthouses_arrows = VGroup(*[
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Arrow(
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identical_lighthouses_words.get_bottom(),
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ls.get_source_point(),
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buff = SMALL_BUFF,
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color = WHITE,
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)
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for ls in lsA, lsB, lsC
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])
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self.wait()
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ls3 = ls1.deepcopy()
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ls3.move_to(np.array([6,3.5,0]))
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new_indicator = indicator.copy()
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new_indicator.light_source = ls3
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new_indicator.measurement_point = C
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self.add(new_indicator)
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self.play(
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indicator.shift, 2 * UP
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)
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#intensity = intensity_for_light_source(ls3)
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self.play(
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SwitchOff(ls1.ambient_light),
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#FadeOut(ls1.lighthouse),
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SwitchOff(ls2.ambient_light),
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#FadeOut(ls2.lighthouse),
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UpdateLightIndicator(new_indicator,0.0)
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)
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# create a *continual* animation for the replacement source
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updater = ContinualLightIndicatorUpdate(new_indicator)
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self.add(updater)
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self.play(
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SwitchOn(ls3.ambient_light),
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FadeIn(ls3.lighthouse),
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)
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self.wait()
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# move the light source around
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# TODO: moving along a path arc
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location = np.array([-3,-2.,0.])
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self.play(ls3.move_source_to,location)
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location = np.array([6.,1.,0.])
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self.play(ls3.move_source_to,location)
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location = np.array([5.,2.,0.])
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self.play(ls3.move_source_to,location)
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closer_location = interpolate(location, C, 0.5)
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self.play(ls3.move_source_to,closer_location)
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self.play(ls3.move_source_to,location)
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# maybe move in a circle around C using a loop?
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self.play(ls3.move_source_to,H)
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# draw lines to complete the geometric picture
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# and label the lengths
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line_a = VMobject()
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line_a.set_points_as_corners([B,C])
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line_b = VMobject()
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line_b.set_points_as_corners([A,C])
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line_c = VMobject()
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line_c.set_points_as_corners([A,B])
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line_h = VMobject()
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line_h.set_points_as_corners([H,C])
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#Lines
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line_a = Line(C, A)
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line_a.highlight(BLUE)
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line_b = Line(C, B)
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line_b.highlight(RED)
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line_c = Line(A, B)
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line_h = Line(H, C)
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line_h.highlight(GREEN)
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label_a = TexMobject("a")
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label_a.next_to(line_a, LEFT, buff = 0.5)
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label_a.match_color(line_a)
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label_a.next_to(line_a, DOWN, buff = SMALL_BUFF)
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label_b = TexMobject("b")
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label_b.next_to(line_b, DOWN, buff = 0.5)
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label_b.match_color(line_b)
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label_b.next_to(line_b, LEFT, buff = SMALL_BUFF)
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label_h = TexMobject("h")
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label_h.next_to(line_h.get_center(), RIGHT, buff = 0.5)
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label_h.match_color(line_h)
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label_h.next_to(line_h.get_center(), RIGHT, buff = SMALL_BUFF)
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perp_mark = VMobject().set_points_as_corners([
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RIGHT, RIGHT+DOWN, DOWN
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])
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perp_mark.scale(0.25, about_point = ORIGIN)
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perp_mark.rotate(line_c.get_angle() + TAU/4, about_point = ORIGIN)
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perp_mark.shift(H)
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# perp_mark.highlight(BLACK)
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#Indicators
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indicator = LightIndicator(
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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 = True,
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precision = 2,
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)
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indicator.next_to(origin_point, UP+LEFT)
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def update_indicator(indicator):
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intensity = 0
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for ls in lsA, lsB, lsC:
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if ls in self.mobjects:
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distance = np.linalg.norm(ls.get_source_point() - origin_point)
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d_indensity = fdiv(
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3./(distance**2),
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indicator.opacity_for_unit_intensity
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)
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d_indensity *= ls.ambient_light.submobjects[1].get_fill_opacity()
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intensity += d_indensity
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indicator.set_intensity(intensity)
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indicator_update_anim = ContinualUpdateFromFunc(indicator, update_indicator)
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new_indicator = indicator.copy()
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new_indicator.light_source = lsC
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new_indicator.measurement_point = C
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#Note sure what this is...
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distance1 = np.linalg.norm(origin_point - lsA.get_source_point())
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intensity = lsA.ambient_light.opacity_function(distance1) / indicator.opacity_for_unit_intensity
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distance2 = np.linalg.norm(origin_point - lsB.get_source_point())
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intensity += lsB.ambient_light.opacity_function(distance2) / indicator.opacity_for_unit_intensity
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# IPT Theorem
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theorem = TexMobject(
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"{1 \over ", "a^2}", "+",
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"{1 \over", "b^2}", "=", "{1 \over","h^2}"
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)
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theorem.highlight_by_tex_to_color_map({
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"a" : line_a.get_color(),
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"b" : line_b.get_color(),
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"h" : line_h.get_color(),
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})
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theorem_name = TextMobject("Inverse Pythagorean Theorem")
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theorem_name.to_corner(UP+RIGHT)
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theorem.next_to(theorem_name, DOWN, buff = MED_LARGE_BUFF)
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theorem_box = SurroundingRectangle(theorem, color = WHITE)
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#Transition from last_scene
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self.play(
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ShowCreation(line_a),
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Write(label_a)
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ShowCreation(axes, run_time = 2),
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MoveToTarget(morty),
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FadeIn(indicator),
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)
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#Move lsC around
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self.add(lsC)
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indicator_update_anim.update(0)
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intensity = indicator.reading.number
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self.play(
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ShowCreation(line_b),
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Write(label_b)
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)
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self.play(
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ShowCreation(line_c),
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SwitchOn(lsC.ambient_light),
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FadeIn(lsC.lighthouse),
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UpdateFromAlphaFunc(
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indicator, lambda i, a : i.set_intensity(a*intensity)
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)
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)
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self.add(indicator_update_anim)
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for point in axes.coords_to_point(5, 2), H:
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self.play(
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lsC.move_source_to, point,
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path_arc = TAU/4,
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run_time = 1.5,
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)
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self.wait()
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# Draw line
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self.play(
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ShowCreation(line_h),
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Write(label_h)
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morty.change, "pondering"
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)
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# state the IPT
|
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theorem_location = np.array([3.,2.,0.])
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theorem = TexMobject("{1\over a^2} + {1\over b^2} = {1\over h^2}")
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theorem_name = TextMobject("Inverse Pythagorean Theorem")
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buffer = 1.2
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theorem_box = Rectangle(width = buffer*theorem.get_width(),
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height = buffer*theorem.get_height())
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theorem.move_to(theorem_location)
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theorem_box.move_to(theorem_location)
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theorem_name.next_to(theorem_box,UP)
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self.wait()
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self.play(
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Write(theorem),
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ShowCreation(line_c),
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ShowCreation(perp_mark)
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)
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self.wait()
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self.add_foreground_mobjects(line_c, line_h)
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#Add alternate light_sources
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for ls in lsA, lsB:
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ls.save_state()
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ls.move_to(lsC)
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ls.fade(1)
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self.add(ls)
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self.play(
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ls.restore,
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run_time = 2
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)
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self.wait()
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A_label.save_state()
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A_label.center().fade(1)
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self.play(A_label.restore)
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self.wait()
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self.play(ReplacementTransform(
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A_label.copy().fade(1), B_label
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))
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||||
self.wait(2)
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||||
|
||||
#Compare combined of laA + lsB with lsC
|
||||
rect = SurroundingRectangle(indicator, color = RED)
|
||||
self.play(
|
||||
FadeOut(lsA),
|
||||
FadeOut(lsB),
|
||||
)
|
||||
self.play(ShowCreation(rect))
|
||||
self.play(FadeOut(rect))
|
||||
self.play(FadeOut(lsC))
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||||
self.add(lsA, lsB)
|
||||
self.play(
|
||||
FadeIn(lsA),
|
||||
FadeIn(lsB),
|
||||
)
|
||||
self.play(ShowCreation(rect))
|
||||
self.play(FadeOut(rect))
|
||||
self.wait(2)
|
||||
|
||||
# All standard lighthouses
|
||||
self.add(lsC)
|
||||
self.play(FadeIn(lsC))
|
||||
self.play(
|
||||
Write(identical_lighthouses_words),
|
||||
LaggedStart(GrowArrow, identical_lighthouses_arrows)
|
||||
)
|
||||
self.wait()
|
||||
self.play(*map(FadeOut, [
|
||||
identical_lighthouses_words,
|
||||
identical_lighthouses_arrows,
|
||||
]))
|
||||
|
||||
#Show labels of lengths
|
||||
self.play(ShowCreation(line_a), Write(label_a))
|
||||
self.wait()
|
||||
self.play(ShowCreation(line_b), Write(label_b))
|
||||
self.wait()
|
||||
self.play(Write(label_h))
|
||||
self.wait()
|
||||
|
||||
#Write IPT
|
||||
self.play(Write(theorem))
|
||||
self.wait()
|
||||
self.play(
|
||||
ShowCreation(theorem_box),
|
||||
Write(theorem_name),
|
||||
ShowCreation(theorem_box)
|
||||
)
|
||||
self.play(morty.change, "confused")
|
||||
self.wait(2)
|
||||
|
||||
|
||||
|
||||
|
||||
class IPTScene1(PiCreatureScene):
|
||||
|
||||
|
||||
Reference in New Issue
Block a user