mirror of
https://github.com/3b1b/manim.git
synced 2025-09-01 00:48:45 +00:00
PondScene, created InfiniteCircleScene
This commit is contained in:
Ben Hambrecht
parent
16cdc01003
commit
56f74388a0
1 changed files with 166 additions and 46 deletions
|
|
@ -3070,6 +3070,7 @@ class PondScene(ThreeDScene):
|
|||
|
||||
self.cumulated_zoom_factor = 1
|
||||
|
||||
#self.force_skipping()
|
||||
|
||||
|
||||
def right_angle(pointA, pointB, pointC, size = 1):
|
||||
|
|
@ -3163,7 +3164,7 @@ class PondScene(ThreeDScene):
|
|||
self.zoomable_mobs.add(lake0)
|
||||
|
||||
# Morty and indicator
|
||||
morty = Randolph().scale(0.3)
|
||||
morty = Randolph(color = MAROON_D).scale(0.3)
|
||||
morty.next_to(OBSERVER_POINT,DOWN)
|
||||
indicator = LightIndicator(precision = 2,
|
||||
radius = INDICATOR_RADIUS,
|
||||
|
|
@ -3436,6 +3437,7 @@ class PondScene(ThreeDScene):
|
|||
self.new_legs_2 = []
|
||||
self.new_hypotenuses = []
|
||||
|
||||
# WE ALWAYS USE THIS CASE BRANCH
|
||||
if simultaneous_splitting == False:
|
||||
|
||||
for i in range(2**n):
|
||||
|
|
@ -3497,6 +3499,9 @@ class PondScene(ThreeDScene):
|
|||
|
||||
self.wait()
|
||||
|
||||
|
||||
|
||||
# WE DON'T USE THIS CASE BRANCH ANYMORE
|
||||
else: # simultaneous splitting
|
||||
|
||||
old_lake = self.outer_lake.copy()
|
||||
|
|
@ -3685,14 +3690,16 @@ class PondScene(ThreeDScene):
|
|||
# simultaneous_splitting = True)
|
||||
|
||||
|
||||
#print "starting simultaneous expansion"
|
||||
|
||||
# simultaneous expansion of light sources from now on
|
||||
self.play(FadeOut(self.inner_lake))
|
||||
|
||||
for n in range(3,max_it + 1):
|
||||
|
||||
print "working on n = ", n, "..."
|
||||
new_lake = self.outer_lake.copy().scale(2,about_point = self.obs_dot.get_center())
|
||||
for ls in self.light_sources_array:
|
||||
for (i,ls) in enumerate(self.light_sources_array[:2**n]):
|
||||
#print i
|
||||
lsp = ls.copy()
|
||||
self.light_sources.add(lsp)
|
||||
self.add(lsp)
|
||||
|
|
@ -3701,26 +3708,32 @@ class PondScene(ThreeDScene):
|
|||
new_lake_center = new_lake.get_center()
|
||||
new_lake_radius = 0.5 * new_lake.get_width()
|
||||
|
||||
shift_list = (Transform(self.outer_lake,new_lake),)
|
||||
|
||||
shift_list = [Transform(self.outer_lake,new_lake)]
|
||||
#print shift_list
|
||||
|
||||
for i in range(2**n):
|
||||
theta = -TAU/4 + (i + 0.5) * TAU / 2**n
|
||||
#print "==========="
|
||||
#print i
|
||||
theta = -TAU/4 + (i + 0.5) * TAU / 2**(n+1)
|
||||
v = np.array([np.cos(theta), np.sin(theta),0])
|
||||
pos1 = new_lake_center + new_lake_radius * v
|
||||
pos2 = new_lake_center - new_lake_radius * v
|
||||
shift_list += (self.light_sources.submobjects[i].move_source_to,pos1)
|
||||
shift_list += (self.light_sources.submobjects[i+2**n].move_source_to,pos2)
|
||||
ls1 = self.light_sources.submobjects[i]
|
||||
ls2 = self.light_sources.submobjects[i+2**n]
|
||||
shift_list.append(ls1.move_source_to)
|
||||
shift_list.append(pos1)
|
||||
shift_list.append(ls2.move_source_to)
|
||||
shift_list.append(pos2)
|
||||
#print shift_list
|
||||
|
||||
self.play(*shift_list)
|
||||
print "...done"
|
||||
|
||||
|
||||
return
|
||||
|
||||
#self.revert_to_original_skipping_status()
|
||||
|
||||
# Now create a straight number line and transform into it
|
||||
MAX_N = 17
|
||||
MAX_N = 7
|
||||
|
||||
origin_point = self.obs_dot.get_center()
|
||||
|
||||
|
|
@ -3731,16 +3744,17 @@ class PondScene(ThreeDScene):
|
|||
number_at_center = 0,
|
||||
stroke_width = LAKE_STROKE_WIDTH,
|
||||
stroke_color = LAKE_STROKE_COLOR,
|
||||
#numbers_with_elongated_ticks = range(-MAX_N,MAX_N + 1),
|
||||
numbers_to_show = range(-MAX_N,MAX_N + 1,2),
|
||||
numbers_with_elongated_ticks = [],
|
||||
numbers_to_show = range(-MAX_N,MAX_N + 1),#,2),
|
||||
unit_size = LAKE0_RADIUS * TAU/4 / 2 * scale,
|
||||
tick_frequency = 1,
|
||||
tick_size = LAKE_STROKE_WIDTH,
|
||||
number_scale_val = 3,
|
||||
line_to_number_buff = LARGE_BUFF,
|
||||
label_direction = UP,
|
||||
).shift(scale * 2.5 * DOWN)
|
||||
|
||||
self.number_line.label_direction = DOWN
|
||||
|
||||
self.number_line.tick_marks.fade(1)
|
||||
self.number_line_labels = self.number_line.get_number_mobjects()
|
||||
self.wait()
|
||||
|
||||
|
|
@ -3757,25 +3771,29 @@ class PondScene(ThreeDScene):
|
|||
|
||||
self.add(pond_sources)
|
||||
self.remove(self.light_sources)
|
||||
for ls in self.light_sources_array:
|
||||
self.remove(ls)
|
||||
|
||||
self.outer_lake.rotate(TAU/8)
|
||||
|
||||
# open sea
|
||||
open_sea = Rectangle(
|
||||
width = 20 * scale,
|
||||
height = 10 * scale,
|
||||
width = 200 * scale,
|
||||
height = 100 * scale,
|
||||
stroke_width = LAKE_STROKE_WIDTH,
|
||||
stroke_color = LAKE_STROKE_COLOR,
|
||||
fill_color = LAKE_COLOR,
|
||||
fill_opacity = LAKE_OPACITY,
|
||||
).flip().next_to(origin_point,UP,buff = 0)
|
||||
|
||||
|
||||
self.revert_to_original_skipping_status()
|
||||
|
||||
self.play(
|
||||
ReplacementTransform(pond_sources,nl_sources),
|
||||
#FadeOut(pond_sources),
|
||||
#FadeIn(nl_sources),
|
||||
ReplacementTransform(self.outer_lake,open_sea),
|
||||
FadeOut(self.inner_lake)
|
||||
#FadeOut(self.inner_lake)
|
||||
)
|
||||
self.play(FadeIn(self.number_line))
|
||||
|
||||
|
|
@ -3797,11 +3815,12 @@ class PondScene(ThreeDScene):
|
|||
origin_point = self.number_line.number_to_point(0)
|
||||
#self.remove(self.obs_dot)
|
||||
self.play(
|
||||
indicator.move_to, origin_point + scale * UP,
|
||||
indicator_reading.move_to, origin_point + scale * UP,
|
||||
indicator.move_to, origin_point + scale * UP + 2 * UP,
|
||||
indicator_reading.move_to, origin_point + scale * UP + 2 * UP,
|
||||
FadeOut(open_sea),
|
||||
FadeOut(morty),
|
||||
FadeIn(self.number_line_labels)
|
||||
FadeIn(self.number_line_labels),
|
||||
FadeIn(self.number_line.tick_marks),
|
||||
)
|
||||
|
||||
two_sided_sum = TexMobject("\dots", "+", "{1\over (-11)^2}",\
|
||||
|
|
@ -3821,13 +3840,20 @@ class PondScene(ThreeDScene):
|
|||
|
||||
self.play(Write(two_sided_sum))
|
||||
|
||||
for i in range(MAX_N - 5, MAX_N):
|
||||
self.remove(nl_sources.submobjects[i].ambient_light)
|
||||
|
||||
for i in range(MAX_N, MAX_N + 5):
|
||||
self.add_foreground_mobject(nl_sources.submobjects[i].ambient_light)
|
||||
self.wait()
|
||||
|
||||
for ls in nl_sources.submobjects:
|
||||
if ls.get_source_point()[0] < 0:
|
||||
self.remove_foreground_mobject(ls.ambient_light)
|
||||
self.remove(ls.ambient_light)
|
||||
else:
|
||||
self.add_foreground_mobject(ls.ambient_light)
|
||||
|
||||
for label in self.number_line_labels.submobjects:
|
||||
if label.get_center()[0] <= 0:
|
||||
self.remove(label)
|
||||
|
||||
|
||||
self.wait()
|
||||
|
||||
covering_rectangle = Rectangle(
|
||||
width = SPACE_WIDTH * scale,
|
||||
|
|
@ -3837,8 +3863,8 @@ class PondScene(ThreeDScene):
|
|||
fill_opacity = 1,
|
||||
)
|
||||
covering_rectangle.next_to(ORIGIN,LEFT,buff = 0)
|
||||
for i in range(10):
|
||||
self.add_foreground_mobject(nl_sources.submobjects[i])
|
||||
#for i in range(10):
|
||||
# self.add_foreground_mobject(nl_sources.submobjects[i])
|
||||
|
||||
self.add_foreground_mobject(indicator)
|
||||
self.add_foreground_mobject(indicator_reading)
|
||||
|
|
@ -3869,7 +3895,7 @@ class PondScene(ThreeDScene):
|
|||
self.revert_to_original_skipping_status()
|
||||
|
||||
# show Randy admiring the result
|
||||
randy = Randolph(color = MAROON_E).scale(scale).move_to(2*scale*DOWN+5*scale*LEFT)
|
||||
randy = Randolph(color = MAROON_D).scale(scale).move_to(2*scale*DOWN+5*scale*LEFT)
|
||||
self.play(FadeIn(randy))
|
||||
self.play(randy.change,"happy")
|
||||
self.play(randy.change,"hooray")
|
||||
|
|
@ -3917,8 +3943,8 @@ class FinalSumManipulationScene(PiCreatureScene):
|
|||
sum_vertical_spacing = 1.5
|
||||
|
||||
randy = self.get_primary_pi_creature()
|
||||
randy.highlight(MAROON_E)
|
||||
randy.color = MAROON_E
|
||||
randy.highlight(MAROON_D)
|
||||
randy.color = MAROON_D
|
||||
randy.scale(0.7).flip().to_edge(DOWN + LEFT)
|
||||
self.wait()
|
||||
|
||||
|
|
@ -4311,14 +4337,17 @@ class ThumbnailScene(Scene):
|
|||
def construct(self):
|
||||
|
||||
equation = TexMobject("1+{1\over 4}+{1\over 9}+{1\over 16}+{1\over 25}+\dots")
|
||||
equation.scale(2.)
|
||||
equation.to_edge(UP)
|
||||
q_mark = TexMobject("?").scale(5)
|
||||
q_mark.next_to(equation)
|
||||
equation.scale(1.5)
|
||||
equation.move_to(1.5 * UP)
|
||||
q_mark = TexMobject("=?", color = LIGHT_COLOR).scale(5)
|
||||
q_mark.next_to(equation, DOWN, buff = 1.5)
|
||||
#equation.move_to(2 * UP)
|
||||
#q_mark = TexMobject("={\pi^2\over 6}", color = LIGHT_COLOR).scale(3)
|
||||
#q_mark.next_to(equation, DOWN, buff = 1)
|
||||
|
||||
lake_radius = 2
|
||||
lake_center = DOWN
|
||||
op_scale = 0.5
|
||||
lake_radius = 6
|
||||
lake_center = ORIGIN
|
||||
op_scale = 0.4
|
||||
|
||||
lake = Circle(
|
||||
fill_color = LAKE_COLOR,
|
||||
|
|
@ -4329,13 +4358,13 @@ class ThumbnailScene(Scene):
|
|||
)
|
||||
lake.move_to(lake_center)
|
||||
|
||||
for i in range(8):
|
||||
theta = -TAU/4 + (i + 0.5) * TAU/8
|
||||
for i in range(16):
|
||||
theta = -TAU/4 + (i + 0.5) * TAU/16
|
||||
pos = lake_center + lake_radius * np.array([np.cos(theta), np.sin(theta), 0])
|
||||
ls = LightSource(
|
||||
radius = 5.0,
|
||||
num_levels = 100,
|
||||
max_opacity_ambient = 0.8,
|
||||
radius = 15.0,
|
||||
num_levels = 150,
|
||||
max_opacity_ambient = 1.0,
|
||||
opacity_function = inverse_quadratic(1,op_scale,1)
|
||||
)
|
||||
ls.move_source_to(pos)
|
||||
|
|
@ -4343,7 +4372,87 @@ class ThumbnailScene(Scene):
|
|||
|
||||
self.add(lake)
|
||||
|
||||
self.add(equation) #, q_mark)
|
||||
self.add(equation, q_mark)
|
||||
|
||||
self.wait()
|
||||
|
||||
|
||||
|
||||
|
||||
class InfiniteCircleScene(PiCreatureScene):
|
||||
|
||||
def construct(self):
|
||||
|
||||
morty = self.get_primary_pi_creature()
|
||||
morty.highlight(MAROON_D).flip()
|
||||
morty.color = MAROON_D
|
||||
morty.scale(0.5).move_to(ORIGIN)
|
||||
|
||||
arrow = Arrow(ORIGIN, 2.4 * RIGHT)
|
||||
dot = Dot(color = BLUE).next_to(arrow)
|
||||
ellipsis = TexMobject("\dots")
|
||||
|
||||
infsum = VGroup()
|
||||
infsum.add(ellipsis.copy())
|
||||
|
||||
for i in range(3):
|
||||
infsum.add(arrow.copy().next_to(infsum.submobjects[-1]))
|
||||
infsum.add(dot.copy().next_to(infsum.submobjects[-1]))
|
||||
|
||||
infsum.add(arrow.copy().next_to(infsum.submobjects[-1]))
|
||||
infsum.add(ellipsis.copy().next_to(infsum.submobjects[-1]))
|
||||
|
||||
infsum.next_to(morty,DOWN, buff = 1)
|
||||
|
||||
self.wait()
|
||||
self.play(
|
||||
LaggedStart(FadeIn,infsum,lag_ratio = 0.2)
|
||||
)
|
||||
self.wait()
|
||||
|
||||
A = infsum.submobjects[-1].get_center() + 0.5 * RIGHT
|
||||
B = A + RIGHT + 1.3 * UP + 0.025 * LEFT
|
||||
right_arc = DashedLine(TAU/4*UP, ORIGIN, stroke_color = YELLOW,
|
||||
stroke_width = 8).apply_complex_function(np.exp)
|
||||
right_arc.rotate(-TAU/4).next_to(infsum, RIGHT).shift(0.5 * UP)
|
||||
right_tip_line = Arrow(B - UP, B, color = WHITE)
|
||||
right_tip_line.add_tip()
|
||||
right_tip = right_tip_line.get_tip()
|
||||
right_tip.set_fill(color = YELLOW)
|
||||
right_arc.add(right_tip)
|
||||
|
||||
|
||||
C = B + 3.2 * UP
|
||||
right_line = DashedLine(B + 0.2 * DOWN,C + 0.2 * UP, stroke_color = YELLOW,
|
||||
stroke_width = 8)
|
||||
|
||||
ru_arc = right_arc.copy().rotate(angle = TAU/4)
|
||||
ru_arc.remove(ru_arc.submobjects[-1])
|
||||
ru_arc.to_edge(UP+RIGHT, buff = 0.15)
|
||||
|
||||
D = np.array([5.85, 3.85,0])
|
||||
E = np.array([-D[0],D[1],0])
|
||||
up_line = DashedLine(D, E, stroke_color = YELLOW,
|
||||
stroke_width = 8)
|
||||
|
||||
lu_arc = ru_arc.copy().flip().to_edge(LEFT + UP, buff = 0.15)
|
||||
left_line = right_line.copy().flip(axis = RIGHT).to_edge(LEFT, buff = 0.15)
|
||||
|
||||
left_arc = right_arc.copy().rotate(-TAU/4)
|
||||
left_arc.next_to(infsum, LEFT).shift(0.5 * UP + 0.1 * LEFT)
|
||||
|
||||
right_arc.shift(0.2 * RIGHT)
|
||||
right_line.shift(0.2 * RIGHT)
|
||||
|
||||
self.play(FadeIn(right_arc))
|
||||
self.play(ShowCreation(right_line))
|
||||
self.play(FadeIn(ru_arc))
|
||||
self.play(ShowCreation(up_line))
|
||||
self.play(FadeIn(lu_arc))
|
||||
self.play(ShowCreation(left_line))
|
||||
self.play(FadeIn(left_arc))
|
||||
|
||||
|
||||
|
||||
self.wait()
|
||||
|
||||
|
|
@ -4353,3 +4462,14 @@ class ThumbnailScene(Scene):
|
|||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue