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Final animations for Fourier montage video

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This commit is contained in:
Grant Sanderson
2019-07-03 11:08:39 -07:00
parent 985ef4518f
commit b3673e93d7
4 changed files with 272 additions and 164 deletions
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1
active_projects/diffyq/all_part4_scenes.py
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@ -4,6 +4,7 @@ from active_projects.diffyq.part4.pi_creature_scenes import *
from active_projects.diffyq.part4.three_d_graphs import *
from active_projects.diffyq.part4.temperature_scenes import *
from active_projects.diffyq.part4.complex_functions import *
from active_projects.diffyq.part4.long_fourier_scenes import *
from active_projects.diffyq.part3.staging import *

23
active_projects/diffyq/fourier_montage_scenes.py Normal file
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@ -0,0 +1,23 @@
from active_projects.diffyq.part4.long_fourier_scenes import *
OUTPUT_DIRECTORY = "diffyq/part4"
SCENES_IN_ORDER = [
ZoomedInFourierSeriesExample,
FourierSeriesExampleWithRectForZoom,
ZoomedInFourierSeriesExample100x,
FourierOfFourier100xZoom,
FourierOfFourierZoomedIn,
FourierOfFourier,
SigmaZoomedInFourierSeriesExample,
SigmaFourierSeriesExampleWithRectForZoom,
NailAndGearZoomedInFourierSeriesExample,
NailAndGearFourierSeriesExampleWithRectForZoom,
TrebleClefZoomedInFourierSeriesExample,
TrebleClefFourierSeriesExampleWithRectForZoom,
FourierOfSeattle,
FourierOfSeattleZoomedIn,
FourierOfBritain,
FourierOfBritainZoomedIn,
FourierOfHilbert,
FourierOfHilbertZoomedIn,
]

170
active_projects/diffyq/part4/fourier_series_scenes.py
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@ -1840,6 +1840,7 @@ class DE4Thumbnail(ComplexFourierSeriesExample):
subname = TextMobject("a.k.a ``everything is rotations''")
subname.match_width(name)
subname.next_to(name, DOWN)
VGroup(name, subname).to_edge(DOWN)
self.add(name)
self.add(subname)
@ -1858,18 +1859,19 @@ class DE4Thumbnail(ComplexFourierSeriesExample):
for n in ns
])
approxs.arrange(RIGHT, buff=2.5)
approxs.set_height(4)
approxs.to_edge(DOWN, buff=LARGE_BUFF)
approxs.set_height(3.75)
approxs.to_edge(UP, buff=1.25)
for a, c, w in zip(approxs, [BLUE, GREEN, YELLOW], [4, 3, 2]):
a.set_stroke(c, w)
a.set_stroke(WHITE, w + w / 2, background=True)
labels = VGroup()
for n, approx in zip(ns, approxs):
label = TexMobject("n = ", str(n))
label[1].match_color(approx)
label.scale(2)
label.next_to(approx, DOWN)
label.to_edge(DOWN, buff=MED_SMALL_BUFF)
label.next_to(approx, UP)
label.to_edge(UP, buff=MED_SMALL_BUFF)
labels.add(label)
self.add(approxs)
@ -1889,163 +1891,3 @@ class DE4Thumbnail(ComplexFourierSeriesExample):
self.add(path, self.circles, self.vectors)
self.update_mobjects(0)
# Pure fourier series with zooming.
# Note to self, put out a single video with nothing
# but these?
class FourierSeriesExampleWithRectForZoom(ComplexFourierSeriesExample):
CONFIG = {
"n_vectors": 100,
"slow_factor": 0.01,
"rect_scale_factor": 0.1,
"start_drawn": True,
"drawing_height": 7,
"rect_stroke_width": 1,
}
def construct(self):
self.add_vectors_circles_path()
self.circles.set_stroke(opacity=0.5)
rect = self.get_rect()
rect.set_height(self.rect_scale_factor * FRAME_HEIGHT)
rect.add_updater(lambda m: m.move_to(
self.get_rect_center()
))
self.add(rect)
self.run_one_cycle()
def get_rect_center(self):
return center_of_mass([
v.get_end()
for v in self.vectors
])
def get_rect(self):
return ScreenRectangle(
color=BLUE,
stroke_width=self.rect_stroke_width,
)
class ZoomedInFourierSeriesExample(FourierSeriesExampleWithRectForZoom, MovingCameraScene):
CONFIG = {
"vector_config": {
"max_tip_length_to_length_ratio": 0.15,
"tip_length": 0.05,
},
"parametric_function_step_size": 0.001,
}
def setup(self):
ComplexFourierSeriesExample.setup(self)
MovingCameraScene.setup(self)
def get_rect(self):
return self.camera_frame
def add_vectors_circles_path(self):
super().add_vectors_circles_path()
for v in self.vectors:
if v.get_stroke_width() < 1:
v.set_stroke(width=1)
class ZoomedInFourierSeriesExample100x(ZoomedInFourierSeriesExample):
CONFIG = {
"vector_config": {
"max_tip_length_to_length_ratio": 0.15 * 0.4,
"tip_length": 0.05 * 0.2,
"max_stroke_width_to_length_ratio": 80,
"stroke_width": 3,
},
"max_circle_stroke_width": 0.5,
"rect_scale_factor": 0.01,
# "parametric_function_step_size": 0.01,
}
def get_rect_center(self):
return self.vectors[-1].get_end()
# def get_drawn_path(self, vectors, stroke_width=2, **kwargs):
# return self.get_path_end(vectors, stroke_width, **kwargs)
class TrebleClefFourierSeriesExampleWithRectForZoom(FourierSeriesExampleWithRectForZoom):
CONFIG = {
"file_name": "TrebleClef",
}
class TrebleClefZoomedInFourierSeriesExample(ZoomedInFourierSeriesExample):
CONFIG = {
"file_name": "TrebleClef",
}
class NailAndGearFourierSeriesExampleWithRectForZoom(FourierSeriesExampleWithRectForZoom):
CONFIG = {
"file_name": "Nail_And_Gear",
"n_vectors": 200,
"drawn_path_color": "#39FF14",
}
class NailAndGearZoomedInFourierSeriesExample(ZoomedInFourierSeriesExample):
CONFIG = {
"file_name": "Nail_And_Gear",
"n_vectors": 200,
"drawn_path_color": "#39FF14",
}
class SigmaFourierSeriesExampleWithRectForZoom(FourierSeriesExampleWithRectForZoom):
CONFIG = {
"n_vectors": 200,
"drawn_path_color": PINK,
"rect_stroke_width": 0,
}
def get_shape(self):
return TexMobject("\\Sigma")
class SigmaZoomedInFourierSeriesExample(SigmaFourierSeriesExampleWithRectForZoom, ZoomedInFourierSeriesExample):
pass
class FourierOfFourier(FourierSeriesExampleWithRectForZoom):
CONFIG = {
"file_name": "FourierOneLine",
"n_vectors": 300,
"rect_stroke_width": 1,
}
class FourierOfFourierZoomedIn(ZoomedInFourierSeriesExample):
CONFIG = {
"file_name": "FourierOneLine",
"max_circle_stroke_width": 0.3,
"n_vectors": 300,
}
class FourierOfFourier100xZoom(ZoomedInFourierSeriesExample100x):
CONFIG = {
"file_name": "FourierOneLine",
"max_circle_stroke_width": 0.3,
"n_vectors": 300,
"slow_factor": 0.001,
}
def run_one_cycle(self):
self.vector_clock.set_value(0.3)
self.wait(40)
class FourierOfFourierOneLineArtsy(FourierSeriesExampleWithRectForZoom):
CONFIG = {
"file_name": "JosephFourierOneLineArtsy",
"n_vectors": 100,
"rect_stroke_width": 1,
}

242
active_projects/diffyq/part4/long_fourier_scenes.py Normal file
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@ -0,0 +1,242 @@
from manimlib.imports import *
from active_projects.diffyq.part4.fourier_series_scenes import ComplexFourierSeriesExample
from manimlib.once_useful_constructs.fractals import HilbertCurve
class FourierSeriesExampleWithRectForZoom(ComplexFourierSeriesExample):
CONFIG = {
"n_vectors": 100,
"slow_factor": 0.01,
"rect_scale_factor": 0.1,
"start_drawn": True,
"drawing_height": 7,
"rect_stroke_width": 1,
}
def construct(self):
self.add_vectors_circles_path()
self.circles.set_stroke(opacity=0.5)
rect = self.rect = self.get_rect()
rect.set_height(self.rect_scale_factor * FRAME_HEIGHT)
rect.add_updater(lambda m: m.move_to(
self.get_rect_center()
))
self.add(rect)
self.run_one_cycle()
def get_rect_center(self):
return center_of_mass([
v.get_end()
for v in self.vectors
])
def get_rect(self):
return ScreenRectangle(
color=BLUE,
stroke_width=self.rect_stroke_width,
)
class ZoomedInFourierSeriesExample(FourierSeriesExampleWithRectForZoom, MovingCameraScene):
CONFIG = {
"vector_config": {
"max_tip_length_to_length_ratio": 0.15,
"tip_length": 0.05,
},
"parametric_function_step_size": 0.001,
}
def setup(self):
ComplexFourierSeriesExample.setup(self)
MovingCameraScene.setup(self)
def get_rect(self):
return self.camera_frame
def add_vectors_circles_path(self):
super().add_vectors_circles_path()
for v in self.vectors:
if v.get_stroke_width() < 1:
v.set_stroke(width=1)
class ZoomedInFourierSeriesExample100x(ZoomedInFourierSeriesExample):
CONFIG = {
"vector_config": {
"max_tip_length_to_length_ratio": 0.15 * 0.4,
"tip_length": 0.05 * 0.2,
"max_stroke_width_to_length_ratio": 80,
"stroke_width": 3,
},
"max_circle_stroke_width": 0.5,
"rect_scale_factor": 0.01,
# "parametric_function_step_size": 0.01,
}
def get_rect_center(self):
return self.vectors[-1].get_end()
# def get_drawn_path(self, vectors, stroke_width=2, **kwargs):
# return self.get_path_end(vectors, stroke_width, **kwargs)
class TrebleClefFourierSeriesExampleWithRectForZoom(FourierSeriesExampleWithRectForZoom):
CONFIG = {
"file_name": "TrebleClef",
"drawn_path_stroke_width": 10,
}
class TrebleClefZoomedInFourierSeriesExample(ZoomedInFourierSeriesExample):
CONFIG = {
"file_name": "TrebleClef",
}
class NailAndGearFourierSeriesExampleWithRectForZoom(FourierSeriesExampleWithRectForZoom):
CONFIG = {
"file_name": "Nail_And_Gear",
"n_vectors": 200,
"drawn_path_color": "#39FF14",
}
class NailAndGearZoomedInFourierSeriesExample(ZoomedInFourierSeriesExample):
CONFIG = {
"file_name": "Nail_And_Gear",
"n_vectors": 200,
"drawn_path_color": "#39FF14",
}
class SigmaFourierSeriesExampleWithRectForZoom(FourierSeriesExampleWithRectForZoom):
CONFIG = {
"n_vectors": 200,
"drawn_path_color": PINK,
"rect_stroke_width": 0,
}
def get_shape(self):
return TexMobject("\\Sigma")
class SigmaZoomedInFourierSeriesExample(SigmaFourierSeriesExampleWithRectForZoom, ZoomedInFourierSeriesExample):
pass
class FourierOfFourier(FourierSeriesExampleWithRectForZoom):
CONFIG = {
"file_name": "FourierOneLine",
"n_vectors": 300,
"rect_stroke_width": 1,
}
class FourierOfFourierZoomedIn(ZoomedInFourierSeriesExample):
CONFIG = {
"file_name": "FourierOneLine",
"max_circle_stroke_width": 0.3,
"n_vectors": 300,
}
class FourierOfFourier100xZoom(ZoomedInFourierSeriesExample100x):
CONFIG = {
"file_name": "FourierOneLine",
"max_circle_stroke_width": 0.3,
"n_vectors": 300,
"slow_factor": 0.001,
}
def run_one_cycle(self):
self.vector_clock.set_value(0.3)
self.wait(40)
class FourierOfHilbert(FourierSeriesExampleWithRectForZoom):
CONFIG = {
"n_vectors": 300,
"rect_stroke_width": 1,
"drawn_path_stroke_width": 4,
"drawn_path_color": BLUE,
}
def get_path(self):
path = HilbertCurve(order=5)
path.set_height(self.drawing_height)
path.to_edge(DOWN)
combined_path = VMobject()
for sm in path.family_members_with_points():
combined_path.append_vectorized_mobject(sm)
start = combined_path.get_start()
end = combined_path.get_end()
points = [
interpolate(end, start, alpha)
for alpha in np.linspace(0, 1, 10)
]
for point in points:
combined_path.add_line_to(point)
combined_path.set_stroke(width=0)
return combined_path
class FourierOfHilbertZoomedIn(FourierOfHilbert, ZoomedInFourierSeriesExample):
pass
class FourierOfBritain(FourierSeriesExampleWithRectForZoom):
CONFIG = {
"file_name": "Britain",
"n_vectors": 500,
"drawn_path_color": RED,
}
class FourierOfBritainZoomedIn(FourierOfBritain, ZoomedInFourierSeriesExample):
pass
class FourierOfSeattle(FourierSeriesExampleWithRectForZoom):
CONFIG = {
"file_name": "SeattleSkyline",
"drawing_height": 7,
"n_vectors": 400,
"drawn_path_color": TEAL,
"drawn_path_stroke_width": 5,
}
class FourierOfSeattleZoomedIn(ZoomedInFourierSeriesExample):
CONFIG = {
"file_name": "SeattleSkyline",
"drawing_height": 7,
"n_vectors": 400,
"drawn_path_color": TEAL,
"drawn_path_stroke_width": 5,
"max_circle_stroke_width": 0.3,
}
class VideoWrapper(Scene):
def construct(self):
fade_rect = FullScreenFadeRectangle()
fade_rect.set_fill(DARK_GREY, 1)
screen_rect = ScreenRectangle()
screen_rect.set_height(4)
screen_rect.set_fill(BLACK, 1)
screen_rect.set_stroke(width=0)
boundary = AnimatedBoundary(screen_rect)
title = TextMobject("Learn the math")
title.scale(1.5)
title.next_to(screen_rect, UP)
self.add(fade_rect)
self.add(screen_rect)
self.add(boundary)
self.play(FadeInFromDown(title))
self.wait(19)