public-mirrors/3b1b-manim
1
0
Fork 0
mirror of https://github.com/3b1b/manim.git synced 2025-09-01 00:48:45 +00:00
Code Issues Projects Releases Packages Wiki Activity Actions

IntroduceTransformationView

Browse source
This commit is contained in:
Grant Sanderson 2018-05-14 18:40:52 -07:00
parent 3dd9999970
commit 80b475f174
1 changed files with 181 additions and 14 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

195
active_projects/alt_calc.py
View file

@ -39,6 +39,8 @@ class NumberlineTransformationScene(ZoomedScene):
"zoom_factor": 0.1,
"zoomed_display_height": 2.5,
"zoomed_display_corner_buff": MED_SMALL_BUFF,
"mini_line_scale_factor": 2,
"default_coordinate_value_dx": 0.05,
}
def setup(self):
@ -78,6 +80,7 @@ class NumberlineTransformationScene(ZoomedScene):
def setup_zoomed_camera_background_rectangle(self):
frame = self.zoomed_camera.frame
frame.next_to(self.camera.frame, UL)
self.zoomed_camera_background_rectangle = BackgroundRectangle(
frame, fill_opacity=1
)
@ -89,17 +92,23 @@ class NumberlineTransformationScene(ZoomedScene):
self.zoomed_camera_background_rectangle,
)
def get_sample_dots(self, x_min=None, x_max=None,
delta_x=None, dot_radius=None, colors=None):
def get_sample_input_points(self, x_min=None, x_max=None, delta_x=None):
x_min = x_min or self.input_line.x_min
x_max = x_max or self.input_line.x_max
delta_x = delta_x or self.default_delta_x
return [
self.get_input_point(x)
for x in np.arange(x_min, x_max + delta_x, delta_x)
]
def get_sample_dots(self, x_min=None, x_max=None,
delta_x=None, dot_radius=None, colors=None):
dot_radius = dot_radius or self.default_sample_dot_radius
colors = colors or self.default_sample_dot_colors
dots = VGroup(*[
Dot(self.get_input_point(x), radius=dot_radius)
for x in np.arange(x_min, x_max + delta_x, delta_x)
Dot(point, radius=dot_radius)
for point in self.get_sample_input_points(x_min, x_max, delta_x)
])
dots.set_color_by_gradient(*colors)
return dots
@ -117,6 +126,13 @@ class NumberlineTransformationScene(ZoomedScene):
config.update(kwargs)
return self.get_sample_dots(**config)
def get_local_coordinate_values(self, x, dx=None, n_neighbors=1):
dx = dx or self.default_coordinate_value_dx
return [
x + n * dx
for n in range(-n_neighbors, n_neighbors + 1)
]
# Mapping animations
def get_mapping_animation(self, func, mobject,
how_to_apply_func=apply_function_to_center,
@ -132,6 +148,7 @@ class NumberlineTransformationScene(ZoomedScene):
def get_line_mapping_animation(self, func, **kwargs):
input_line_copy = self.input_line.deepcopy()
self.moving_input_line = input_line_copy
input_line_copy.remove(input_line_copy.numbers)
# input_line_copy.set_stroke(width=2)
input_line_copy.main_line.insert_n_anchor_points(
@ -150,7 +167,7 @@ class NumberlineTransformationScene(ZoomedScene):
def get_sample_dots_mapping_animation(self, func, dots, **kwargs):
return self.get_mapping_animation(
func, dots, apply_function_to_submobjects
func, dots, how_to_apply_func=apply_function_to_submobjects
)
def get_zoomed_camera_frame_mapping_animation(self, func, x=None, **kwargs):
@ -177,7 +194,7 @@ class NumberlineTransformationScene(ZoomedScene):
if hasattr(self, "mini_line"): # Test for if mini_line is in self?
anims.append(self.get_mapping_animation(
func, self.mini_line,
how_to_apply_func=apply_function_to_points
how_to_apply_func=apply_function_to_center
))
if sample_dots:
anims.append(
@ -190,7 +207,7 @@ class NumberlineTransformationScene(ZoomedScene):
zoom_anim.update(1)
target_mini_line = Line(frame.get_left(), frame.get_right())
target_mini_line.scale(2)
target_mini_line.scale(self.mini_line_scale_factor)
target_mini_line.match_style(self.output_line.main_line)
zoom_anim.update(0)
zcbr_group.submobjects.insert(1, target_mini_line)
@ -239,11 +256,12 @@ class NumberlineTransformationScene(ZoomedScene):
# Add miniature number_line
mini_line = self.mini_line = Line(frame.get_left(), frame.get_right())
mini_line.scale(2)
mini_line.scale(self.mini_line_scale_factor)
mini_line.insert_n_anchor_points(self.num_inserted_number_line_anchors)
mini_line.match_style(self.input_line.main_line)
zcbr_group.add(mini_line.copy(), mini_line)
anims.append(FadeIn(mini_line))
mini_line_copy = mini_line.copy()
zcbr_group.add(mini_line_copy, mini_line)
anims += [FadeIn(mini_line), FadeIn(mini_line_copy)]
# Add tiny coordiantes
if local_coordinate_values is None:
@ -306,6 +324,9 @@ class NumberlineTransformationScene(ZoomedScene):
def get_input_point(self, x):
return self.input_line.number_to_point(x)
def get_output_point(self, fx):
return self.output_line.number_to_point(fx)
def number_func_to_point_func(self, number_func):
input_line, output_line = self.number_lines
@ -325,12 +346,13 @@ class ExampleNumberlineTransformationScene(NumberlineTransformationScene):
},
"output_line_config": {
"x_max": 20,
}
},
}
def construct(self):
func = lambda x: x**2
x = 0.5
x = 3
dx = 0.05
sample_dots = self.get_sample_dots()
local_sample_dots = self.get_local_sample_dots(x)
@ -339,14 +361,14 @@ class ExampleNumberlineTransformationScene(NumberlineTransformationScene):
self.zoom_in_on_input(
x,
local_sample_dots=local_sample_dots,
local_coordinate_values=[x - 0.05, x, x + 0.05],
local_coordinate_values=[x - dx, x, x + dx],
)
self.wait()
self.apply_function(
func,
sample_dots=sample_dots,
local_sample_dots=local_sample_dots,
target_coordinate_values=[func(x) - 0.05, func(x), func(x) + 0.05],
target_coordinate_values=[func(x) - dx, func(x), func(x) + dx],
)
self.wait()
@ -674,3 +696,148 @@ class EoCWrapper(Scene):
title = Title("Essence of calculus")
self.play(Write(title))
self.wait()
class IntroduceTransformationView(NumberlineTransformationScene):
CONFIG = {
"func": lambda x: 0.5 * np.sin(2 * x) + x,
"number_line_config": {
"x_min": 0,
"x_max": 6,
"unit_size": 2.0
},
}
def construct(self):
self.add_title()
self.show_animation_preview()
self.indicate_indicate_point_densities()
self.show_zoomed_transformation()
def add_title(self):
title = self.title = TextMobject("$f(x)$ as a transformation")
title.to_edge(UP)
self.add(title)
def show_animation_preview(self):
input_points = self.get_sample_input_points()
output_points = map(
self.number_func_to_point_func(self.func),
input_points
)
sample_dots = self.get_sample_dots()
sample_dot_ghosts = sample_dots.copy().fade(0.5)
arrows = VGroup(*[
Arrow(ip, op, buff=MED_SMALL_BUFF)
for ip, op in zip(input_points, output_points)
])
arrows = arrows[1::3]
arrows.set_stroke(BLACK, 1)
self.play(
LaggedStart(GrowFromCenter, sample_dots, run_time=1),
LaggedStart(GrowArrow, arrows)
)
self.add(sample_dot_ghosts)
self.apply_function(
self.func, sample_dots=sample_dots
)
self.wait()
self.play(LaggedStart(FadeOut, arrows, run_time=1))
self.sample_dots = sample_dots
self.sample_dot_ghosts = sample_dot_ghosts
def indicate_indicate_point_densities(self):
lower_brace = Brace(Line(LEFT, RIGHT), UP)
upper_brace = lower_brace.copy()
input_tracker = ValueTracker(0.5)
dx = 0.5
def update_upper_brace(brace):
x = input_tracker.get_value()
line = Line(
self.get_input_point(x),
self.get_input_point(x + dx),
)
brace.match_width(line, stretch=True)
brace.next_to(line, UP, buff=SMALL_BUFF)
return brace
def update_lower_brace(brace):
x = input_tracker.get_value()
line = Line(
self.get_output_point(self.func(x)),
self.get_output_point(self.func(x + dx)),
)
brace.match_width(line, stretch=True)
brace.next_to(line, UP, buff=SMALL_BUFF)
return brace
lower_brace_anim = UpdateFromFunc(lower_brace, update_lower_brace)
upper_brace_anim = UpdateFromFunc(upper_brace, update_upper_brace)
new_title = TextMobject(
"$\\frac{df}{dx}(x)$ measures stretch/squishing"
)
new_title.move_to(self.title, UP)
stretch_factor = DecimalNumber(0, color=YELLOW)
stretch_factor_anim = ChangingDecimal(
stretch_factor, lambda a: lower_brace.get_width() / upper_brace.get_width(),
position_update_func=lambda m: m.next_to(lower_brace, UP, SMALL_BUFF)
)
self.play(
GrowFromCenter(upper_brace),
FadeOut(self.title),
# FadeIn(new_title)
Write(new_title, run_time=2)
)
self.title = new_title
self.play(
ReplacementTransform(upper_brace.copy(), lower_brace),
GrowFromPoint(stretch_factor, upper_brace.get_center())
)
self.play(
input_tracker.set_value, self.input_line.x_max - dx,
lower_brace_anim,
upper_brace_anim,
stretch_factor_anim,
run_time=8,
rate_func=bezier([0, 0, 1, 1])
)
self.wait()
new_sample_dots = self.get_sample_dots()
self.play(
FadeOut(VGroup(
upper_brace, lower_brace, stretch_factor,
self.sample_dots, self.moving_input_line,
)),
FadeIn(new_sample_dots),
)
self.sample_dots = new_sample_dots
def show_zoomed_transformation(self):
x = 2.75
local_sample_dots = self.get_local_sample_dots(x)
self.zoom_in_on_input(
x,
local_sample_dots=local_sample_dots,
local_coordinate_values=self.get_local_coordinate_values(x),
)
self.wait()
self.apply_function(
self.func,
sample_dots=self.sample_dots,
local_sample_dots=local_sample_dots,
target_coordinate_values=self.get_local_coordinate_values(self.func(x))
)
self.wait()
class TalkThroughXSquaredExample(IntroduceTransformationView):
def construct(self):
pass