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ZoomInOnXSquaredNearOne of alt-calc

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This commit is contained in:
Grant Sanderson 2018-05-15 12:01:34 -07:00
parent 53abc18be2
commit 90da42e034
1 changed files with 231 additions and 7 deletions
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238
active_projects/alt_calc.py
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@ -41,6 +41,7 @@ class NumberlineTransformationScene(ZoomedScene):
"zoomed_display_corner_buff": MED_SMALL_BUFF,
"mini_line_scale_factor": 2,
"default_coordinate_value_dx": 0.05,
"zoomed_camera_background_rectangle_fill_opacity": 1.0,
}
def setup(self):
@ -82,7 +83,7 @@ class NumberlineTransformationScene(ZoomedScene):
frame = self.zoomed_camera.frame
frame.next_to(self.camera.frame, UL)
self.zoomed_camera_background_rectangle = BackgroundRectangle(
frame, fill_opacity=1
frame, fill_opacity=self.zoomed_camera_background_rectangle_fill_opacity
)
self.zoomed_camera_background_rectangle_anim = UpdateFromFunc(
self.zoomed_camera_background_rectangle,
@ -114,14 +115,18 @@ class NumberlineTransformationScene(ZoomedScene):
return dots
def get_local_sample_dots(self, x, sample_radius=None, **kwargs):
if sample_radius is None:
sample_radius = self.zoomed_camera.frame.get_width() / 2
zoom_factor = self.get_zoom_factor()
delta_x = kwargs.get("delta_x", self.default_delta_x * zoom_factor)
dot_radius = kwargs.get("dot_radius", self.default_sample_dot_radius * zoom_factor)
if sample_radius is None:
unrounded_radius = self.zoomed_camera.frame.get_width() / 2
sample_radius = int(unrounded_radius / delta_x) * delta_x
config = {
"x_min": x - sample_radius,
"x_max": x + sample_radius,
"delta_x": self.default_delta_x * zoom_factor,
"dot_radius": self.default_sample_dot_radius * zoom_factor,
"delta_x": delta_x,
"dot_radius": dot_radius,
}
config.update(kwargs)
return self.get_sample_dots(**config)
@ -183,14 +188,19 @@ class NumberlineTransformationScene(ZoomedScene):
)
def apply_function(self, func,
apply_function_to_number_line=True,
sample_dots=None,
local_sample_dots=None,
target_coordinate_values=None):
target_coordinate_values=None,
added_anims=None
):
zcbr_group = self.zoomed_camera_background_rectangle_group
zcbr_anim = self.zoomed_camera_background_rectangle_anim
frame = self.zoomed_camera.frame
anims = [self.get_line_mapping_animation(func)]
anims = []
if apply_function_to_number_line:
anims.append(self.get_line_mapping_animation(func))
if hasattr(self, "mini_line"): # Test for if mini_line is in self?
anims.append(self.get_mapping_animation(
func, self.mini_line,
@ -218,11 +228,14 @@ class NumberlineTransformationScene(ZoomedScene):
)
anims.append(FadeIn(coordinates))
zcbr_group.add(coordinates)
self.local_target_coordinates = coordinates
if local_sample_dots:
anims.append(
self.get_sample_dots_mapping_animation(func, local_sample_dots)
)
zcbr_group.add(local_sample_dots)
if added_anims:
anims += added_anims
anims.append(Animation(zcbr_group))
self.play(*anims)
@ -272,6 +285,7 @@ class NumberlineTransformationScene(ZoomedScene):
)
anims.append(FadeIn(local_coordinates))
zcbr_group.add(local_coordinates)
self.local_coordinates = local_coordinates
# Add tiny dots
if local_sample_dots is not None:
@ -839,5 +853,215 @@ class IntroduceTransformationView(NumberlineTransformationScene):
class TalkThroughXSquaredExample(IntroduceTransformationView):
CONFIG = {
"func": lambda x: x**2,
"number_line_config": {
"x_min": 0,
"x_max": 5,
"unit_size": 1.25,
},
"output_line_config": {
"x_max": 25,
},
"default_delta_x": 0.2
}
def construct(self):
self.add_title()
self.show_specific_points_mapping()
def add_title(self):
title = self.title = TextMobject("$f(x) = x^2$")
title.to_edge(UP)
self.add(title)
def show_specific_points_mapping(self):
# First, just show integers as examples
int_dots = self.get_sample_dots(1, 6, 1)
int_dot_ghosts = int_dots.copy().fade(0.5)
int_arrows = VGroup(*[
Arrow(
# num.get_bottom(),
self.get_input_point(x),
self.get_output_point(self.func(x)),
buff=MED_SMALL_BUFF
)
for x, num in zip(range(1, 6), self.input_line.numbers[1:])
])
point_func = self.number_func_to_point_func(self.func)
numbers = self.input_line.numbers
numbers.next_to(self.input_line, UP, SMALL_BUFF)
self.titles[0].next_to(numbers, UP, MED_SMALL_BUFF, LEFT)
# map(TexMobject.add_background_rectangle, numbers)
# self.add_foreground_mobject(numbers)
for dot, dot_ghost, arrow in zip(int_dots, int_dot_ghosts, int_arrows):
arrow.match_color(dot)
self.play(DrawBorderThenFill(dot, run_time=1))
self.add(dot_ghost)
self.play(
GrowArrow(arrow),
dot.apply_function_to_position, point_func
)
self.wait()
# Show more sample_dots
sample_dots = self.get_sample_dots()
sample_dot_ghosts = sample_dots.copy().fade(0.5)
self.play(
LaggedStart(DrawBorderThenFill, sample_dots),
LaggedStart(FadeOut, int_arrows),
)
self.remove(int_dot_ghosts)
self.add(sample_dot_ghosts)
self.apply_function(self.func, sample_dots=sample_dots)
self.remove(int_dots)
self.wait()
self.sample_dots = sample_dots
self.sample_dot_ghosts = sample_dot_ghosts
class ZoomInOnXSquaredNearOne(TalkThroughXSquaredExample):
def setup(self):
TalkThroughXSquaredExample.setup(self)
self.force_skipping()
self.add_title()
self.show_specific_points_mapping()
self.revert_to_original_skipping_status()
def construct(self):
zoom_words = TextMobject("Zoomed view \\\\ near 1")
zoom_words.next_to(self.zoomed_display, DOWN)
# zoom_words.shift_onto_screen()
x = 1
local_sample_dots = self.get_local_sample_dots(x)
local_coords = self.get_local_coordinate_values(x, dx=0.1)
zcbr_anim = self.zoomed_camera_background_rectangle_anim
zcbr_group = self.zoomed_camera_background_rectangle_group
frame = self.zoomed_camera.frame
self.zoom_in_on_input(x, local_sample_dots, local_coords)
self.play(FadeIn(zoom_words))
self.wait()
local_sample_dots.save_state()
frame.save_state()
self.mini_line.save_state()
sample_dot_ghost_copies = self.sample_dot_ghosts.copy()
self.apply_function(
self.func,
apply_function_to_number_line=False,
local_sample_dots=local_sample_dots,
target_coordinate_values=local_coords
)
self.remove(sample_dot_ghost_copies)
self.wait()
# Go back
self.play(
frame.restore,
self.mini_line.restore,
local_sample_dots.restore,
zcbr_anim,
Animation(zcbr_group)
)
self.wait()
# Zoom in even more
extra_zoom_factor = 0.3
one_group = VGroup(
self.local_coordinates.tick_marks[1],
self.local_coordinates.numbers[1],
)
all_other_coordinates = VGroup(
self.local_coordinates.tick_marks[::2],
self.local_coordinates.numbers[::2],
self.local_target_coordinates,
)
self.play(frame.scale, extra_zoom_factor)
new_local_sample_dots = self.get_local_sample_dots(x, delta_x=0.005)
new_coordinate_values = self.get_local_coordinate_values(x, dx=0.02)
new_local_coordinates = self.get_local_coordinates(
self.input_line, *new_coordinate_values
)
self.play(
Write(new_local_coordinates),
Write(new_local_sample_dots),
one_group.scale, extra_zoom_factor, {"about_point": self.get_input_point(1)},
FadeOut(all_other_coordinates),
*[
ApplyMethod(dot.scale, extra_zoom_factor)
for dot in local_sample_dots
]
)
self.remove(one_group, local_sample_dots)
zcbr_group.remove(
self.local_coordinates, self.local_target_coordinates,
local_sample_dots
)
# Transform new zoomed view
stretch_by_two_words = TextMobject("Stretch by 2")
stretch_by_two_words.scale(0.5)
la, ra = TexMobject("\\leftarrow \\rightarrow")
la.next_to(stretch_by_two_words, LEFT)
ra.next_to(stretch_by_two_words, RIGHT)
stretch_by_two_words.add(la, ra)
stretch_by_two_words.next_to(
self.zoomed_display.get_top(), DOWN
)
self.add_foreground_mobject(stretch_by_two_words)
sample_dot_ghost_copies = self.sample_dot_ghosts.copy()
self.apply_function(
self.func,
apply_function_to_number_line=False,
sample_dots=sample_dot_ghost_copies,
local_sample_dots=new_local_sample_dots,
target_coordinate_values=new_coordinate_values,
added_anims=[FadeIn(stretch_by_two_words)]
)
self.remove(sample_dot_ghost_copies)
self.wait()
# Write derivative
deriv_equation = self.deriv_equation = TexMobject(
"\\frac{df}{dx}(", "1", ")", "=", "2",
tex_to_color_map={"1": RED, "2": RED}
)
deriv_equation.next_to(self.title, DOWN)
self.play(
Write(deriv_equation),
self.title.shift, MED_SMALL_BUFF * UP
)
self.wait()
class ZoomInOnXSquaredNearThree(ZoomInOnXSquaredNearOne):
def construct(self):
pass
class ZoomInOnXSquaredNearOneFourth(ZoomInOnXSquaredNearOne):
def construct(self):
pass
class ZoomInOnXSquaredNearZero(ZoomInOnXSquaredNearOne):
def construct(self):
pass
class XSquaredForNegativeInput(TalkThroughXSquaredExample):
CONFIG = {
"input_line_config": {},
"output_line_config": {},
}
def construct(self):
pass