mirror of
https://github.com/3b1b/manim.git
synced 2025-04-13 09:47:07 +00:00
602809758e
* Enable setting points to a null list, and adding one point at a time.
* Add refresh_locked_data
* Add presenter mode to scenes with -p option
* Allow for an embed by hitting e during interaction
* Add set_min_height, etc.
* Make sure null parametric curve has at least one point
* Account for edge case where \{ is used in Tex
* Allow for logging notes in wait calls, useful for presenter mode
* Simplify choose, and add gen_choose for fractional amounts
* Default to no top on axes
* Allow match_x, match_y, etc. to take in a point
* Allow wait calls to ignore presenter mode
* Just use math.combo, no caching with choose(n, r)
* Use generator instead of list in bezier
* Bubble init_colors should override
* Account for "px" values read in from an svg
* Stop displaying when writing is happening
* Update the way Bubble override SVG colors
548 lines
18 KiB
Python
548 lines
18 KiB
Python
from abc import abstractmethod
|
|
import numpy as np
|
|
import numbers
|
|
|
|
from manimlib.constants import *
|
|
from manimlib.mobject.functions import ParametricCurve
|
|
from manimlib.mobject.geometry import Arrow
|
|
from manimlib.mobject.geometry import Line
|
|
from manimlib.mobject.geometry import DashedLine
|
|
from manimlib.mobject.geometry import Rectangle
|
|
from manimlib.mobject.number_line import NumberLine
|
|
from manimlib.mobject.svg.tex_mobject import Tex
|
|
from manimlib.mobject.types.vectorized_mobject import VGroup
|
|
from manimlib.utils.config_ops import digest_config
|
|
from manimlib.utils.config_ops import merge_dicts_recursively
|
|
from manimlib.utils.simple_functions import binary_search
|
|
from manimlib.utils.space_ops import angle_of_vector
|
|
from manimlib.utils.space_ops import get_norm
|
|
from manimlib.utils.space_ops import rotate_vector
|
|
|
|
EPSILON = 1e-8
|
|
|
|
|
|
class CoordinateSystem():
|
|
"""
|
|
Abstract class for Axes and NumberPlane
|
|
"""
|
|
CONFIG = {
|
|
"dimension": 2,
|
|
"default_x_range": [-8.0, 8.0, 1.0],
|
|
"default_y_range": [-4.0, 4.0, 1.0],
|
|
"width": FRAME_WIDTH,
|
|
"height": FRAME_HEIGHT,
|
|
"num_sampled_graph_points_per_tick": 20,
|
|
}
|
|
|
|
def __init__(self, **kwargs):
|
|
digest_config(self, kwargs)
|
|
self.x_range = np.array(self.default_x_range)
|
|
self.y_range = np.array(self.default_y_range)
|
|
|
|
def coords_to_point(self, *coords):
|
|
raise Exception("Not implemented")
|
|
|
|
def point_to_coords(self, point):
|
|
raise Exception("Not implemented")
|
|
|
|
def c2p(self, *coords):
|
|
"""Abbreviation for coords_to_point"""
|
|
return self.coords_to_point(*coords)
|
|
|
|
def p2c(self, point):
|
|
"""Abbreviation for point_to_coords"""
|
|
return self.point_to_coords(point)
|
|
|
|
def get_origin(self):
|
|
return self.c2p(*[0] * self.dimension)
|
|
|
|
@abstractmethod
|
|
def get_axes(self):
|
|
raise Exception("Not implemented")
|
|
|
|
@abstractmethod
|
|
def get_all_ranges(self):
|
|
raise Exception("Not implemented")
|
|
|
|
def get_axis(self, index):
|
|
return self.get_axes()[index]
|
|
|
|
def get_x_axis(self):
|
|
return self.get_axis(0)
|
|
|
|
def get_y_axis(self):
|
|
return self.get_axis(1)
|
|
|
|
def get_z_axis(self):
|
|
return self.get_axis(2)
|
|
|
|
def get_x_axis_label(self, label_tex, edge=RIGHT, direction=DL, **kwargs):
|
|
return self.get_axis_label(
|
|
label_tex, self.get_x_axis(),
|
|
edge, direction, **kwargs
|
|
)
|
|
|
|
def get_y_axis_label(self, label_tex, edge=UP, direction=DR, **kwargs):
|
|
return self.get_axis_label(
|
|
label_tex, self.get_y_axis(),
|
|
edge, direction, **kwargs
|
|
)
|
|
|
|
def get_axis_label(self, label_tex, axis, edge, direction, buff=MED_SMALL_BUFF):
|
|
label = Tex(label_tex)
|
|
label.next_to(
|
|
axis.get_edge_center(edge), direction,
|
|
buff=buff
|
|
)
|
|
label.shift_onto_screen(buff=MED_SMALL_BUFF)
|
|
return label
|
|
|
|
def get_axis_labels(self, x_label_tex="x", y_label_tex="y"):
|
|
self.axis_labels = VGroup(
|
|
self.get_x_axis_label(x_label_tex),
|
|
self.get_y_axis_label(y_label_tex),
|
|
)
|
|
return self.axis_labels
|
|
|
|
def get_line_from_axis_to_point(self, index, point,
|
|
line_func=DashedLine,
|
|
color=GREY_A,
|
|
stroke_width=2):
|
|
axis = self.get_axis(index)
|
|
line = line_func(axis.get_projection(point), point)
|
|
line.set_stroke(color, stroke_width)
|
|
return line
|
|
|
|
def get_v_line(self, point, **kwargs):
|
|
return self.get_line_from_axis_to_point(0, point, **kwargs)
|
|
|
|
def get_h_line(self, point, **kwargs):
|
|
return self.get_line_from_axis_to_point(1, point, **kwargs)
|
|
|
|
# Useful for graphing
|
|
def get_graph(self, function, x_range=None, **kwargs):
|
|
t_range = np.array(self.x_range, dtype=float)
|
|
if x_range is not None:
|
|
t_range[:len(x_range)] = x_range
|
|
# For axes, the third coordinate of x_range indicates
|
|
# tick frequency. But for functions, it indicates a
|
|
# sample frequency
|
|
if x_range is None or len(x_range) < 3:
|
|
t_range[2] /= self.num_sampled_graph_points_per_tick
|
|
|
|
graph = ParametricCurve(
|
|
lambda t: self.c2p(t, function(t)),
|
|
t_range=t_range,
|
|
**kwargs
|
|
)
|
|
graph.underlying_function = function
|
|
graph.x_range = x_range
|
|
return graph
|
|
|
|
def get_parametric_curve(self, function, **kwargs):
|
|
dim = self.dimension
|
|
graph = ParametricCurve(
|
|
lambda t: self.coords_to_point(*function(t)[:dim]),
|
|
**kwargs
|
|
)
|
|
graph.underlying_function = function
|
|
return graph
|
|
|
|
def input_to_graph_point(self, x, graph):
|
|
if hasattr(graph, "underlying_function"):
|
|
return self.coords_to_point(x, graph.underlying_function(x))
|
|
else:
|
|
alpha = binary_search(
|
|
function=lambda a: self.point_to_coords(
|
|
graph.quick_point_from_proportion(a)
|
|
)[0],
|
|
target=x,
|
|
lower_bound=self.x_range[0],
|
|
upper_bound=self.x_range[1],
|
|
)
|
|
if alpha is not None:
|
|
return graph.quick_point_from_proportion(alpha)
|
|
else:
|
|
return None
|
|
|
|
def i2gp(self, x, graph):
|
|
"""
|
|
Alias for input_to_graph_point
|
|
"""
|
|
return self.input_to_graph_point(x, graph)
|
|
|
|
def get_graph_label(self,
|
|
graph,
|
|
label="f(x)",
|
|
x=None,
|
|
direction=RIGHT,
|
|
buff=MED_SMALL_BUFF,
|
|
color=None):
|
|
if isinstance(label, str):
|
|
label = Tex(label)
|
|
if color is None:
|
|
label.match_color(graph)
|
|
if x is None:
|
|
# Searching from the right, find a point
|
|
# whose y value is in bounds
|
|
max_y = FRAME_Y_RADIUS - label.get_height()
|
|
max_x = FRAME_X_RADIUS - label.get_width()
|
|
for x0 in np.arange(*self.x_range)[::-1]:
|
|
pt = self.i2gp(x0, graph)
|
|
if abs(pt[0]) < max_x and abs(pt[1]) < max_y:
|
|
x = x0
|
|
break
|
|
if x is None:
|
|
x = self.x_range[1]
|
|
|
|
point = self.input_to_graph_point(x, graph)
|
|
angle = self.angle_of_tangent(x, graph)
|
|
normal = rotate_vector(RIGHT, angle + 90 * DEGREES)
|
|
if normal[1] < 0:
|
|
normal *= -1
|
|
label.next_to(point, normal, buff=buff)
|
|
label.shift_onto_screen()
|
|
return label
|
|
|
|
def get_v_line_to_graph(self, x, graph, **kwargs):
|
|
return self.get_v_line(self.i2gp(x, graph), **kwargs)
|
|
|
|
def get_h_line_to_graph(self, x, graph, **kwargs):
|
|
return self.get_h_line(self.i2gp(x, graph), **kwargs)
|
|
|
|
# For calculus
|
|
def angle_of_tangent(self, x, graph, dx=EPSILON):
|
|
p0 = self.input_to_graph_point(x, graph)
|
|
p1 = self.input_to_graph_point(x + dx, graph)
|
|
return angle_of_vector(p1 - p0)
|
|
|
|
def slope_of_tangent(self, x, graph, **kwargs):
|
|
return np.tan(self.angle_of_tangent(x, graph, **kwargs))
|
|
|
|
def get_tangent_line(self, x, graph, length=5, line_func=Line):
|
|
line = line_func(LEFT, RIGHT)
|
|
line.set_width(length)
|
|
line.rotate(self.angle_of_tangent(x, graph))
|
|
line.move_to(self.input_to_graph_point(x, graph))
|
|
return line
|
|
|
|
def get_riemann_rectangles(self,
|
|
graph,
|
|
x_range=None,
|
|
dx=None,
|
|
input_sample_type="left",
|
|
stroke_width=1,
|
|
stroke_color=BLACK,
|
|
fill_opacity=1,
|
|
colors=(BLUE, GREEN),
|
|
show_signed_area=True):
|
|
if x_range is None:
|
|
x_range = self.x_range[:2]
|
|
if dx is None:
|
|
dx = self.x_range[2]
|
|
if len(x_range) < 3:
|
|
x_range = [*x_range, dx]
|
|
|
|
rects = []
|
|
xs = np.arange(*x_range)
|
|
for x0, x1 in zip(xs, xs[1:]):
|
|
if input_sample_type == "left":
|
|
sample = x0
|
|
elif input_sample_type == "right":
|
|
sample = x1
|
|
elif input_sample_type == "center":
|
|
sample = 0.5 * x0 + 0.5 * x1
|
|
else:
|
|
raise Exception("Invalid input sample type")
|
|
height = get_norm(
|
|
self.i2gp(sample, graph) - self.c2p(sample, 0)
|
|
)
|
|
rect = Rectangle(width=x1 - x0, height=height)
|
|
rect.move_to(self.c2p(x0, 0), DL)
|
|
rects.append(rect)
|
|
result = VGroup(*rects)
|
|
result.set_submobject_colors_by_gradient(*colors)
|
|
result.set_style(
|
|
stroke_width=stroke_width,
|
|
stroke_color=stroke_color,
|
|
fill_opacity=fill_opacity,
|
|
)
|
|
return result
|
|
|
|
def get_area_under_graph(self, graph, x_range, fill_color=BLUE, fill_opacity=1):
|
|
# TODO
|
|
pass
|
|
|
|
|
|
class Axes(VGroup, CoordinateSystem):
|
|
CONFIG = {
|
|
"axis_config": {
|
|
"include_tip": False,
|
|
"numbers_to_exclude": [0],
|
|
},
|
|
"x_axis_config": {},
|
|
"y_axis_config": {
|
|
"line_to_number_direction": LEFT,
|
|
},
|
|
"height": FRAME_HEIGHT - 2,
|
|
"width": FRAME_WIDTH - 2,
|
|
}
|
|
|
|
def __init__(self,
|
|
x_range=None,
|
|
y_range=None,
|
|
**kwargs):
|
|
CoordinateSystem.__init__(self, **kwargs)
|
|
VGroup.__init__(self, **kwargs)
|
|
|
|
if x_range is not None:
|
|
self.x_range[:len(x_range)] = x_range
|
|
if y_range is not None:
|
|
self.y_range[:len(y_range)] = y_range
|
|
|
|
self.x_axis = self.create_axis(
|
|
self.x_range, self.x_axis_config, self.width,
|
|
)
|
|
self.y_axis = self.create_axis(
|
|
self.y_range, self.y_axis_config, self.height
|
|
)
|
|
self.y_axis.rotate(90 * DEGREES, about_point=ORIGIN)
|
|
# Add as a separate group in case various other
|
|
# mobjects are added to self, as for example in
|
|
# NumberPlane below
|
|
self.axes = VGroup(self.x_axis, self.y_axis)
|
|
self.add(*self.axes)
|
|
self.center()
|
|
|
|
def create_axis(self, range_terms, axis_config, length):
|
|
new_config = merge_dicts_recursively(self.axis_config, axis_config)
|
|
new_config["width"] = length
|
|
axis = NumberLine(range_terms, **new_config)
|
|
axis.shift(-axis.n2p(0))
|
|
return axis
|
|
|
|
def coords_to_point(self, *coords):
|
|
origin = self.x_axis.number_to_point(0)
|
|
result = origin.copy()
|
|
for axis, coord in zip(self.get_axes(), coords):
|
|
result += (axis.number_to_point(coord) - origin)
|
|
return result
|
|
|
|
def point_to_coords(self, point):
|
|
return tuple([
|
|
axis.point_to_number(point)
|
|
for axis in self.get_axes()
|
|
])
|
|
|
|
def get_axes(self):
|
|
return self.axes
|
|
|
|
def get_all_ranges(self):
|
|
return [self.x_range, self.y_range]
|
|
|
|
def add_coordinate_labels(self,
|
|
x_values=None,
|
|
y_values=None,
|
|
**kwargs):
|
|
axes = self.get_axes()
|
|
self.coordinate_labels = VGroup()
|
|
for axis, values in zip(axes, [x_values, y_values]):
|
|
labels = axis.add_numbers(values, **kwargs)
|
|
self.coordinate_labels.add(labels)
|
|
return self.coordinate_labels
|
|
|
|
|
|
class ThreeDAxes(Axes):
|
|
CONFIG = {
|
|
"dimension": 3,
|
|
"x_range": np.array([-6.0, 6.0, 1.0]),
|
|
"y_range": np.array([-5.0, 5.0, 1.0]),
|
|
"z_range": np.array([-4.0, 4.0, 1.0]),
|
|
"z_axis_config": {},
|
|
"z_normal": DOWN,
|
|
"height": None,
|
|
"width": None,
|
|
"depth": None,
|
|
"num_axis_pieces": 20,
|
|
"gloss": 0.5,
|
|
}
|
|
|
|
def __init__(self, x_range=None, y_range=None, z_range=None, **kwargs):
|
|
Axes.__init__(self, x_range, y_range, **kwargs)
|
|
if z_range is not None:
|
|
self.z_range[:len(z_range)] = z_range
|
|
|
|
z_axis = self.create_axis(
|
|
self.z_range,
|
|
self.z_axis_config,
|
|
self.depth,
|
|
)
|
|
z_axis.rotate(-PI / 2, UP, about_point=ORIGIN)
|
|
z_axis.rotate(
|
|
angle_of_vector(self.z_normal), OUT,
|
|
about_point=ORIGIN
|
|
)
|
|
z_axis.shift(self.x_axis.n2p(0))
|
|
self.axes.add(z_axis)
|
|
self.add(z_axis)
|
|
self.z_axis = z_axis
|
|
|
|
for axis in self.axes:
|
|
axis.insert_n_curves(self.num_axis_pieces - 1)
|
|
|
|
def get_all_ranges(self):
|
|
return [self.x_range, self.y_range, self.z_range]
|
|
|
|
|
|
class NumberPlane(Axes):
|
|
CONFIG = {
|
|
"axis_config": {
|
|
"stroke_color": WHITE,
|
|
"stroke_width": 2,
|
|
"include_ticks": False,
|
|
"include_tip": False,
|
|
"line_to_number_buff": SMALL_BUFF,
|
|
"line_to_number_direction": DL,
|
|
},
|
|
"y_axis_config": {
|
|
"line_to_number_direction": DL,
|
|
},
|
|
"background_line_style": {
|
|
"stroke_color": BLUE_D,
|
|
"stroke_width": 2,
|
|
"stroke_opacity": 1,
|
|
},
|
|
"height": None,
|
|
"width": None,
|
|
# Defaults to a faded version of line_config
|
|
"faded_line_style": None,
|
|
"faded_line_ratio": 4,
|
|
"make_smooth_after_applying_functions": True,
|
|
}
|
|
|
|
def __init__(self, x_range=None, y_range=None, **kwargs):
|
|
super().__init__(x_range, y_range, **kwargs)
|
|
self.init_background_lines()
|
|
|
|
def init_background_lines(self):
|
|
if self.faded_line_style is None:
|
|
style = dict(self.background_line_style)
|
|
# For anything numerical, like stroke_width
|
|
# and stroke_opacity, chop it in half
|
|
for key in style:
|
|
if isinstance(style[key], numbers.Number):
|
|
style[key] *= 0.5
|
|
self.faded_line_style = style
|
|
|
|
self.background_lines, self.faded_lines = self.get_lines()
|
|
self.background_lines.set_style(**self.background_line_style)
|
|
self.faded_lines.set_style(**self.faded_line_style)
|
|
self.add_to_back(
|
|
self.faded_lines,
|
|
self.background_lines,
|
|
)
|
|
|
|
def get_lines(self):
|
|
x_axis = self.get_x_axis()
|
|
y_axis = self.get_y_axis()
|
|
|
|
x_lines1, x_lines2 = self.get_lines_parallel_to_axis(x_axis, y_axis)
|
|
y_lines1, y_lines2 = self.get_lines_parallel_to_axis(y_axis, x_axis)
|
|
lines1 = VGroup(*x_lines1, *y_lines1)
|
|
lines2 = VGroup(*x_lines2, *y_lines2)
|
|
return lines1, lines2
|
|
|
|
def get_lines_parallel_to_axis(self, axis1, axis2):
|
|
freq = axis2.x_step
|
|
ratio = self.faded_line_ratio
|
|
line = Line(axis1.get_start(), axis1.get_end())
|
|
dense_freq = (1 + ratio)
|
|
step = (1 / dense_freq) * freq
|
|
|
|
lines1 = VGroup()
|
|
lines2 = VGroup()
|
|
inputs = np.arange(axis2.x_min, axis2.x_max + step, step)
|
|
for i, x in enumerate(inputs):
|
|
new_line = line.copy()
|
|
new_line.shift(axis2.n2p(x) - axis2.n2p(0))
|
|
if i % (1 + ratio) == 0:
|
|
lines1.add(new_line)
|
|
else:
|
|
lines2.add(new_line)
|
|
return lines1, lines2
|
|
|
|
def get_x_unit_size(self):
|
|
return self.get_x_axis().get_unit_size()
|
|
|
|
def get_y_unit_size(self):
|
|
return self.get_x_axis().get_unit_size()
|
|
|
|
def get_axes(self):
|
|
return self.axes
|
|
|
|
def get_vector(self, coords, **kwargs):
|
|
kwargs["buff"] = 0
|
|
return Arrow(self.c2p(0, 0), self.c2p(*coords), **kwargs)
|
|
|
|
def prepare_for_nonlinear_transform(self, num_inserted_curves=50):
|
|
for mob in self.family_members_with_points():
|
|
num_curves = mob.get_num_curves()
|
|
if num_inserted_curves > num_curves:
|
|
mob.insert_n_curves(num_inserted_curves - num_curves)
|
|
mob.make_smooth_after_applying_functions = True
|
|
return self
|
|
|
|
|
|
class ComplexPlane(NumberPlane):
|
|
CONFIG = {
|
|
"color": BLUE,
|
|
"line_frequency": 1,
|
|
}
|
|
|
|
def number_to_point(self, number):
|
|
number = complex(number)
|
|
return self.coords_to_point(number.real, number.imag)
|
|
|
|
def n2p(self, number):
|
|
return self.number_to_point(number)
|
|
|
|
def point_to_number(self, point):
|
|
x, y = self.point_to_coords(point)
|
|
return complex(x, y)
|
|
|
|
def p2n(self, point):
|
|
return self.point_to_number(point)
|
|
|
|
def get_default_coordinate_values(self, skip_first=True):
|
|
x_numbers = self.get_x_axis().get_tick_range()[1:]
|
|
y_numbers = self.get_y_axis().get_tick_range()[1:]
|
|
y_numbers = [complex(0, y) for y in y_numbers if y != 0]
|
|
return [*x_numbers, *y_numbers]
|
|
|
|
def add_coordinate_labels(self, numbers=None, skip_first=True, **kwargs):
|
|
if numbers is None:
|
|
numbers = self.get_default_coordinate_values(skip_first)
|
|
|
|
self.coordinate_labels = VGroup()
|
|
for number in numbers:
|
|
z = complex(number)
|
|
if abs(z.imag) > abs(z.real):
|
|
axis = self.get_y_axis()
|
|
value = z.imag
|
|
kwargs["unit"] = "i"
|
|
else:
|
|
axis = self.get_x_axis()
|
|
value = z.real
|
|
number_mob = axis.get_number_mobject(value, **kwargs)
|
|
# For i and -i, remove the "1"
|
|
if z.imag == 1:
|
|
number_mob.remove(number_mob[0])
|
|
if z.imag == -1:
|
|
number_mob.remove(number_mob[1])
|
|
number_mob[0].next_to(
|
|
number_mob[1], LEFT,
|
|
buff=number_mob[0].get_width() / 4
|
|
)
|
|
self.coordinate_labels.add(number_mob)
|
|
self.add(self.coordinate_labels)
|
|
return self
|