/
coordinate_systems.py
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/
coordinate_systems.py
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import numpy as np
import numbers
from manimlib.constants import *
from manimlib.mobject.functions import ParametricFunction
from manimlib.mobject.geometry import Arrow
from manimlib.mobject.geometry import Line
from manimlib.mobject.number_line import NumberLine
from manimlib.mobject.svg.tex_mobject import TexMobject
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
# TODO: There should be much more code reuse between Axes, NumberPlane and GraphScene
class CoordinateSystem():
"""
Abstract class for Axes and NumberPlane
"""
CONFIG = {
"dimension": 2,
"x_min": -FRAME_X_RADIUS,
"x_max": FRAME_X_RADIUS,
"y_min": -FRAME_Y_RADIUS,
"y_max": FRAME_Y_RADIUS,
}
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_axes(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 = TexMobject(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_graph(self, function, **kwargs):
x_min = kwargs.pop("x_min", self.x_min)
x_max = kwargs.pop("x_max", self.x_max)
graph = ParametricFunction(
lambda t: self.coords_to_point(t, function(t)),
t_min=x_min,
t_max=x_max,
**kwargs
)
graph.underlying_function = function
return graph
def get_parametric_curve(self, function, **kwargs):
dim = self.dimension
graph = ParametricFunction(
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.point_from_proportion(a)
)[0],
target=x,
lower_bound=self.x_min,
upper_bound=self.x_max,
)
if alpha is not None:
return graph.point_from_proportion(alpha)
else:
return None
class Axes(VGroup, CoordinateSystem):
CONFIG = {
"number_line_config": {
"color": LIGHT_GREY,
"include_tip": True,
"exclude_zero_from_default_numbers": True,
},
"x_axis_config": {},
"y_axis_config": {
"label_direction": LEFT,
},
"center_point": ORIGIN,
}
def __init__(self, **kwargs):
VGroup.__init__(self, **kwargs)
self.x_axis = self.create_axis(
self.x_min, self.x_max, self.x_axis_config
)
self.y_axis = self.create_axis(
self.y_min, self.y_max, self.y_axis_config
)
self.y_axis.rotate(90 * DEGREES, about_point=ORIGIN)
# Add as a separate group incase 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.shift(self.center_point)
def create_axis(self, min_val, max_val, axis_config):
new_config = merge_dicts_recursively(
self.number_line_config,
{"x_min": min_val, "x_max": max_val},
axis_config,
)
return NumberLine(**new_config)
def coords_to_point(self, *coords):
origin = self.x_axis.number_to_point(0)
result = np.array(origin)
for axis, coord in zip(self.get_axes(), coords):
result += (axis.number_to_point(coord) - origin)
return result
def c2p(self, *coords):
return self.coords_to_point(*coords)
def point_to_coords(self, point):
return tuple([
axis.point_to_number(point)
for axis in self.get_axes()
])
def p2c(self, point):
return self.point_to_coords(point)
def get_axes(self):
return self.axes
def get_coordinate_labels(self, x_vals=None, y_vals=None):
if x_vals is None:
x_vals = []
if y_vals is None:
y_vals = []
x_mobs = self.get_x_axis().get_number_mobjects(*x_vals)
y_mobs = self.get_y_axis().get_number_mobjects(*y_vals)
self.coordinate_labels = VGroup(x_mobs, y_mobs)
return self.coordinate_labels
def add_coordinates(self, x_vals=None, y_vals=None):
self.add(self.get_coordinate_labels(x_vals, y_vals))
return self
class ThreeDAxes(Axes):
CONFIG = {
"dimension": 3,
"x_min": -5.5,
"x_max": 5.5,
"y_min": -5.5,
"y_max": 5.5,
"z_axis_config": {},
"z_min": -3.5,
"z_max": 3.5,
"z_normal": DOWN,
"num_axis_pieces": 20,
"light_source": 9 * DOWN + 7 * LEFT + 10 * OUT,
}
def __init__(self, **kwargs):
Axes.__init__(self, **kwargs)
z_axis = self.z_axis = self.create_axis(
self.z_min, self.z_max, self.z_axis_config
)
z_axis.rotate(-np.pi / 2, UP, about_point=ORIGIN)
z_axis.rotate(
angle_of_vector(self.z_normal), OUT,
about_point=ORIGIN
)
self.axes.add(z_axis)
self.add(z_axis)
self.add_3d_pieces()
self.set_axis_shading()
def add_3d_pieces(self):
for axis in self.axes:
axis.pieces = VGroup(
*axis.get_pieces(self.num_axis_pieces)
)
axis.add(axis.pieces)
axis.set_stroke(width=0, family=False)
axis.set_shade_in_3d(True)
def set_axis_shading(self):
def make_func(axis):
vect = self.light_source
return lambda: (
axis.get_edge_center(-vect),
axis.get_edge_center(vect),
)
for axis in self:
for submob in axis.family_members_with_points():
submob.get_gradient_start_and_end_points = make_func(axis)
submob.get_unit_normal = lambda a: np.ones(3)
submob.set_sheen(0.2)
class NumberPlane(Axes):
CONFIG = {
"axis_config": {
"stroke_color": WHITE,
"stroke_width": 2,
"include_ticks": False,
"include_tip": False,
"line_to_number_buff": SMALL_BUFF,
"label_direction": DR,
"number_scale_val": 0.5,
},
"y_axis_config": {
"label_direction": DR,
},
"background_line_style": {
"stroke_color": BLUE_D,
"stroke_width": 2,
"stroke_opacity": 1,
},
# Defaults to a faded version of line_config
"faded_line_style": None,
"x_line_frequency": 1,
"y_line_frequency": 1,
"faded_line_ratio": 1,
"make_smooth_after_applying_functions": True,
}
def __init__(self, **kwargs):
digest_config(self, kwargs)
kwargs["number_line_config"] = self.axis_config
Axes.__init__(self, **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_freq = self.x_line_frequency
y_freq = self.y_line_frequency
x_lines1, x_lines2 = self.get_lines_parallel_to_axis(
x_axis, y_axis, x_freq,
self.faded_line_ratio,
)
y_lines1, y_lines2 = self.get_lines_parallel_to_axis(
y_axis, x_axis, y_freq,
self.faded_line_ratio,
)
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, ratio):
line = Line(axis1.get_start(), axis1.get_end())
dense_freq = (1 + ratio)
step = (1 / dense_freq) * freq
lines1 = VGroup()
lines2 = VGroup()
ranges = (
np.arange(0, axis2.x_max, step),
np.arange(0, axis2.x_min, -step),
)
for inputs in ranges:
for k, x in enumerate(inputs):
new_line = line.copy()
new_line.move_to(axis2.number_to_point(x))
if k % (1 + ratio) == 0:
lines1.add(new_line)
else:
lines2.add(new_line)
return lines1, lines2
def get_center_point(self):
return self.coords_to_point(0, 0)
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.coords_to_point(0, 0),
self.coords_to_point(*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
)
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):
x_numbers = self.get_x_axis().default_numbers_to_display()
y_numbers = self.get_y_axis().default_numbers_to_display()
y_numbers = [
complex(0, y) for y in y_numbers if y != 0
]
return [*x_numbers, *y_numbers]
def get_coordinate_labels(self, *numbers, **kwargs):
if len(numbers) == 0:
numbers = self.get_default_coordinate_values()
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 = merge_dicts_recursively(
kwargs,
{"number_config": {"unit": "i"}},
)
else:
axis = self.get_x_axis()
value = z.real
number_mob = axis.get_number_mobject(value, **kwargs)
self.coordinate_labels.add(number_mob)
return self.coordinate_labels
def add_coordinates(self, *numbers):
self.add(self.get_coordinate_labels(*numbers))
return self