def get_partial_points_array(self, points, a, b, resolution, axis):
if len(points) == 0:
return points
nu, nv = resolution[:2]
points = points.reshape(resolution)
max_index = resolution[axis] - 1
lower_index, lower_residue = integer_interpolate(0, max_index, a)
upper_index, upper_residue = integer_interpolate(0, max_index, b)
if axis == 0:
points[:lower_index] = interpolate(
points[lower_index],
points[lower_index + 1],
lower_residue,
)
points[upper_index + 1:] = interpolate(
points[upper_index],
points[upper_index + 1],
upper_residue,
)
else:
shape = (nu, 1, resolution[2])
points[:, :lower_index] = interpolate(
points[:, lower_index],
points[:, lower_index + 1],
lower_residue,
).reshape(shape)
points[:, upper_index + 1:] = interpolate(
points[:, upper_index],
points[:, upper_index + 1],
upper_residue,
).reshape(shape)
return points.reshape((nu * nv, *resolution[2:]))
def point_to_number(self, point: Sequence[float]) -> float:
"""Accepts a point with respect to the scene and returns
a float along the number line.
Parameters
----------
point
A sequence of values consisting of ``(x_coord, y_coord, z_coord)``.
Returns
-------
float
A float representing a value along the number line.
Examples
--------
>>> from manim import NumberLine
>>> number_line = NumberLine()
>>> number_line.point_to_number((0,0,0))
0.0
>>> number_line.point_to_number((1,0,0))
1.0
>>> number_line.point_to_number([[0.5,0,0],[1,0,0],[1.5,0,0]])
array([0.5, 1. , 1.5])
"""
point = np.asarray(point)
start, end = self.get_start_and_end()
unit_vect = normalize(end - start)
proportion = np.dot(point - start, unit_vect) / np.dot(
end - start, unit_vect)
return interpolate(self.x_min, self.x_max, proportion)
def point_to_number(self, point: Sequence[float]) -> float:
"""Accepts a point with respect to the scene and returns
a float along the number line.
Parameters
----------
point
A sequence of values consisting of ``(x_coord, y_coord, z_coord)``.
Returns
-------
float
A float representing a value along the number line.
"""
start, end = self.get_start_and_end()
unit_vect = normalize(end - start)
proportion = np.dot(point - start, unit_vect) / np.dot(
end - start, unit_vect)
return interpolate(self.x_min, self.x_max, proportion)
def number_to_point(self, number: float) -> np.ndarray:
"""Accepts a value along the number line and returns a point with
respect to the scene.
Parameters
----------
number
The value to be transformed into a coordinate.
Returns
-------
np.ndarray
A point with respect to the scene's coordinate system.
"""
number = self.scaling.inverse_function(number)
alpha = float(number - self.x_range[0]) / (self.x_range[1] -
self.x_range[0])
val = interpolate(self.get_start(), self.get_end(), alpha)
return val
def set_colors_by_radial_gradient(
self,
center=None,
radius=1,
inner_color=WHITE,
outer_color=BLACK,
):
start_rgba, end_rgba = list(
map(color_to_rgba, [inner_color, outer_color]))
if center is None:
center = self.get_center()
for mob in self.family_members_with_points():
distances = np.abs(self.points - center)
alphas = np.linalg.norm(distances, axis=1) / radius
mob.rgbas = np.array(
np.array([
interpolate(start_rgba, end_rgba, alpha)
for alpha in alphas
], ), )
return self
def number_to_point(self, number: float | np.ndarray) -> np.ndarray:
"""Accepts a value along the number line and returns a point with
respect to the scene.
Parameters
----------
number
The value to be transformed into a coordinate. Or a list of values.
Returns
-------
np.ndarray
A point with respect to the scene's coordinate system. Or a list of points.
Examples
--------
>>> from manim import NumberLine
>>> number_line = NumberLine()
>>> number_line.number_to_point(0)
array([0., 0., 0.])
>>> number_line.number_to_point(1)
array([1., 0., 0.])
>>> number_line.number_to_point([1,2,3])
array([[1., 0., 0.],
[2., 0., 0.],
[3., 0., 0.]])
"""
number = np.asarray(number)
scalar = number.ndim == 0
number = self.scaling.inverse_function(number)
alphas = (number - self.x_range[0]) / (self.x_range[1] -
self.x_range[0])
alphas = float(alphas) if scalar else np.vstack(alphas)
val = interpolate(self.get_start(), self.get_end(), alphas)
return val
def fade_to(self, color, alpha, family=True):
rgbas = interpolate(self.rgbas, color_to_rgba(color), alpha)
for mob in self.submobjects:
mob.fade_to(color, alpha, family)
self.set_rgba_array_direct(rgbas)
return self
def parameterized_function(alpha):
x = interpolate(x_min if x_min else x_axis.x_min,
x_max if x_max else x_axis.x_max, alpha)
y = f(x)
return coords_to_point(x, y)