"""Mobjects representing point clouds."""
from __future__ import annotations
__all__ = ["PMobject", "Mobject1D", "Mobject2D", "PGroup", "PointCloudDot", "Point"]
import numpy as np
from manim.mobject.opengl.opengl_compatibility import ConvertToOpenGL
from manim.mobject.opengl.opengl_point_cloud_mobject import OpenGLPMobject
from ...constants import *
from ...mobject.mobject import Mobject
from ...utils.bezier import interpolate
from ...utils.color import (
BLACK,
WHITE,
YELLOW,
ManimColor,
color_gradient,
color_to_rgba,
rgba_to_color,
)
from ...utils.iterables import stretch_array_to_length
[docs]class PMobject(Mobject, metaclass=ConvertToOpenGL):
"""A disc made of a cloud of Dots
Examples
--------
.. manim:: PMobjectExample
:save_last_frame:
class PMobjectExample(Scene):
def construct(self):
pG = PGroup() # This is just a collection of PMobject's
# As the scale factor increases, the number of points
# removed increases.
for sf in range(1, 9 + 1):
p = PointCloudDot(density=20, radius=1).thin_out(sf)
# PointCloudDot is a type of PMobject
# and can therefore be added to a PGroup
pG.add(p)
# This organizes all the shapes in a grid.
pG.arrange_in_grid()
self.add(pG)
"""
def __init__(self, stroke_width=DEFAULT_STROKE_WIDTH, **kwargs):
self.stroke_width = stroke_width
super().__init__(**kwargs)
[docs] def reset_points(self):
self.rgbas = np.zeros((0, 4))
self.points = np.zeros((0, 3))
return self
def get_array_attrs(self):
return super().get_array_attrs() + ["rgbas"]
[docs] def add_points(self, points, rgbas=None, color=None, alpha=1):
"""Add points.
Points must be a Nx3 numpy array.
Rgbas must be a Nx4 numpy array if it is not None.
"""
if not isinstance(points, np.ndarray):
points = np.array(points)
num_new_points = len(points)
self.points = np.append(self.points, points, axis=0)
if rgbas is None:
color = ManimColor(color) if color else self.color
rgbas = np.repeat([color_to_rgba(color, alpha)], num_new_points, axis=0)
elif len(rgbas) != len(points):
raise ValueError("points and rgbas must have same length")
self.rgbas = np.append(self.rgbas, rgbas, axis=0)
return self
[docs] def set_color(self, color=YELLOW, family=True):
rgba = color_to_rgba(color)
mobs = self.family_members_with_points() if family else [self]
for mob in mobs:
mob.rgbas[:, :] = rgba
self.color = color
return self
def get_stroke_width(self):
return self.stroke_width
def set_stroke_width(self, width, family=True):
mobs = self.family_members_with_points() if family else [self]
for mob in mobs:
mob.stroke_width = width
return self
[docs] def set_color_by_gradient(self, *colors):
self.rgbas = np.array(
list(map(color_to_rgba, color_gradient(*colors, len(self.points)))),
)
return self
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 match_colors(self, mobject):
Mobject.align_data(self, mobject)
self.rgbas = np.array(mobject.rgbas)
return self
def filter_out(self, condition):
for mob in self.family_members_with_points():
to_eliminate = ~np.apply_along_axis(condition, 1, mob.points)
mob.points = mob.points[to_eliminate]
mob.rgbas = mob.rgbas[to_eliminate]
return self
[docs] def thin_out(self, factor=5):
"""
Removes all but every nth point for n = factor
"""
for mob in self.family_members_with_points():
num_points = self.get_num_points()
mob.apply_over_attr_arrays(
lambda arr: arr[np.arange(0, num_points, factor)],
)
return self
[docs] def sort_points(self, function=lambda p: p[0]):
"""
Function is any map from R^3 to R
"""
for mob in self.family_members_with_points():
indices = np.argsort(np.apply_along_axis(function, 1, mob.points))
mob.apply_over_attr_arrays(lambda arr: arr[indices])
return self
def fade_to(self, color, alpha, family=True):
self.rgbas = interpolate(self.rgbas, color_to_rgba(color), alpha)
for mob in self.submobjects:
mob.fade_to(color, alpha, family)
return self
def get_all_rgbas(self):
return self.get_merged_array("rgbas")
def ingest_submobjects(self):
attrs = self.get_array_attrs()
arrays = list(map(self.get_merged_array, attrs))
for attr, array in zip(attrs, arrays):
setattr(self, attr, array)
self.submobjects = []
return self
[docs] def get_color(self):
return rgba_to_color(self.rgbas[0, :])
def point_from_proportion(self, alpha):
index = alpha * (self.get_num_points() - 1)
return self.points[index]
[docs] @staticmethod
def get_mobject_type_class():
return PMobject
# Alignment
def align_points_with_larger(self, larger_mobject):
assert isinstance(larger_mobject, PMobject)
self.apply_over_attr_arrays(
lambda a: stretch_array_to_length(a, larger_mobject.get_num_points()),
)
[docs] def get_point_mobject(self, center=None):
if center is None:
center = self.get_center()
return Point(center)
def interpolate_color(self, mobject1, mobject2, alpha):
self.rgbas = interpolate(mobject1.rgbas, mobject2.rgbas, alpha)
self.set_stroke_width(
interpolate(
mobject1.get_stroke_width(),
mobject2.get_stroke_width(),
alpha,
),
)
return self
def pointwise_become_partial(self, mobject, a, b):
lower_index, upper_index = (int(x * mobject.get_num_points()) for x in (a, b))
for attr in self.get_array_attrs():
full_array = getattr(mobject, attr)
partial_array = full_array[lower_index:upper_index]
setattr(self, attr, partial_array)
# TODO, Make the two implementations below non-redundant
[docs]class Mobject1D(PMobject, metaclass=ConvertToOpenGL):
def __init__(self, density=DEFAULT_POINT_DENSITY_1D, **kwargs):
self.density = density
self.epsilon = 1.0 / self.density
super().__init__(**kwargs)
def add_line(self, start, end, color=None):
start, end = list(map(np.array, [start, end]))
length = np.linalg.norm(end - start)
if length == 0:
points = [start]
else:
epsilon = self.epsilon / length
points = [interpolate(start, end, t) for t in np.arange(0, 1, epsilon)]
self.add_points(points, color=color)
[docs]class Mobject2D(PMobject, metaclass=ConvertToOpenGL):
def __init__(self, density=DEFAULT_POINT_DENSITY_2D, **kwargs):
self.density = density
self.epsilon = 1.0 / self.density
super().__init__(**kwargs)
[docs]class PGroup(PMobject):
"""A group for several point mobjects.
Examples
--------
.. manim:: PgroupExample
:save_last_frame:
class PgroupExample(Scene):
def construct(self):
p1 = PointCloudDot(radius=1, density=20, color=BLUE)
p1.move_to(4.5 * LEFT)
p2 = PointCloudDot()
p3 = PointCloudDot(radius=1.5, stroke_width=2.5, color=PINK)
p3.move_to(4.5 * RIGHT)
pList = PGroup(p1, p2, p3)
self.add(pList)
"""
def __init__(self, *pmobs, **kwargs):
if not all(isinstance(m, (PMobject, OpenGLPMobject)) for m in pmobs):
raise ValueError(
"All submobjects must be of type PMobject or OpenGLPMObject"
" if using the opengl renderer",
)
super().__init__(**kwargs)
self.add(*pmobs)
def fade_to(self, color, alpha, family=True):
if family:
for mob in self.submobjects:
mob.fade_to(color, alpha, family)
[docs]class PointCloudDot(Mobject1D):
"""A disc made of a cloud of dots.
Examples
--------
.. manim:: PointCloudDotExample
:save_last_frame:
class PointCloudDotExample(Scene):
def construct(self):
cloud_1 = PointCloudDot(color=RED)
cloud_2 = PointCloudDot(stroke_width=4, radius=1)
cloud_3 = PointCloudDot(density=15)
group = Group(cloud_1, cloud_2, cloud_3).arrange()
self.add(group)
.. manim:: PointCloudDotExample2
class PointCloudDotExample2(Scene):
def construct(self):
plane = ComplexPlane()
cloud = PointCloudDot(color=RED)
self.add(
plane, cloud
)
self.wait()
self.play(
cloud.animate.apply_complex_function(lambda z: np.exp(z))
)
"""
def __init__(
self,
center=ORIGIN,
radius=2.0,
stroke_width=2,
density=DEFAULT_POINT_DENSITY_1D,
color=YELLOW,
**kwargs,
):
self.radius = radius
self.epsilon = 1.0 / density
super().__init__(
stroke_width=stroke_width, density=density, color=color, **kwargs
)
self.shift(center)
def init_points(self):
self.reset_points()
self.generate_points()
[docs] def generate_points(self):
self.add_points(
[
r * (np.cos(theta) * RIGHT + np.sin(theta) * UP)
for r in np.arange(self.epsilon, self.radius, self.epsilon)
# Num is equal to int(stop - start)/ (step + 1) reformulated.
for theta in np.linspace(
0,
2 * np.pi,
num=int(2 * np.pi * (r + self.epsilon) / self.epsilon),
)
],
)
[docs]class Point(PMobject):
"""A mobject representing a point.
Examples
--------
.. manim:: ExamplePoint
:save_last_frame:
class ExamplePoint(Scene):
def construct(self):
colorList = [RED, GREEN, BLUE, YELLOW]
for i in range(200):
point = Point(location=[0.63 * np.random.randint(-4, 4), 0.37 * np.random.randint(-4, 4), 0], color=np.random.choice(colorList))
self.add(point)
for i in range(200):
point = Point(location=[0.37 * np.random.randint(-4, 4), 0.63 * np.random.randint(-4, 4), 0], color=np.random.choice(colorList))
self.add(point)
self.add(point)
"""
def __init__(self, location=ORIGIN, color=BLACK, **kwargs):
self.location = location
super().__init__(color=color, **kwargs)
def init_points(self):
self.reset_points()
self.generate_points()
self.set_points([self.location])
[docs] def generate_points(self):
self.add_points([self.location])