mirror of
https://github.com/3b1b/manim.git
synced 2025-04-13 09:47:07 +00:00
575 lines
18 KiB
Python
575 lines
18 KiB
Python
import numpy as np
|
|
import itertools as it
|
|
import operator as op
|
|
import os
|
|
from PIL import Image
|
|
from random import random
|
|
from copy import deepcopy
|
|
from colour import Color
|
|
|
|
import displayer as disp
|
|
from helpers import *
|
|
|
|
|
|
class Mobject(object):
|
|
"""
|
|
Mathematical Object
|
|
"""
|
|
#Number of numbers used to describe a point (3 for pos, 3 for normal vector)
|
|
DEFAULT_CONFIG = {
|
|
"color" : WHITE,
|
|
"point_thickness" : DEFAULT_POINT_THICKNESS,
|
|
"name" : None,
|
|
}
|
|
DIM = 3
|
|
def __init__(self, *sub_mobjects, **kwargs):
|
|
digest_config(self, kwargs)
|
|
self.sub_mobjects = list(sub_mobjects)
|
|
self.color = Color(self.color)
|
|
if self.name is None:
|
|
self.name = self.__class__.__name__
|
|
self.has_normals = hasattr(self, 'unit_normal')
|
|
self.init_points()
|
|
self.generate_points()
|
|
if self.has_normals:
|
|
self.unit_normals = np.apply_along_axis(
|
|
self.unit_normal,
|
|
1,
|
|
self.points,
|
|
)
|
|
|
|
def init_points(self):
|
|
for attr in self.get_array_attrs():
|
|
setattr(self, attr, np.zeros((0, 3)))
|
|
|
|
def __str__(self):
|
|
return self.name
|
|
|
|
def add_points(self, points, rgbs = None, color = None):
|
|
"""
|
|
points must be a Nx3 numpy array, as must rgbs if it is not None
|
|
"""
|
|
if not isinstance(points, np.ndarray):
|
|
points = np.array(points)
|
|
num_new_points = points.shape[0]
|
|
self.points = np.append(self.points, points, axis = 0)
|
|
if rgbs is None:
|
|
color = Color(color) if color else self.color
|
|
rgbs = np.array([color.get_rgb()] * num_new_points)
|
|
elif rgbs.shape != points.shape:
|
|
raise Exception("points and rgbs must have same shape")
|
|
self.rgbs = np.append(self.rgbs, rgbs, axis = 0)
|
|
if self.has_normals:
|
|
self.unit_normals = np.append(
|
|
self.unit_normals,
|
|
np.apply_along_axis(self.unit_normal, 1, points),
|
|
axis = 0
|
|
)
|
|
return self
|
|
|
|
def add(self, *mobjects):
|
|
self.sub_mobjects = list_update(self.sub_mobjects, mobjects)
|
|
return self
|
|
|
|
def get_array_attrs(self):
|
|
result = ["points", "rgbs"]
|
|
if self.has_normals:
|
|
result.append("unit_normals")
|
|
return result
|
|
|
|
def digest_mobject_attrs(self):
|
|
"""
|
|
Ensures all attributes which are mobjects are included
|
|
in the sub_mobjects list.
|
|
"""
|
|
mobject_attrs = filter(
|
|
lambda x : isinstance(x, Mobject),
|
|
self.__dict__.values()
|
|
)
|
|
self.sub_mobjects = list_update(self.sub_mobjects, mobject_attrs)
|
|
return self
|
|
|
|
|
|
def apply_over_attr_arrays(self, func):
|
|
for attr in self.get_array_attrs():
|
|
setattr(self, attr, func(getattr(self, attr)))
|
|
return self
|
|
|
|
def show(self):
|
|
Image.fromarray(disp.paint_mobject(self)).show()
|
|
|
|
def save_image(self, name = None):
|
|
Image.fromarray(disp.paint_mobject(self)).save(
|
|
os.path.join(MOVIE_DIR, (name or str(self)) + ".png")
|
|
)
|
|
|
|
def copy(self):
|
|
return deepcopy(self)
|
|
|
|
#### Fundamental operations ######
|
|
|
|
def shift(self, *vectors):
|
|
total_vector = reduce(op.add, vectors)
|
|
for mob in self.nonempty_family_members():
|
|
mob.points += total_vector
|
|
return self
|
|
|
|
def scale(self, scale_factor):
|
|
for mob in self.nonempty_family_members():
|
|
mob.points *= scale_factor
|
|
return self
|
|
|
|
def rotate(self, angle, axis = OUT, axes = []):
|
|
if len(axes) == 0:
|
|
axes = [axis]
|
|
rot_matrix = np.identity(self.DIM)
|
|
for axis in axes:
|
|
rot_matrix = np.dot(rot_matrix, rotation_matrix(angle, axis))
|
|
t_rot_matrix = np.transpose(rot_matrix)
|
|
for mob in self.nonempty_family_members():
|
|
mob.points = np.dot(mob.points, t_rot_matrix)
|
|
if mob.has_normals:
|
|
mob.unit_normals = np.dot(mob.unit_normals, t_rot_matrix)
|
|
return self
|
|
|
|
def stretch(self, factor, dim):
|
|
for mob in self.nonempty_family_members():
|
|
mob.points[:,dim] *= factor
|
|
return self
|
|
|
|
def apply_function(self, function):
|
|
for mob in self.nonempty_family_members():
|
|
mob.points = np.apply_along_axis(function, 1, mob.points)
|
|
return self
|
|
|
|
def wag(self, direction = RIGHT, axis = DOWN, wag_factor = 1.0):
|
|
for mob in self.nonempty_family_members():
|
|
alphas = np.dot(mob.points, np.transpose(axis))
|
|
alphas -= min(alphas)
|
|
alphas /= max(alphas)
|
|
alphas = alphas**wag_factor
|
|
mob.points += np.dot(
|
|
alphas.reshape((len(alphas), 1)),
|
|
np.array(direction).reshape((1, mob.DIM))
|
|
)
|
|
return self
|
|
|
|
def highlight(self, color = YELLOW_C, condition = None):
|
|
"""
|
|
Condition is function which takes in one arguments, (x, y, z).
|
|
"""
|
|
rgb = Color(color).get_rgb()
|
|
for mob in self.nonempty_family_members():
|
|
if condition:
|
|
to_change = np.apply_along_axis(condition, 1, mob.points)
|
|
mob.rgbs[to_change, :] = rgb
|
|
else:
|
|
mob.rgbs[:,:] = rgb
|
|
return self
|
|
|
|
def gradient_highlight(self, start_color, end_color):
|
|
start_rgb, end_rgb = [
|
|
np.array(Color(color).get_rgb())
|
|
for color in start_color, end_color
|
|
]
|
|
for mob in self.nonempty_family_members():
|
|
num_points = mob.get_num_points()
|
|
mob.rgbs = np.array([
|
|
interpolate(start_rgb, end_rgb, alpha)
|
|
for alpha in np.arange(num_points)/float(num_points)
|
|
])
|
|
return self
|
|
|
|
def match_colors(self, mobject):
|
|
Mobject.align_data(self, mobject)
|
|
self.rgbs = np.array(mobject.rgbs)
|
|
return self
|
|
|
|
def filter_out(self, condition):
|
|
for mob in self.nonempty_family_members():
|
|
to_eliminate = ~np.apply_along_axis(condition, 1, mob.points)
|
|
mob.points = mob.points[to_eliminate]
|
|
mob.rgbs = mob.rgbs[to_eliminate]
|
|
return self
|
|
|
|
def thin_out(self, factor = 5):
|
|
"""
|
|
Removes all but every nth point for n = factor
|
|
"""
|
|
for mob in self.nonempty_family_members():
|
|
num_points = self.get_num_points()
|
|
mob.apply_over_attr_arrays(
|
|
lambda arr : arr[
|
|
np.arange(0, num_points, factor)
|
|
]
|
|
)
|
|
return self
|
|
|
|
def sort_points(self, function = lambda p : p[0]):
|
|
"""
|
|
function is any map from R^3 to R
|
|
"""
|
|
for mob in self.nonempty_family_members():
|
|
indices = np.argsort(
|
|
np.apply_along_axis(function, 1, mob.points)
|
|
)
|
|
mob.apply_over_attr_arrays(lambda arr : arr[indices])
|
|
return self
|
|
|
|
def reverse_points(self):
|
|
for mob in self.nonempty_family_members():
|
|
mob.apply_over_attr_arrays(
|
|
lambda arr : np.array(list(reversed(arr)))
|
|
)
|
|
return self
|
|
|
|
|
|
def repeat(self, count):
|
|
"""
|
|
This can make transition animations nicer
|
|
"""
|
|
def repeat_array(array):
|
|
return reduce(
|
|
lambda a1, a2 : np.append(a1, a2, axis = 0),
|
|
[array]*count
|
|
)
|
|
for mob in self.nonempty_family_members():
|
|
mob.apply_over_attr_arrays(repeat_array)
|
|
return self
|
|
|
|
#### In place operations ######
|
|
|
|
def do_in_place(self, method, *args, **kwargs):
|
|
center = self.get_center()
|
|
self.shift(-center)
|
|
method(*args, **kwargs)
|
|
self.shift(center)
|
|
return self
|
|
|
|
def rotate_in_place(self, angle, axis = OUT, axes = []):
|
|
self.do_in_place(self.rotate, angle, axis, axes)
|
|
return self
|
|
|
|
def scale_in_place(self, scale_factor):
|
|
self.do_in_place(self.scale, scale_factor)
|
|
return self
|
|
|
|
def pose_at_angle(self):
|
|
self.rotate_in_place(np.pi / 7, RIGHT+UP)
|
|
return self
|
|
|
|
def center(self):
|
|
self.shift(-self.get_center())
|
|
return self
|
|
|
|
def align_on_border(self, direction, buff = DEFAULT_MOBJECT_TO_EDGE_BUFFER):
|
|
"""
|
|
Direction just needs to be a vector pointing towards side or
|
|
corner in the 2d plane.
|
|
"""
|
|
target_point = np.sign(direction) * (SPACE_WIDTH, SPACE_HEIGHT, 0)
|
|
anchor_point = self.get_critical_point(direction)
|
|
shift_val = target_point - anchor_point - buff * np.array(direction)
|
|
shift_val = shift_val * abs(np.sign(direction))
|
|
self.shift(shift_val)
|
|
return self
|
|
|
|
def to_corner(self, corner = LEFT+DOWN, buff = DEFAULT_MOBJECT_TO_EDGE_BUFFER):
|
|
return self.align_on_border(corner, buff)
|
|
|
|
def to_edge(self, edge = LEFT, buff = DEFAULT_MOBJECT_TO_EDGE_BUFFER):
|
|
return self.align_on_border(edge, buff)
|
|
|
|
def next_to(self, mobject,
|
|
direction = RIGHT,
|
|
buff = DEFAULT_MOBJECT_TO_MOBJECT_BUFFER,
|
|
aligned_edge = ORIGIN):
|
|
anchor_point = self.get_critical_point(aligned_edge-direction)
|
|
target_point = mobject.get_critical_point(aligned_edge+direction)
|
|
self.shift(target_point - anchor_point + buff*direction)
|
|
return self
|
|
|
|
def stretch_to_fit(self, length, dim):
|
|
old_length = self.length_over_dim(dim)
|
|
self.do_in_place(self.stretch, length/old_length, dim)
|
|
return self
|
|
|
|
def stretch_to_fit_width(self, width):
|
|
return self.stretch_to_fit(width, 0)
|
|
|
|
def stretch_to_fit_height(self, height):
|
|
return self.stretch_to_fit(height, 1)
|
|
|
|
def scale_to_fit_width(self, width):
|
|
return self.scale(width/self.get_width())
|
|
|
|
def scale_to_fit_height(self, height):
|
|
return self.scale(height/self.get_height())
|
|
|
|
def replace(self, mobject, stretch = False):
|
|
if mobject.get_num_points() == 0:
|
|
raise Warning("Attempting to replace mobject with no points")
|
|
return self
|
|
if stretch:
|
|
self.stretch_to_fit_width(mobject.get_width())
|
|
self.stretch_to_fit_height(mobject.get_height())
|
|
else:
|
|
self.scale(mobject.get_width()/self.get_width())
|
|
self.center().shift(mobject.get_center())
|
|
return self
|
|
|
|
def apply_complex_function(self, function):
|
|
return self.apply_function(
|
|
lambda (x, y, z) : complex_to_R3(function(complex(x, y)))
|
|
)
|
|
|
|
def set_color(self, color):
|
|
self.highlight(color)
|
|
self.color = Color(color)
|
|
return self
|
|
|
|
def to_original_color(self):
|
|
self.highlight(self.color)
|
|
return self
|
|
|
|
def fade_to(self, color, alpha):
|
|
self.rgbs = interpolate(self.rgbs, np.array(Color(color).rgb), alpha)
|
|
for mob in self.sub_mobjects:
|
|
mob.fade_to(color, alpha)
|
|
return self
|
|
|
|
def fade(self, darkness = 0.5):
|
|
self.fade_to(BLACK, darkness)
|
|
return self
|
|
|
|
def reduce_across_dimension(self, points_func, reduce_func, dim):
|
|
try:
|
|
values = [points_func(self.points[:, dim])]
|
|
except:
|
|
values = []
|
|
values += [
|
|
mob.reduce_across_dimension(points_func, reduce_func, dim)
|
|
for mob in self.sub_mobjects
|
|
]
|
|
try:
|
|
return reduce_func(values)
|
|
except:
|
|
return 0
|
|
|
|
def get_merged_array(self, array_attr):
|
|
result = np.zeros((0, self.DIM))
|
|
for mob in self.nonempty_family_members():
|
|
result = np.append(result, getattr(mob, array_attr), 0)
|
|
return result
|
|
|
|
def get_all_points(self):
|
|
return self.get_merged_array("points")
|
|
|
|
def get_all_rgbs(self):
|
|
return self.get_merged_array("rgbs")
|
|
|
|
def ingest_sub_mobjects(self):
|
|
attrs = self.get_array_attrs()
|
|
arrays = map(self.get_merged_array, attrs)
|
|
for attr, array in zip(attrs, arrays):
|
|
setattr(self, attr, array)
|
|
self.sub_mobjects = []
|
|
return self
|
|
|
|
def split(self):
|
|
result = [self] if len(self.points) > 0 else []
|
|
return result + self.sub_mobjects
|
|
|
|
def submobject_family(self):
|
|
sub_families = map(Mobject.submobject_family, self.sub_mobjects)
|
|
all_mobjects = [self] + reduce(op.add, sub_families, [])
|
|
return remove_list_redundancies(all_mobjects)
|
|
|
|
def nonempty_family_members(self):
|
|
return filter(
|
|
lambda m : m.get_num_points() > 0,
|
|
self.submobject_family()
|
|
)
|
|
|
|
### Getters ###
|
|
|
|
def get_num_points(self, including_submobjects = False):
|
|
if including_submobjects:
|
|
return self.reduce_across_dimension(len, sum, 0)
|
|
else:
|
|
return len(self.points)
|
|
|
|
def get_critical_point(self, direction):
|
|
result = np.zeros(self.DIM)
|
|
for dim in [0, 1]:
|
|
if direction[dim] <= 0:
|
|
min_point = self.reduce_across_dimension(np.min, np.min, dim)
|
|
if direction[dim] >= 0:
|
|
max_point = self.reduce_across_dimension(np.max, np.max, dim)
|
|
|
|
if direction[dim] == 0:
|
|
result[dim] = (max_point+min_point)/2
|
|
elif direction[dim] < 0:
|
|
result[dim] = min_point
|
|
else:
|
|
result[dim] = max_point
|
|
return result
|
|
|
|
# Pseudonyms for more general get_critical_point method
|
|
def get_edge_center(self, direction):
|
|
return self.get_critical_point(direction)
|
|
|
|
def get_corner(self, direction):
|
|
return self.get_critical_point(direction)
|
|
|
|
def get_center(self):
|
|
return self.get_critical_point(np.zeros(self.DIM))
|
|
|
|
def get_center_of_mass(self):
|
|
return np.apply_along_axis(np.mean, 0, self.get_all_points())
|
|
|
|
def get_boundary_point(self, direction):
|
|
all_points = self.get_all_points()
|
|
return all_points[np.argmax(np.dot(all_points, direction))]
|
|
|
|
def get_top(self):
|
|
return self.get_edge_center(UP)
|
|
|
|
def get_bottom(self):
|
|
return self.get_edge_center(DOWN)
|
|
|
|
def get_right(self):
|
|
return self.get_edge_center(RIGHT)
|
|
|
|
def get_left(self):
|
|
return self.get_edge_center(LEFT)
|
|
|
|
def length_over_dim(self, dim):
|
|
return (
|
|
self.reduce_across_dimension(np.max, np.max, dim) -
|
|
self.reduce_across_dimension(np.min, np.min, dim)
|
|
)
|
|
|
|
def get_width(self):
|
|
return self.length_over_dim(0)
|
|
|
|
def get_height(self):
|
|
return self.length_over_dim(1)
|
|
|
|
|
|
def get_color(self):
|
|
color = Color()
|
|
color.set_rgb(self.rgbs[0, :])
|
|
return color
|
|
|
|
### Stuff subclasses should deal with ###
|
|
def generate_points(self):
|
|
#Typically implemented in subclass, unless purposefully left blank
|
|
pass
|
|
|
|
@staticmethod
|
|
def align_data(mobject1, mobject2):
|
|
count1 = len(mobject1.points)
|
|
count2 = len(mobject2.points)
|
|
if count1 != count2:
|
|
if count1 < count2:
|
|
smaller = mobject1
|
|
target_size = count2
|
|
else:
|
|
smaller = mobject2
|
|
target_size = count1
|
|
if len(smaller.points) == 0:
|
|
smaller.add_points(
|
|
[np.zeros(smaller.DIM)],
|
|
color = BLACK
|
|
)
|
|
smaller.apply_over_attr_arrays(
|
|
lambda a : streth_array_to_length(a, target_size)
|
|
)
|
|
#Recurse
|
|
diff = len(mobject1.sub_mobjects) - len(mobject2.sub_mobjects)
|
|
|
|
if diff < 0:
|
|
larger, smaller = mobject2, mobject1
|
|
elif diff > 0:
|
|
larger, smaller = mobject1, mobject2
|
|
if diff != 0:
|
|
for sub_mob in larger.sub_mobjects[-abs(diff):]:
|
|
smaller.add(Point(sub_mob.get_center()))
|
|
for m1, m2 in zip(mobject1.sub_mobjects, mobject2.sub_mobjects):
|
|
Mobject.align_data(m1, m2)
|
|
|
|
def interpolate(self, mobject1, mobject2, alpha):
|
|
"""
|
|
Turns target_mobject into an interpolation between mobject1
|
|
and mobject2.
|
|
"""
|
|
#TODO
|
|
Mobject.align_data(mobject1, mobject2)
|
|
for attr in self.get_array_attrs():
|
|
setattr(target_mobject, attr, interpolate(
|
|
getattr(mobject1, attr),
|
|
getattr(mobject2, attr),
|
|
alpha))
|
|
|
|
|
|
class Point(Mobject):
|
|
DEFAULT_CONFIG = {
|
|
"color" : BLACK,
|
|
}
|
|
def __init__(self, location = ORIGIN, **kwargs):
|
|
digest_locals(self)
|
|
Mobject.__init__(self, **kwargs)
|
|
|
|
def generate_points(self):
|
|
self.add_points([self.location])
|
|
|
|
#TODO, Make the two implementations bellow non-redundant
|
|
class Mobject1D(Mobject):
|
|
DEFAULT_CONFIG = {
|
|
"density" : DEFAULT_POINT_DENSITY_1D,
|
|
}
|
|
def __init__(self, **kwargs):
|
|
digest_config(self, kwargs)
|
|
self.epsilon = 1.0 / self.density
|
|
Mobject.__init__(self, **kwargs)
|
|
|
|
|
|
def add_line(self, start, end, color = None):
|
|
start, end = 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)
|
|
|
|
class Mobject2D(Mobject):
|
|
DEFAULT_CONFIG = {
|
|
"density" : DEFAULT_POINT_DENSITY_2D,
|
|
}
|
|
def __init__(self, **kwargs):
|
|
digest_config(self, kwargs)
|
|
self.epsilon = 1.0 / self.density
|
|
Mobject.__init__(self, **kwargs)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|