3b1b-manim/manimlib/mobject/mobject.py

import copy
import itertools as it
import random
import sys
import moderngl
from functools import wraps

import numpy as np

from manimlib.constants import *
from manimlib.utils.color import color_gradient
from manimlib.utils.color import get_colormap_list
from manimlib.utils.color import rgb_to_hex
from manimlib.utils.color import color_to_rgb
from manimlib.utils.config_ops import digest_config
from manimlib.utils.iterables import batch_by_property
from manimlib.utils.iterables import list_update
from manimlib.utils.iterables import resize_array
from manimlib.utils.iterables import resize_preserving_order
from manimlib.utils.iterables import resize_with_interpolation
from manimlib.utils.iterables import make_even
from manimlib.utils.iterables import listify
from manimlib.utils.bezier import interpolate
from manimlib.utils.bezier import integer_interpolate
from manimlib.utils.paths import straight_path
from manimlib.utils.simple_functions import get_parameters
from manimlib.utils.space_ops import angle_of_vector
from manimlib.utils.space_ops import get_norm
from manimlib.utils.space_ops import rotation_matrix_transpose
from manimlib.shader_wrapper import ShaderWrapper
from manimlib.shader_wrapper import get_colormap_code
from manimlib.event_handler import EVENT_DISPATCHER
from manimlib.event_handler.event_listner import EventListner
from manimlib.event_handler.event_type import EventType


class Mobject(object):
    """
    Mathematical Object
    """
    CONFIG = {
        "color": WHITE,
        "opacity": 1,
        "dim": 3,  # TODO, get rid of this
        # Lighting parameters
        # Positive gloss up to 1 makes it reflect the light.
        "gloss": 0.0,
        # Positive shadow up to 1 makes a side opposite the light darker
        "shadow": 0.0,
        # For shaders
        "shader_folder": "",
        "render_primitive": moderngl.TRIANGLE_STRIP,
        "texture_paths": None,
        "depth_test": False,
        # If true, the mobject will not get rotated according to camera position
        "is_fixed_in_frame": False,
        # Must match in attributes of vert shader
        "shader_dtype": [
            ('point', np.float32, (3,)),
        ]
    }

    def __init__(self, **kwargs):
        digest_config(self, kwargs)
        self.submobjects = []
        self.parents = []
        self.family = [self]
        self.locked_data_keys = set()
        self.needs_new_bounding_box = True

        self.init_data()
        self.init_uniforms()
        self.init_updaters()
        self.init_event_listners()
        self.init_points()
        self.init_colors()
        self.init_shader_data()

        if self.depth_test:
            self.apply_depth_test()

    def __str__(self):
        return self.__class__.__name__

    def init_data(self):
        self.data = {
            "points": np.zeros((0, 3)),
            "bounding_box": np.zeros((3, 3)),
            "rgbas": np.zeros((1, 4)),
        }

    def init_uniforms(self):
        self.uniforms = {
            "is_fixed_in_frame": float(self.is_fixed_in_frame),
            "gloss": self.gloss,
            "shadow": self.shadow,
        }

    def init_colors(self):
        self.set_color(self.color, self.opacity)

    def init_points(self):
        # Typically implemented in subclass, unlpess purposefully left blank
        pass

    def set_data(self, data):
        for key in data:
            self.data[key] = data[key].copy()
        return self

    def set_uniforms(self, uniforms):
        for key in uniforms:
            self.uniforms[key] = uniforms[key]  # Copy?
        return self

    @property
    def animate(self):
        # Borrowed from https://github.com/ManimCommunity/manim/
        return _AnimationBuilder(self)

    # Only these methods should directly affect points

    def resize_points(self, new_length, resize_func=resize_array):
        if new_length != len(self.data["points"]):
            self.data["points"] = resize_func(self.data["points"], new_length)
        self.refresh_bounding_box()
        return self

    def set_points(self, points):
        if len(points) == len(self.data["points"]):
            self.data["points"][:] = points
        elif isinstance(points, np.ndarray):
            self.data["points"] = points.copy()
        else:
            self.data["points"] = np.array(points)
        self.refresh_bounding_box()
        return self

    def append_points(self, new_points):
        self.data["points"] = np.vstack([self.data["points"], new_points])
        self.refresh_bounding_box()
        return self

    def reverse_points(self):
        for mob in self.get_family():
            for key in mob.data:
                mob.data[key] = mob.data[key][::-1]
        return self

    def apply_points_function(self, func, about_point=None, about_edge=ORIGIN, works_on_bounding_box=False):
        if about_point is None and about_edge is not None:
            about_point = self.get_bounding_box_point(about_edge)

        for mob in self.get_family():
            arrs = []
            if mob.has_points():
                arrs.append(mob.get_points())
            if works_on_bounding_box:
                arrs.append(mob.get_bounding_box())

            for arr in arrs:
                if about_point is None:
                    arr[:] = func(arr)
                else:
                    arr[:] = func(arr - about_point) + about_point

        if not works_on_bounding_box:
            self.refresh_bounding_box(recurse_down=True)
        else:
            for parent in self.parents:
                parent.refresh_bounding_box()
        return self

    # Others related to points

    def match_points(self, mobject):
        self.set_points(mobject.get_points())
        return self

    def get_points(self):
        return self.data["points"]

    def clear_points(self):
        self.resize_points(0)

    def get_num_points(self):
        return len(self.data["points"])

    def get_all_points(self):
        if self.submobjects:
            return np.vstack([sm.get_points() for sm in self.get_family()])
        else:
            return self.get_points()

    def has_points(self):
        return self.get_num_points() > 0

    def get_bounding_box(self):
        if self.needs_new_bounding_box:
            self.data["bounding_box"] = self.compute_bounding_box()
            self.needs_new_bounding_box = False
        return self.data["bounding_box"]

    def compute_bounding_box(self):
        all_points = np.vstack([
            self.get_points(),
            *(
                mob.get_bounding_box()
                for mob in self.get_family()[1:]
                if mob.has_points()
            )
        ])
        if len(all_points) == 0:
            return np.zeros((3, self.dim))
        else:
            # Lower left and upper right corners
            mins = all_points.min(0)
            maxs = all_points.max(0)
            mids = (mins + maxs) / 2
            return np.array([mins, mids, maxs])

    def refresh_bounding_box(self, recurse_down=False, recurse_up=True):
        for mob in self.get_family(recurse_down):
            mob.needs_new_bounding_box = True
        if recurse_up:
            for parent in self.parents:
                parent.refresh_bounding_box()
        return self

    def is_point_touching(self, point, buff=MED_SMALL_BUFF):
        bb = self.get_bounding_box()
        mins = (bb[0] - buff)
        maxs = (bb[2] + buff)
        return (point >= mins).all() and (point <= maxs).all()

    # Family matters

    def __getitem__(self, value):
        if isinstance(value, slice):
            GroupClass = self.get_group_class()
            return GroupClass(*self.split().__getitem__(value))
        return self.split().__getitem__(value)

    def __iter__(self):
        return iter(self.split())

    def __len__(self):
        return len(self.split())

    def split(self):
        return self.submobjects

    def assemble_family(self):
        sub_families = (sm.get_family() for sm in self.submobjects)
        self.family = [self, *it.chain(*sub_families)]
        self.refresh_has_updater_status()
        self.refresh_bounding_box()
        for parent in self.parents:
            parent.assemble_family()
        return self

    def get_family(self, recurse=True):
        if recurse:
            return self.family
        else:
            return [self]

    def family_members_with_points(self):
        return [m for m in self.get_family() if m.has_points()]

    def add(self, *mobjects):
        if self in mobjects:
            raise Exception("Mobject cannot contain self")
        for mobject in mobjects:
            if mobject not in self.submobjects:
                self.submobjects.append(mobject)
            if self not in mobject.parents:
                mobject.parents.append(self)
        self.assemble_family()
        return self

    def remove(self, *mobjects):
        for mobject in mobjects:
            if mobject in self.submobjects:
                self.submobjects.remove(mobject)
            if self in mobject.parents:
                mobject.parents.remove(self)
        self.assemble_family()
        return self

    def add_to_back(self, *mobjects):
        self.set_submobjects(list_update(mobjects, self.submobjects))
        return self

    def replace_submobject(self, index, new_submob):
        old_submob = self.submobjects[index]
        if self in old_submob.parents:
            old_submob.parents.remove(self)
        self.submobjects[index] = new_submob
        self.assemble_family()
        return self

    def set_submobjects(self, submobject_list):
        self.remove(*self.submobjects)
        self.add(*submobject_list)
        return self

    def digest_mobject_attrs(self):
        """
        Ensures all attributes which are mobjects are included
        in the submobjects list.
        """
        mobject_attrs = [x for x in list(self.__dict__.values()) if isinstance(x, Mobject)]
        self.set_submobjects(list_update(self.submobjects, mobject_attrs))
        return self

    # Submobject organization

    def arrange(self, direction=RIGHT, center=True, **kwargs):
        for m1, m2 in zip(self.submobjects, self.submobjects[1:]):
            m2.next_to(m1, direction, **kwargs)
        if center:
            self.center()
        return self

    def arrange_in_grid(self, n_rows=None, n_cols=None,
                        buff=None,
                        h_buff=None,
                        v_buff=None,
                        buff_ratio=None,
                        h_buff_ratio=0.5,
                        v_buff_ratio=0.5,
                        aligned_edge=ORIGIN,
                        fill_rows_first=True):
        submobs = self.submobjects
        if n_rows is None and n_cols is None:
            n_rows = int(np.sqrt(len(submobs)))
        if n_rows is None:
            n_rows = len(submobs) // n_cols
        if n_cols is None:
            n_cols = len(submobs) // n_rows

        if buff is not None:
            h_buff = buff
            v_buff = buff
        else:
            if buff_ratio is not None:
                v_buff_ratio = buff_ratio
                h_buff_ratio = buff_ratio
            if h_buff is None:
                h_buff = h_buff_ratio * self[0].get_width()
            if v_buff is None:
                v_buff = v_buff_ratio * self[0].get_height()

        x_unit = h_buff + max([sm.get_width() for sm in submobs])
        y_unit = v_buff + max([sm.get_height() for sm in submobs])

        for index, sm in enumerate(submobs):
            if fill_rows_first:
                x, y = index % n_cols, index // n_cols
            else:
                x, y = index // n_rows, index % n_rows
            sm.move_to(ORIGIN, aligned_edge)
            sm.shift(x * x_unit * RIGHT + y * y_unit * DOWN)
        self.center()
        return self

    def get_grid(self, n_rows, n_cols, height=None, **kwargs):
        """
        Returns a new mobject containing multiple copies of this one
        arranged in a grid
        """
        grid = self.get_group_class()(
            *(self.copy() for n in range(n_rows * n_cols))
        )
        grid.arrange_in_grid(n_rows, n_cols, **kwargs)
        if height is not None:
            grid.set_height(height)
        return grid

    def sort(self, point_to_num_func=lambda p: p[0], submob_func=None):
        if submob_func is not None:
            self.submobjects.sort(key=submob_func)
        else:
            self.submobjects.sort(key=lambda m: point_to_num_func(m.get_center()))
        return self

    def shuffle(self, recurse=False):
        if recurse:
            for submob in self.submobjects:
                submob.shuffle(recurse=True)
        random.shuffle(self.submobjects)
        return self

    # Copying

    def copy(self):
        # TODO, either justify reason for shallow copy, or
        # remove this redundancy everywhere
        # return self.deepcopy()

        parents = self.parents
        self.parents = []
        copy_mobject = copy.copy(self)
        self.parents = parents

        copy_mobject.data = dict(self.data)
        for key in self.data:
            copy_mobject.data[key] = self.data[key].copy()

        # TODO, are uniforms ever numpy arrays?
        copy_mobject.uniforms = dict(self.uniforms)

        copy_mobject.submobjects = []
        copy_mobject.add(*[sm.copy() for sm in self.submobjects])
        copy_mobject.match_updaters(self)

        copy_mobject.needs_new_bounding_box = self.needs_new_bounding_box

        # Make sure any mobject or numpy array attributes are copied
        family = self.get_family()
        for attr, value in list(self.__dict__.items()):
            if isinstance(value, Mobject) and value in family and value is not self:
                setattr(copy_mobject, attr, value.copy())
            if isinstance(value, np.ndarray):
                setattr(copy_mobject, attr, value.copy())
            if isinstance(value, ShaderWrapper):
                setattr(copy_mobject, attr, value.copy())
        return copy_mobject

    def deepcopy(self):
        parents = self.parents
        self.parents = []
        result = copy.deepcopy(self)
        self.parents = parents
        return result

    def generate_target(self, use_deepcopy=False):
        self.target = None  # Prevent exponential explosion
        if use_deepcopy:
            self.target = self.deepcopy()
        else:
            self.target = self.copy()
        return self.target

    def save_state(self, use_deepcopy=False):
        if hasattr(self, "saved_state"):
            # Prevent exponential growth of data
            self.saved_state = None
        if use_deepcopy:
            self.saved_state = self.deepcopy()
        else:
            self.saved_state = self.copy()
        return self

    def restore(self):
        if not hasattr(self, "saved_state") or self.save_state is None:
            raise Exception("Trying to restore without having saved")
        self.become(self.saved_state)
        return self

    # Updating

    def init_updaters(self):
        self.time_based_updaters = []
        self.non_time_updaters = []
        self.has_updaters = False
        self.updating_suspended = False

    def update(self, dt=0, recurse=True):
        if not self.has_updaters or self.updating_suspended:
            return self
        for updater in self.time_based_updaters:
            updater(self, dt)
        for updater in self.non_time_updaters:
            updater(self)
        if recurse:
            for submob in self.submobjects:
                submob.update(dt, recurse)
        return self

    def get_time_based_updaters(self):
        return self.time_based_updaters

    def has_time_based_updater(self):
        return len(self.time_based_updaters) > 0

    def get_updaters(self):
        return self.time_based_updaters + self.non_time_updaters

    def get_family_updaters(self):
        return list(it.chain(*[sm.get_updaters() for sm in self.get_family()]))

    def add_updater(self, update_function, index=None, call_updater=True):
        if "dt" in get_parameters(update_function):
            updater_list = self.time_based_updaters
        else:
            updater_list = self.non_time_updaters

        if index is None:
            updater_list.append(update_function)
        else:
            updater_list.insert(index, update_function)

        self.refresh_has_updater_status()
        if call_updater:
            self.update(dt=0)
        return self

    def remove_updater(self, update_function):
        for updater_list in [self.time_based_updaters, self.non_time_updaters]:
            while update_function in updater_list:
                updater_list.remove(update_function)
        self.refresh_has_updater_status()
        return self

    def clear_updaters(self, recurse=True):
        self.time_based_updaters = []
        self.non_time_updaters = []
        self.refresh_has_updater_status()
        if recurse:
            for submob in self.submobjects:
                submob.clear_updaters()
        return self

    def match_updaters(self, mobject):
        self.clear_updaters()
        for updater in mobject.get_updaters():
            self.add_updater(updater)
        return self

    def suspend_updating(self, recurse=True):
        self.updating_suspended = True
        if recurse:
            for submob in self.submobjects:
                submob.suspend_updating(recurse)
        return self

    def resume_updating(self, recurse=True, call_updater=True):
        self.updating_suspended = False
        if recurse:
            for submob in self.submobjects:
                submob.resume_updating(recurse)
        for parent in self.parents:
            parent.resume_updating(recurse=False, call_updater=False)
        if call_updater:
            self.update(dt=0, recurse=recurse)
        return self

    def refresh_has_updater_status(self):
        self.has_updaters = any(mob.get_updaters() for mob in self.get_family())
        return self

    # Transforming operations

    def shift(self, vector):
        self.apply_points_function(
            lambda points: points + vector,
            about_edge=None,
            works_on_bounding_box=True,
        )
        return self

    def scale(self, scale_factor, min_scale_factor=1e-8, about_point=None, about_edge=ORIGIN):
        """
        Default behavior is to scale about the center of the mobject.
        The argument about_edge can be a vector, indicating which side of
        the mobject to scale about, e.g., mob.scale(about_edge = RIGHT)
        scales about mob.get_right().

        Otherwise, if about_point is given a value, scaling is done with
        respect to that point.
        """
        scale_factor = max(scale_factor, min_scale_factor)
        for mob in self.get_family():
            mob._handle_scale_side_effects(scale_factor)
        self.apply_points_function(
            lambda points: scale_factor * points,
            about_point=about_point,
            about_edge=about_edge,
            works_on_bounding_box=True,
        )
        return self

    def _handle_scale_side_effects(self, scale_factor):
        # In case subclasses, such as DecimalNumber, need to make
        # any other changes when the size gets altered
        pass

    def stretch(self, factor, dim, **kwargs):
        def func(points):
            points[:, dim] *= factor
            return points
        self.apply_points_function(func, works_on_bounding_box=True, **kwargs)
        return self

    def rotate_about_origin(self, angle, axis=OUT):
        return self.rotate(angle, axis, about_point=ORIGIN)

    def rotate(self, angle, axis=OUT, **kwargs):
        rot_matrix_T = rotation_matrix_transpose(angle, axis)
        self.apply_points_function(
            lambda points: np.dot(points, rot_matrix_T),
            **kwargs
        )
        return self

    def flip(self, axis=UP, **kwargs):
        return self.rotate(TAU / 2, axis, **kwargs)

    def apply_function(self, function, **kwargs):
        # Default to applying matrix about the origin, not mobjects center
        if len(kwargs) == 0:
            kwargs["about_point"] = ORIGIN
        self.apply_points_function(
            lambda points: np.array([function(p) for p in points]),
            **kwargs
        )
        return self

    def apply_function_to_position(self, function):
        self.move_to(function(self.get_center()))
        return self

    def apply_function_to_submobject_positions(self, function):
        for submob in self.submobjects:
            submob.apply_function_to_position(function)
        return self

    def apply_matrix(self, matrix, **kwargs):
        # Default to applying matrix about the origin, not mobjects center
        if ("about_point" not in kwargs) and ("about_edge" not in kwargs):
            kwargs["about_point"] = ORIGIN
        full_matrix = np.identity(self.dim)
        matrix = np.array(matrix)
        full_matrix[:matrix.shape[0], :matrix.shape[1]] = matrix
        self.apply_points_function(
            lambda points: np.dot(points, full_matrix.T),
            **kwargs
        )
        return self

    def apply_complex_function(self, function, **kwargs):
        def R3_func(point):
            x, y, z = point
            xy_complex = function(complex(x, y))
            return [
                xy_complex.real,
                xy_complex.imag,
                z
            ]
        return self.apply_function(R3_func)

    def wag(self, direction=RIGHT, axis=DOWN, wag_factor=1.0):
        for mob in self.family_members_with_points():
            alphas = np.dot(mob.get_points(), np.transpose(axis))
            alphas -= min(alphas)
            alphas /= max(alphas)
            alphas = alphas**wag_factor
            mob.set_points(mob.get_points() + np.dot(
                alphas.reshape((len(alphas), 1)),
                np.array(direction).reshape((1, mob.dim))
            ))
        return self

    # Positioning methods

    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) * (FRAME_X_RADIUS, FRAME_Y_RADIUS, 0)
        point_to_align = self.get_bounding_box_point(direction)
        shift_val = target_point - point_to_align - 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_or_point,
                direction=RIGHT,
                buff=DEFAULT_MOBJECT_TO_MOBJECT_BUFFER,
                aligned_edge=ORIGIN,
                submobject_to_align=None,
                index_of_submobject_to_align=None,
                coor_mask=np.array([1, 1, 1]),
                ):
        if isinstance(mobject_or_point, Mobject):
            mob = mobject_or_point
            if index_of_submobject_to_align is not None:
                target_aligner = mob[index_of_submobject_to_align]
            else:
                target_aligner = mob
            target_point = target_aligner.get_bounding_box_point(
                aligned_edge + direction
            )
        else:
            target_point = mobject_or_point
        if submobject_to_align is not None:
            aligner = submobject_to_align
        elif index_of_submobject_to_align is not None:
            aligner = self[index_of_submobject_to_align]
        else:
            aligner = self
        point_to_align = aligner.get_bounding_box_point(aligned_edge - direction)
        self.shift((target_point - point_to_align + buff * direction) * coor_mask)
        return self

    def shift_onto_screen(self, **kwargs):
        space_lengths = [FRAME_X_RADIUS, FRAME_Y_RADIUS]
        for vect in UP, DOWN, LEFT, RIGHT:
            dim = np.argmax(np.abs(vect))
            buff = kwargs.get("buff", DEFAULT_MOBJECT_TO_EDGE_BUFFER)
            max_val = space_lengths[dim] - buff
            edge_center = self.get_edge_center(vect)
            if np.dot(edge_center, vect) > max_val:
                self.to_edge(vect, **kwargs)
        return self

    def is_off_screen(self):
        if self.get_left()[0] > FRAME_X_RADIUS:
            return True
        if self.get_right()[0] < -FRAME_X_RADIUS:
            return True
        if self.get_bottom()[1] > FRAME_Y_RADIUS:
            return True
        if self.get_top()[1] < -FRAME_Y_RADIUS:
            return True
        return False

    def stretch_about_point(self, factor, dim, point):
        return self.stretch(factor, dim, about_point=point)

    def stretch_in_place(self, factor, dim):
        # Now redundant with stretch
        return self.stretch(factor, dim)

    def rescale_to_fit(self, length, dim, stretch=False, **kwargs):
        old_length = self.length_over_dim(dim)
        if old_length == 0:
            return self
        if stretch:
            self.stretch(length / old_length, dim, **kwargs)
        else:
            self.scale(length / old_length, **kwargs)
        return self

    def stretch_to_fit_width(self, width, **kwargs):
        return self.rescale_to_fit(width, 0, stretch=True, **kwargs)

    def stretch_to_fit_height(self, height, **kwargs):
        return self.rescale_to_fit(height, 1, stretch=True, **kwargs)

    def stretch_to_fit_depth(self, depth, **kwargs):
        return self.rescale_to_fit(depth, 1, stretch=True, **kwargs)

    def set_width(self, width, stretch=False, **kwargs):
        return self.rescale_to_fit(width, 0, stretch=stretch, **kwargs)

    def set_height(self, height, stretch=False, **kwargs):
        return self.rescale_to_fit(height, 1, stretch=stretch, **kwargs)

    def set_depth(self, depth, stretch=False, **kwargs):
        return self.rescale_to_fit(depth, 2, stretch=stretch, **kwargs)

    def set_coord(self, value, dim, direction=ORIGIN):
        curr = self.get_coord(dim, direction)
        shift_vect = np.zeros(self.dim)
        shift_vect[dim] = value - curr
        self.shift(shift_vect)
        return self

    def set_x(self, x, direction=ORIGIN):
        return self.set_coord(x, 0, direction)

    def set_y(self, y, direction=ORIGIN):
        return self.set_coord(y, 1, direction)

    def set_z(self, z, direction=ORIGIN):
        return self.set_coord(z, 2, direction)

    def space_out_submobjects(self, factor=1.5, **kwargs):
        self.scale(factor, **kwargs)
        for submob in self.submobjects:
            submob.scale(1. / factor)
        return self

    def move_to(self, point_or_mobject, aligned_edge=ORIGIN,
                coor_mask=np.array([1, 1, 1])):
        if isinstance(point_or_mobject, Mobject):
            target = point_or_mobject.get_bounding_box_point(aligned_edge)
        else:
            target = point_or_mobject
        point_to_align = self.get_bounding_box_point(aligned_edge)
        self.shift((target - point_to_align) * coor_mask)
        return self

    def replace(self, mobject, dim_to_match=0, stretch=False):
        if not mobject.get_num_points() and not mobject.submobjects:
            self.scale(0)
            return self
        if stretch:
            for i in range(self.dim):
                self.rescale_to_fit(mobject.length_over_dim(i), i, stretch=True)
        else:
            self.rescale_to_fit(
                mobject.length_over_dim(dim_to_match),
                dim_to_match,
                stretch=False
            )
        self.shift(mobject.get_center() - self.get_center())
        return self

    def surround(self, mobject,
                 dim_to_match=0,
                 stretch=False,
                 buff=MED_SMALL_BUFF):
        self.replace(mobject, dim_to_match, stretch)
        length = mobject.length_over_dim(dim_to_match)
        self.scale((length + buff) / length)
        return self

    def put_start_and_end_on(self, start, end):
        curr_start, curr_end = self.get_start_and_end()
        curr_vect = curr_end - curr_start
        if np.all(curr_vect == 0):
            raise Exception("Cannot position endpoints of closed loop")
        target_vect = end - start
        self.scale(
            get_norm(target_vect) / get_norm(curr_vect),
            about_point=curr_start,
        )
        self.rotate(
            angle_of_vector(target_vect) - angle_of_vector(curr_vect),
        )
        self.rotate(
            np.arctan2(curr_vect[2], get_norm(curr_vect[:2])) - np.arctan2(target_vect[2], get_norm(target_vect[:2])), 
            axis = np.array([-target_vect[1], target_vect[0], 0]),
        )
        self.shift(start - self.get_start())
        return self

    # Color functions

    def set_rgba_array(self, rgba_array, name="rgbas", recurse=False):
        for mob in self.get_family(recurse):
            mob.data[name] = np.array(rgba_array)
        return self

    def set_color_by_rgba_func(self, func, recurse=True):
        """
        Func should take in a point in R3 and output an rgba value
        """
        for mob in self.get_family(recurse):
            rgba_array = [func(point) for point in mob.get_points()]
            mob.set_rgba_array(rgba_array)
        return self

    def set_color_by_rgb_func(self, func, opacity=1, recurse=True):
        """
        Func should take in a point in R3 and output an rgb value
        """
        for mob in self.get_family(recurse):
            rgba_array = [[*func(point), opacity] for point in mob.get_points()]
            mob.set_rgba_array(rgba_array)
        return self

    def set_rgba_array_by_color(self, color=None, opacity=None, name="rgbas", recurse=True):
        if color is not None:
            rgbs = np.array([color_to_rgb(c) for c in listify(color)])
        if opacity is not None:
            opacities = listify(opacity)

        # Color only
        if color is not None and opacity is None:
            for mob in self.get_family(recurse):
                mob.data[name] = resize_array(mob.data[name], len(rgbs))
                mob.data[name][:, :3] = rgbs

        # Opacity only
        if color is None and opacity is not None:
            for mob in self.get_family(recurse):
                mob.data[name] = resize_array(mob.data[name], len(opacities))
                mob.data[name][:, 3] = opacities

        # Color and opacity
        if color is not None and opacity is not None:
            rgbas = np.array([
                [*rgb, o]
                for rgb, o in zip(*make_even(rgbs, opacities))
            ])
            for mob in self.get_family(recurse):
                mob.data[name] = rgbas.copy()
        return self

    def set_color(self, color, opacity=None, recurse=True):
        self.set_rgba_array_by_color(color, opacity, recurse=False)
        # Recurse to submobjects differently from how set_rgba_array_by_color
        # in case they implement set_color differently
        if recurse:
            for submob in self.submobjects:
                submob.set_color(color, recurse=True)
        return self

    def set_opacity(self, opacity, recurse=True):
        self.set_rgba_array_by_color(color=None, opacity=opacity, recurse=False)
        if recurse:
            for submob in self.submobjects:
                submob.set_opacity(opacity, recurse=True)
        return self

    def get_color(self):
        return rgb_to_hex(self.data["rgbas"][0, :3])

    def get_opacity(self):
        return self.data["rgbas"][0, 3]

    def set_color_by_gradient(self, *colors):
        self.set_submobject_colors_by_gradient(*colors)
        return self

    def set_submobject_colors_by_gradient(self, *colors):
        if len(colors) == 0:
            raise Exception("Need at least one color")
        elif len(colors) == 1:
            return self.set_color(*colors)

        # mobs = self.family_members_with_points()
        mobs = self.submobjects
        new_colors = color_gradient(colors, len(mobs))

        for mob, color in zip(mobs, new_colors):
            mob.set_color(color)
        return self

    def fade(self, darkness=0.5, recurse=True):
        self.set_opacity(1.0 - darkness, recurse=recurse)

    def get_gloss(self):
        return self.uniforms["gloss"]

    def set_gloss(self, gloss, recurse=True):
        for mob in self.get_family(recurse):
            mob.uniforms["gloss"] = gloss
        return self

    def get_shadow(self):
        return self.uniforms["shadow"]

    def set_shadow(self, shadow, recurse=True):
        for mob in self.get_family(recurse):
            mob.uniforms["shadow"] = shadow
        return self

    # Background rectangle

    def add_background_rectangle(self, color=None, opacity=0.75, **kwargs):
        # TODO, this does not behave well when the mobject has points,
        # since it gets displayed on top
        from manimlib.mobject.shape_matchers import BackgroundRectangle
        self.background_rectangle = BackgroundRectangle(
            self, color=color,
            fill_opacity=opacity,
            **kwargs
        )
        self.add_to_back(self.background_rectangle)
        return self

    def add_background_rectangle_to_submobjects(self, **kwargs):
        for submobject in self.submobjects:
            submobject.add_background_rectangle(**kwargs)
        return self

    def add_background_rectangle_to_family_members_with_points(self, **kwargs):
        for mob in self.family_members_with_points():
            mob.add_background_rectangle(**kwargs)
        return self

    # Getters

    def get_bounding_box_point(self, direction):
        bb = self.get_bounding_box()
        indices = (np.sign(direction) + 1).astype(int)
        return np.array([
            bb[indices[i]][i]
            for i in range(3)
        ])

    def get_edge_center(self, direction):
        return self.get_bounding_box_point(direction)

    def get_corner(self, direction):
        return self.get_bounding_box_point(direction)

    def get_center(self):
        return self.get_bounding_box()[1]

    def get_center_of_mass(self):
        return self.get_all_points().mean(0)

    def get_boundary_point(self, direction):
        all_points = self.get_all_points()
        boundary_directions = all_points - self.get_center()
        norms = np.linalg.norm(boundary_directions, axis=1)
        boundary_directions /= np.repeat(norms, 3).reshape((len(norms), 3))
        index = np.argmax(np.dot(boundary_directions, np.array(direction).T))
        return all_points[index]

    def get_continuous_bounding_box_point(self, direction):
        dl, center, ur = self.get_bounding_box()
        corner_vect = (ur - center)
        return center + direction / np.max(np.abs(np.true_divide(
            direction, corner_vect,
            out=np.zeros(len(direction)),
            where=((corner_vect) != 0)
        )))

    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 get_zenith(self):
        return self.get_edge_center(OUT)

    def get_nadir(self):
        return self.get_edge_center(IN)

    def length_over_dim(self, dim):
        bb = self.get_bounding_box()
        return abs((bb[2] - bb[0])[dim])

    def get_width(self):
        return self.length_over_dim(0)

    def get_height(self):
        return self.length_over_dim(1)

    def get_depth(self):
        return self.length_over_dim(2)

    def get_coord(self, dim, direction=ORIGIN):
        """
        Meant to generalize get_x, get_y, get_z
        """
        return self.get_bounding_box_point(direction)[dim]

    def get_x(self, direction=ORIGIN):
        return self.get_coord(0, direction)

    def get_y(self, direction=ORIGIN):
        return self.get_coord(1, direction)

    def get_z(self, direction=ORIGIN):
        return self.get_coord(2, direction)

    def get_start(self):
        self.throw_error_if_no_points()
        return np.array(self.get_points()[0])

    def get_end(self):
        self.throw_error_if_no_points()
        return np.array(self.get_points()[-1])

    def get_start_and_end(self):
        return self.get_start(), self.get_end()

    def point_from_proportion(self, alpha):
        points = self.get_points()
        i, subalpha = integer_interpolate(0, len(points) - 1, alpha)
        return interpolate(points[i], points[i + 1], subalpha)

    def pfp(self, alpha):
        """Abbreviation fo point_from_proportion"""
        return self.point_from_proportion(alpha)

    def get_pieces(self, n_pieces):
        template = self.copy()
        template.set_submobjects([])
        alphas = np.linspace(0, 1, n_pieces + 1)
        return Group(*[
            template.copy().pointwise_become_partial(
                self, a1, a2
            )
            for a1, a2 in zip(alphas[:-1], alphas[1:])
        ])

    def get_z_index_reference_point(self):
        # TODO, better place to define default z_index_group?
        z_index_group = getattr(self, "z_index_group", self)
        return z_index_group.get_center()

    # Match other mobject properties

    def match_color(self, mobject):
        return self.set_color(mobject.get_color())

    def match_dim_size(self, mobject, dim, **kwargs):
        return self.rescale_to_fit(
            mobject.length_over_dim(dim), dim,
            **kwargs
        )

    def match_width(self, mobject, **kwargs):
        return self.match_dim_size(mobject, 0, **kwargs)

    def match_height(self, mobject, **kwargs):
        return self.match_dim_size(mobject, 1, **kwargs)

    def match_depth(self, mobject, **kwargs):
        return self.match_dim_size(mobject, 2, **kwargs)

    def match_coord(self, mobject, dim, direction=ORIGIN):
        return self.set_coord(
            mobject.get_coord(dim, direction),
            dim=dim,
            direction=direction,
        )

    def match_x(self, mobject, direction=ORIGIN):
        return self.match_coord(mobject, 0, direction)

    def match_y(self, mobject, direction=ORIGIN):
        return self.match_coord(mobject, 1, direction)

    def match_z(self, mobject, direction=ORIGIN):
        return self.match_coord(mobject, 2, direction)

    def align_to(self, mobject_or_point, direction=ORIGIN):
        """
        Examples:
        mob1.align_to(mob2, UP) moves mob1 vertically so that its
        top edge lines ups with mob2's top edge.

        mob1.align_to(mob2, alignment_vect = RIGHT) moves mob1
        horizontally so that it's center is directly above/below
        the center of mob2
        """
        if isinstance(mobject_or_point, Mobject):
            point = mobject_or_point.get_bounding_box_point(direction)
        else:
            point = mobject_or_point

        for dim in range(self.dim):
            if direction[dim] != 0:
                self.set_coord(point[dim], dim, direction)
        return self

    def get_group_class(self):
        return Group

    # Alignment

    def align_data_and_family(self, mobject):
        self.align_family(mobject)
        self.align_data(mobject)

    def align_data(self, mobject):
        # In case any data arrays get resized when aligned to shader data
        self.refresh_shader_data()
        for mob1, mob2 in zip(self.get_family(), mobject.get_family()):
            # Separate out how points are treated so that subclasses
            # can handle that case differently if they choose
            mob1.align_points(mob2)
            for key in mob1.data.keys() & mob2.data.keys():
                if key == "points":
                    continue
                arr1 = mob1.data[key]
                arr2 = mob2.data[key]
                if len(arr2) > len(arr1):
                    mob1.data[key] = resize_preserving_order(arr1, len(arr2))
                elif len(arr1) > len(arr2):
                    mob2.data[key] = resize_preserving_order(arr2, len(arr1))

    def align_points(self, mobject):
        max_len = max(self.get_num_points(), mobject.get_num_points())
        for mob in (self, mobject):
            mob.resize_points(max_len, resize_func=resize_preserving_order)
        return self

    def align_family(self, mobject):
        mob1 = self
        mob2 = mobject
        n1 = len(mob1)
        n2 = len(mob2)
        if n1 != n2:
            mob1.add_n_more_submobjects(max(0, n2 - n1))
            mob2.add_n_more_submobjects(max(0, n1 - n2))
        # Recurse
        for sm1, sm2 in zip(mob1.submobjects, mob2.submobjects):
            sm1.align_family(sm2)
        return self

    def push_self_into_submobjects(self):
        copy = self.deepcopy()
        copy.set_submobjects([])
        self.resize_points(0)
        self.add(copy)
        return self

    def add_n_more_submobjects(self, n):
        if n == 0:
            return self

        curr = len(self.submobjects)
        if curr == 0:
            # If empty, simply add n point mobjects
            null_mob = self.copy()
            null_mob.set_points([self.get_center()])
            self.set_submobjects([
                null_mob.copy()
                for k in range(n)
            ])
            return self
        target = curr + n
        repeat_indices = (np.arange(target) * curr) // target
        split_factors = [
            (repeat_indices == i).sum()
            for i in range(curr)
        ]
        new_submobs = []
        for submob, sf in zip(self.submobjects, split_factors):
            new_submobs.append(submob)
            for k in range(1, sf):
                new_submob = submob.copy()
                # If the submobject is at all transparent, then
                # make the copy completely transparent
                if submob.get_opacity() < 1:
                    new_submob.set_opacity(0)
                new_submobs.append(new_submob)
        self.set_submobjects(new_submobs)
        return self

    # Interpolate

    def interpolate(self, mobject1, mobject2, alpha, path_func=straight_path):
        for key in self.data:
            if key in self.locked_data_keys:
                continue
            if len(self.data[key]) == 0:
                continue
            if key not in mobject1.data or key not in mobject2.data:
                continue

            if key in ("points", "bounding_box"):
                func = path_func
            else:
                func = interpolate

            self.data[key][:] = func(
                mobject1.data[key],
                mobject2.data[key],
                alpha
            )
        for key in self.uniforms:
            self.uniforms[key] = interpolate(
                mobject1.uniforms[key],
                mobject2.uniforms[key],
                alpha
            )
        return self

    def pointwise_become_partial(self, mobject, a, b):
        """
        Set points in such a way as to become only
        part of mobject.
        Inputs 0 <= a < b <= 1 determine what portion
        of mobject to become.
        """
        pass  # To implement in subclass

    def become(self, mobject):
        """
        Edit all data and submobjects to be idential
        to another mobject
        """
        self.align_family(mobject)
        for sm1, sm2 in zip(self.get_family(), mobject.get_family()):
            sm1.set_data(sm2.data)
            sm1.set_uniforms(sm2.uniforms)
        self.refresh_bounding_box(recurse_down=True)
        return self

    # Locking data

    def lock_data(self, keys):
        """
        To speed up some animations, particularly transformations,
        it can be handy to acknowledge which pieces of data
        won't change during the animation so that calls to
        interpolate can skip this, and so that it's not
        read into the shader_wrapper objects needlessly
        """
        if self.has_updaters:
            return
        # Be sure shader data has most up to date information
        self.refresh_shader_data()
        self.locked_data_keys = set(keys)

    def lock_matching_data(self, mobject1, mobject2):
        for sm, sm1, sm2 in zip(self.get_family(), mobject1.get_family(), mobject2.get_family()):
            keys = sm.data.keys() & sm1.data.keys() & sm2.data.keys()
            sm.lock_data(list(filter(
                lambda key: np.all(sm1.data[key] == sm2.data[key]),
                keys,
            )))
        return self

    def unlock_data(self):
        for mob in self.get_family():
            mob.locked_data_keys = set()

    # Operations touching shader uniforms

    def affects_shader_info_id(func):
        @wraps(func)
        def wrapper(self):
            for mob in self.get_family():
                func(mob)
                mob.refresh_shader_wrapper_id()
            return self
        return wrapper

    @affects_shader_info_id
    def fix_in_frame(self):
        self.uniforms["is_fixed_in_frame"] = 1.0
        return self

    @affects_shader_info_id
    def unfix_from_frame(self):
        self.uniforms["is_fixed_in_frame"] = 0.0
        return self

    @affects_shader_info_id
    def apply_depth_test(self):
        self.depth_test = True
        return self

    @affects_shader_info_id
    def deactivate_depth_test(self):
        self.depth_test = False
        return self

    # Shader code manipulation

    def replace_shader_code(self, old, new):
        # TODO, will this work with VMobject structure, given
        # that it does not simpler return shader_wrappers of
        # family?
        for wrapper in self.get_shader_wrapper_list():
            wrapper.replace_code(old, new)
        return self

    def set_color_by_code(self, glsl_code):
        """
        Takes a snippet of code and inserts it into a
        context which has the following variables:
        vec4 color, vec3 point, vec3 unit_normal.
        The code should change the color variable
        """
        self.replace_shader_code(
            "///// INSERT COLOR FUNCTION HERE /////",
            glsl_code
        )
        return self

    def set_color_by_xyz_func(self, glsl_snippet,
                              min_value=-5.0, max_value=5.0,
                              colormap="viridis"):
        """
        Pass in a glsl expression in terms of x, y and z which returns
        a float.
        """
        # TODO, add a version of this which changes the point data instead
        # of the shader code
        for char in "xyz":
            glsl_snippet = glsl_snippet.replace(char, "point." + char)
        rgb_list = get_colormap_list(colormap)
        self.set_color_by_code(
            "color.rgb = float_to_color({}, {}, {}, {});".format(
                glsl_snippet,
                float(min_value),
                float(max_value),
                get_colormap_code(rgb_list)
            )
        )
        return self

    # For shader data

    def init_shader_data(self):
        # TODO, only call this when needed?
        self.shader_data = np.zeros(len(self.get_points()), dtype=self.shader_dtype)
        self.shader_indices = None
        self.shader_wrapper = ShaderWrapper(
            vert_data=self.shader_data,
            shader_folder=self.shader_folder,
            texture_paths=self.texture_paths,
            depth_test=self.depth_test,
            render_primitive=self.render_primitive,
        )

    def refresh_shader_wrapper_id(self):
        self.shader_wrapper.refresh_id()
        return self

    def get_shader_wrapper(self):
        self.shader_wrapper.vert_data = self.get_shader_data()
        self.shader_wrapper.vert_indices = self.get_shader_vert_indices()
        self.shader_wrapper.uniforms = self.get_shader_uniforms()
        self.shader_wrapper.depth_test = self.depth_test
        return self.shader_wrapper

    def get_shader_wrapper_list(self):
        shader_wrappers = it.chain(
            [self.get_shader_wrapper()],
            *[sm.get_shader_wrapper_list() for sm in self.submobjects]
        )
        batches = batch_by_property(shader_wrappers, lambda sw: sw.get_id())

        result = []
        for wrapper_group, sid in batches:
            shader_wrapper = wrapper_group[0]
            if not shader_wrapper.is_valid():
                continue
            shader_wrapper.combine_with(*wrapper_group[1:])
            if len(shader_wrapper.vert_data) > 0:
                result.append(shader_wrapper)
        return result

    def check_data_alignment(self, array, data_key):
        # Makes sure that self.data[key] can be broadcast into
        # the given array, meaning its length has to be either 1
        # or the length of the array
        d_len = len(self.data[data_key])
        if d_len != 1 and d_len != len(array):
            self.data[data_key] = resize_with_interpolation(
                self.data[data_key], len(array)
            )
        return self

    def get_resized_shader_data_array(self, length):
        # If possible, try to populate an existing array, rather
        # than recreating it each frame
        if len(self.shader_data) != length:
            self.shader_data = resize_array(self.shader_data, length)
        return self.shader_data

    def read_data_to_shader(self, shader_data, shader_data_key, data_key):
        if data_key in self.locked_data_keys:
            return
        self.check_data_alignment(shader_data, data_key)
        shader_data[shader_data_key] = self.data[data_key]

    def get_shader_data(self):
        shader_data = self.get_resized_shader_data_array(self.get_num_points())
        self.read_data_to_shader(shader_data, "point", "points")
        return shader_data

    def refresh_shader_data(self):
        self.get_shader_data()

    def get_shader_uniforms(self):
        return self.uniforms

    def get_shader_vert_indices(self):
        return self.shader_indices

    # Event Handlers
    """
        Event handling follows the Event Bubbling model of DOM in javascript.
        Return false to stop the event bubbling.
        To learn more visit https://www.quirksmode.org/js/events_order.html

        Event Callback Argument is a callable function taking two arguments:
            1. Mobject
            2. EventData
    """

    def init_event_listners(self):
        self.event_listners = []

    def add_event_listner(self, event_type, event_callback):
        event_listner = EventListner(self, event_type, event_callback)
        self.event_listners.append(event_listner)
        EVENT_DISPATCHER.add_listner(event_listner)
        return self

    def remove_event_listner(self, event_type, event_callback):
        event_listner = EventListner(self, event_type, event_callback)
        while event_listner in self.event_listners:
            self.event_listners.remove(event_listner)
        EVENT_DISPATCHER.remove_listner(event_listner)
        return self

    def clear_event_listners(self, recurse=True):
        self.event_listners = []
        if recurse:
            for submob in self.submobjects:
                submob.clear_event_listners(recurse=recurse)
        return self

    def get_event_listners(self):
        return self.event_listners

    def get_family_event_listners(self):
        return list(it.chain(*[sm.get_event_listners() for sm in self.get_family()]))

    def get_has_event_listner(self):
        return any(
            mob.get_event_listners()
            for mob in self.get_family()
        )

    def add_mouse_motion_listner(self, callback):
        self.add_event_listner(EventType.MouseMotionEvent, callback)

    def remove_mouse_motion_listner(self, callback):
        self.remove_event_listner(EventType.MouseMotionEvent, callback)

    def add_mouse_press_listner(self, callback):
        self.add_event_listner(EventType.MousePressEvent, callback)

    def remove_mouse_press_listner(self, callback):
        self.remove_event_listner(EventType.MousePressEvent, callback)

    def add_mouse_release_listner(self, callback):
        self.add_event_listner(EventType.MouseReleaseEvent, callback)

    def remove_mouse_release_listner(self, callback):
        self.remove_event_listner(EventType.MouseReleaseEvent, callback)

    def add_mouse_drag_listner(self, callback):
        self.add_event_listner(EventType.MouseDragEvent, callback)

    def remove_mouse_drag_listner(self, callback):
        self.remove_event_listner(EventType.MouseDragEvent, callback)

    def add_mouse_scroll_listner(self, callback):
        self.add_event_listner(EventType.MouseScrollEvent, callback)

    def remove_mouse_scroll_listner(self, callback):
        self.remove_event_listner(EventType.MouseScrollEvent, callback)

    def add_key_press_listner(self, callback):
        self.add_event_listner(EventType.KeyPressEvent, callback)

    def remove_key_press_listner(self, callback):
        self.remove_event_listner(EventType.KeyPressEvent, callback)

    def add_key_release_listner(self, callback):
        self.add_event_listner(EventType.KeyReleaseEvent, callback)

    def remove_key_release_listner(self, callback):
        self.remove_event_listner(EventType.KeyReleaseEvent, callback)

    # Errors

    def throw_error_if_no_points(self):
        if not self.has_points():
            message = "Cannot call Mobject.{} " +\
                      "for a Mobject with no points"
            caller_name = sys._getframe(1).f_code.co_name
            raise Exception(message.format(caller_name))


class Group(Mobject):
    def __init__(self, *mobjects, **kwargs):
        if not all([isinstance(m, Mobject) for m in mobjects]):
            raise Exception("All submobjects must be of type Mobject")
        Mobject.__init__(self, **kwargs)
        self.add(*mobjects)


class Point(Mobject):
    CONFIG = {
        "artificial_width": 1e-6,
        "artificial_height": 1e-6,
    }

    def __init__(self, location=ORIGIN, **kwargs):
        Mobject.__init__(self, **kwargs)
        self.set_location(location)

    def get_width(self):
        return self.artificial_width

    def get_height(self):
        return self.artificial_height

    def get_location(self):
        return self.get_points()[0].copy()

    def get_bounding_box_point(self, *args, **kwargs):
        return self.get_location()

    def set_location(self, new_loc):
        self.set_points(np.array(new_loc, ndmin=2, dtype=float))


class _AnimationBuilder:
    def __init__(self, mobject):
        self.mobject = mobject
        self.overridden_animation = None
        self.mobject.generate_target()
        self.is_chaining = False
        self.methods = []

    def __getattr__(self, method_name):
        method = getattr(self.mobject.target, method_name)
        self.methods.append(method)
        has_overridden_animation = hasattr(method, "_override_animate")

        if (self.is_chaining and has_overridden_animation) or self.overridden_animation:
            raise NotImplementedError(
                "Method chaining is currently not supported for "
                "overridden animations"
            )

        def update_target(*method_args, **method_kwargs):
            if has_overridden_animation:
                self.overridden_animation = method._override_animate(
                    self.mobject, *method_args, **method_kwargs
                )
            else:
                method(*method_args, **method_kwargs)
            return self

        self.is_chaining = True
        return update_target

    def build(self):
        from manimlib.animation.transform import _MethodAnimation

        if self.overridden_animation:
            return self.overridden_animation

        return _MethodAnimation(self.mobject, self.methods)


def override_animate(method):
    def decorator(animation_method):
        method._override_animate = animation_method
        return animation_method

    return decorator