import numpy as np from manimlib.animation.animation import Animation from manimlib.animation.creation import ShowCreation from manimlib.animation.creation import Write from manimlib.animation.fading import FadeOut from manimlib.animation.growing import GrowArrow from manimlib.animation.transform import ApplyFunction from manimlib.animation.transform import ApplyPointwiseFunction from manimlib.animation.transform import Transform from manimlib.constants import * from manimlib.mobject.coordinate_systems import Axes from manimlib.mobject.coordinate_systems import NumberPlane from manimlib.mobject.geometry import Arrow from manimlib.mobject.geometry import Dot from manimlib.mobject.geometry import Line from manimlib.mobject.geometry import Rectangle from manimlib.mobject.geometry import Vector from manimlib.mobject.matrix import Matrix from manimlib.mobject.matrix import VECTOR_LABEL_SCALE_FACTOR from manimlib.mobject.matrix import vector_coordinate_label from manimlib.mobject.mobject import Mobject from manimlib.mobject.svg.tex_mobject import TexMobject from manimlib.mobject.svg.tex_mobject import TextMobject from manimlib.mobject.types.vectorized_mobject import VGroup from manimlib.mobject.types.vectorized_mobject import VMobject from manimlib.scene.scene import Scene from manimlib.utils.rate_functions import rush_from from manimlib.utils.rate_functions import rush_into from manimlib.utils.space_ops import angle_of_vector from manimlib.utils.space_ops import get_norm X_COLOR = GREEN_C Y_COLOR = RED_C Z_COLOR = BLUE_D # TODO: Much of this scene type seems dependent on the coordinate system chosen. # That is, being centered at the origin with grid units corresponding to the # arbitrary space units. Change it! # # Also, methods I would have thought of as getters, like coords_to_vector, are # actually doing a lot of animating. class VectorScene(Scene): CONFIG = { "basis_vector_stroke_width": 6 } def add_plane(self, animate=False, **kwargs): """ Adds a NumberPlane object to the background. Parameters ---------- animate : (bool=False) Whether or not to animate the addition of the plane via ShowCreation. **kwargs Any valid keyword arguments accepted by NumberPlane. Returns ------- NumberPlane The NumberPlane object. """ plane = NumberPlane(**kwargs) if animate: self.play(ShowCreation(plane, lag_ratio=0.5)) self.add(plane) return plane def add_axes(self, animate=False, color=WHITE, **kwargs): """ Adds a pair of Axes to the Scene. Parameters ---------- animate (bool=False) Whether or not to animate the addition of the axes through ShowCreation. color (str) The color of the axes. Defaults to WHITE. """ axes = Axes(color=color, tick_frequency=1) if animate: self.play(ShowCreation(axes)) self.add(axes) return axes def lock_in_faded_grid(self, dimness=0.7, axes_dimness=0.5): """ This method freezes the NumberPlane and Axes that were already in the background, and adds new, manipulatable ones to the foreground. Parameters ---------- dimness (Union[int,float=0.7]) The required dimness of the NumberPlane axes_dimness (Union[int,float=0.5]) The required dimness of the Axes. """ plane = self.add_plane() axes = plane.get_axes() plane.fade(dimness) axes.set_color(WHITE) axes.fade(axes_dimness) self.add(axes) self.freeze_background() def get_vector(self, numerical_vector, **kwargs): """ Returns an arrow on the Plane given an input numerical vector. Parameters ---------- numerical_vector : Union(np.ndarray, list, tuple) The Vector to plot. **kwargs Any valid keyword argument of Arrow. Returns ------- Arrow The Arrow representing the Vector. """ return Arrow( self.plane.coords_to_point(0, 0), self.plane.coords_to_point(*numerical_vector[:2]), buff=0, **kwargs ) def add_vector(self, vector, color=YELLOW, animate=True, **kwargs): """ Returns the Vector after adding it to the Plane. Parameters ---------- vector Union(Arrow,list,tuple,np.ndarray) It can be a pre-made graphical vector, or the coordinates of one. color (str) The string of the hex color of the vector. This is only taken into consideration if 'vector' is not an Arrow. Defaults to YELLOW. animate (bool=True) Whether or not to animate the addition of the vector by using GrowArrow **kwargs Any valid keyword argument of Arrow. These are only considered if vector is not an Arrow. Returns ------- Arrow The arrow representing the vector. """ if not isinstance(vector, Arrow): vector = Vector(vector, color=color, **kwargs) if animate: self.play(GrowArrow(vector)) self.add(vector) return vector def write_vector_coordinates(self, vector, **kwargs): """ Returns a column matrix indicating the vector coordinates, after writing them to the screen. Parameters ---------- vector (Arrow) The arrow representing the vector. **kwargs Any valid keyword arguments of matrix.vector_coordinate_label integer_labels (True) : Whether or not to round the coordinates to integers. n_dim (2) : The number of dimensions of the vector. color (WHITE) : The color of the label. Returns ------- Matrix The column matrix representing the vector. """ coords = vector_coordinate_label(vector, **kwargs) self.play(Write(coords)) return coords def get_basis_vectors(self, i_hat_color=X_COLOR, j_hat_color=Y_COLOR): """ Returns a VGroup of the Basis Vectors (1,0) and (0,1) Parameters ---------- i_hat_color (str) The hex colour to use for the basis vector in the x direction j_hat_color (str) The hex colour to use for the basis vector in the y direction Returns ------- VGroup VGroup of the Vector Mobjects representing the basis vectors. """ return VGroup(*[ Vector( vect, color=color, stroke_width=self.basis_vector_stroke_width ) for vect, color in [ ([1, 0], i_hat_color), ([0, 1], j_hat_color) ] ]) def get_basis_vector_labels(self, **kwargs): """ Returns naming labels for the basis vectors. Parameters ---------- **kwargs Any valid keyword arguments of get_vector_label: vector, label (str,TexMobject) at_tip (bool=False), direction (str="left"), rotate (bool), color (str), label_scale_factor=VECTOR_LABEL_SCALE_FACTOR (int, float), """ i_hat, j_hat = self.get_basis_vectors() return VGroup(*[ self.get_vector_label( vect, label, color=color, label_scale_factor=1, **kwargs ) for vect, label, color in [ (i_hat, "\\hat{\\imath}", X_COLOR), (j_hat, "\\hat{\\jmath}", Y_COLOR), ] ]) def get_vector_label(self, vector, label, at_tip=False, direction="left", rotate=False, color=None, label_scale_factor=VECTOR_LABEL_SCALE_FACTOR): """ Returns naming labels for the passed vector. Parameters ---------- vector Vector Object for which to get the label. at_tip (bool) Whether or not to place the label at the tip of the vector. direction (str="left") If the label should be on the "left" or right of the vector. rotate (bool=False) Whether or not to rotate it to align it with the vector. color (str) The color to give the label. label_scale_factor (Union[int,float]) How much to scale the label by. Returns ------- TexMobject The TexMobject of the label. """ if not isinstance(label, TexMobject): if len(label) == 1: label = "\\vec{\\textbf{%s}}" % label label = TexMobject(label) if color is None: color = vector.get_color() label.set_color(color) label.scale(label_scale_factor) label.add_background_rectangle() if at_tip: vect = vector.get_vector() vect /= get_norm(vect) label.next_to(vector.get_end(), vect, buff=SMALL_BUFF) else: angle = vector.get_angle() if not rotate: label.rotate(-angle, about_point=ORIGIN) if direction == "left": label.shift(-label.get_bottom() + 0.1 * UP) else: label.shift(-label.get_top() + 0.1 * DOWN) label.rotate(angle, about_point=ORIGIN) label.shift((vector.get_end() - vector.get_start()) / 2) return label def label_vector(self, vector, label, animate=True, **kwargs): """ Shortcut method for creating, and animating the addition of a label for the vector. Parameters ---------- vector (Vector) The vector for which the label must be added. label (TexMobject,str) The TexMobject/string of the label. animate (bool=True) Whether or not to animate the labelling w/ Write **kwargs Any valid keyword argument of get_vector_label Returns ------- TexMobject The TexMobject of the label. """ label = self.get_vector_label(vector, label, **kwargs) if animate: self.play(Write(label, run_time=1)) self.add(label) return label def position_x_coordinate(self, x_coord, x_line, vector): #TODO Write DocStrings for this. x_coord.next_to(x_line, -np.sign(vector[1]) * UP) x_coord.set_color(X_COLOR) return x_coord def position_y_coordinate(self, y_coord, y_line, vector): #TODO Write DocStrings for this. y_coord.next_to(y_line, np.sign(vector[0]) * RIGHT) y_coord.set_color(Y_COLOR) return y_coord def coords_to_vector(self, vector, coords_start=2 * RIGHT + 2 * UP, clean_up=True): """ This method writes the vector as a column matrix (henceforth called the label), takes the values in it one by one, and form the corresponding lines that make up the x and y components of the vector. Then, an Vector() based vector is created between the lines on the Screen. Parameters ---------- vector Union(np.ndarray, list, tuple) The vector to show. coords_start Union(np.ndarray,list,tuple) The starting point of the location of the label of the vector that shows it numerically. Defaults to 2 * RIGHT + 2 * UP or (2,2) clean_up (bool=True) Whether or not to remove whatever this method did after it's done. """ starting_mobjects = list(self.mobjects) array = Matrix(vector) array.shift(coords_start) arrow = Vector(vector) x_line = Line(ORIGIN, vector[0] * RIGHT) y_line = Line(x_line.get_end(), arrow.get_end()) x_line.set_color(X_COLOR) y_line.set_color(Y_COLOR) x_coord, y_coord = array.get_mob_matrix().flatten() self.play(Write(array, run_time=1)) self.wait() self.play(ApplyFunction( lambda x: self.position_x_coordinate(x, x_line, vector), x_coord )) self.play(ShowCreation(x_line)) self.play( ApplyFunction( lambda y: self.position_y_coordinate(y, y_line, vector), y_coord ), FadeOut(array.get_brackets()) ) y_coord, brackets = self.get_mobjects_from_last_animation() self.play(ShowCreation(y_line)) self.play(ShowCreation(arrow)) self.wait() if clean_up: self.clear() self.add(*starting_mobjects) def vector_to_coords(self, vector, integer_labels=True, clean_up=True): """ This method displays vector as a Vector() based vector, and then shows the corresponding lines that make up the x and y components of the vector. Then, a column matrix (henceforth called the label) is created near the head of the Vector. Parameters ---------- vector Union(np.ndarray, list, tuple) The vector to show. integer_label (bool=True) Whether or not to round the value displayed. in the vector's label to the nearest integer clean_up (bool=True) Whether or not to remove whatever this method did after it's done. """ starting_mobjects = list(self.mobjects) show_creation = False if isinstance(vector, Arrow): arrow = vector vector = arrow.get_end()[:2] else: arrow = Vector(vector) show_creation = True array = vector_coordinate_label(arrow, integer_labels=integer_labels) x_line = Line(ORIGIN, vector[0] * RIGHT) y_line = Line(x_line.get_end(), arrow.get_end()) x_line.set_color(X_COLOR) y_line.set_color(Y_COLOR) x_coord, y_coord = array.get_mob_matrix().flatten() x_coord_start = self.position_x_coordinate( x_coord.copy(), x_line, vector ) y_coord_start = self.position_y_coordinate( y_coord.copy(), y_line, vector ) brackets = array.get_brackets() if show_creation: self.play(ShowCreation(arrow)) self.play( ShowCreation(x_line), Write(x_coord_start), run_time=1 ) self.play( ShowCreation(y_line), Write(y_coord_start), run_time=1 ) self.wait() self.play( Transform(x_coord_start, x_coord, lag_ratio=0), Transform(y_coord_start, y_coord, lag_ratio=0), Write(brackets, run_time=1), ) self.wait() self.remove(x_coord_start, y_coord_start, brackets) self.add(array) if clean_up: self.clear() self.add(*starting_mobjects) return array, x_line, y_line def show_ghost_movement(self, vector): """ This method plays an animation that partially shows the entire plane moving in the direction of a particular vector. This is useful when you wish to convey the idea of mentally moving the entire plane in a direction, without actually moving the plane. Parameters ---------- vector (Union[Arrow, list, tuple, np.ndarray]) The vector which indicates the direction of movement. """ if isinstance(vector, Arrow): vector = vector.get_end() - vector.get_start() elif len(vector) == 2: vector = np.append(np.array(vector), 0.0) x_max = int(FRAME_X_RADIUS + abs(vector[0])) y_max = int(FRAME_Y_RADIUS + abs(vector[1])) dots = VMobject(*[ Dot(x * RIGHT + y * UP) for x in range(-x_max, x_max) for y in range(-y_max, y_max) ]) dots.set_fill(BLACK, opacity=0) dots_halfway = dots.copy().shift(vector / 2).set_fill(WHITE, 1) dots_end = dots.copy().shift(vector) self.play(Transform( dots, dots_halfway, rate_func=rush_into )) self.play(Transform( dots, dots_end, rate_func=rush_from )) self.remove(dots) class LinearTransformationScene(VectorScene): """ This scene contains special methods that make it especially suitable for showing Linear Transformations. """ CONFIG = { "include_background_plane": True, "include_foreground_plane": True, "foreground_plane_kwargs": { "x_max": FRAME_WIDTH / 2, "x_min": -FRAME_WIDTH / 2, "y_max": FRAME_WIDTH / 2, "y_min": -FRAME_WIDTH / 2, "faded_line_ratio": 0 }, "background_plane_kwargs": { "color": GREY, "axis_config": { "stroke_color": LIGHT_GREY, }, "axis_config": { "color": GREY, }, "background_line_style": { "stroke_color": GREY, "stroke_width": 1, }, }, "show_coordinates": False, "show_basis_vectors": True, "basis_vector_stroke_width": 6, "i_hat_color": X_COLOR, "j_hat_color": Y_COLOR, "leave_ghost_vectors": False, "t_matrix": [[3, 0], [1, 2]], } def setup(self): # The has_already_setup attr is to not break all the old Scenes if hasattr(self, "has_already_setup"): return self.has_already_setup = True self.background_mobjects = [] self.foreground_mobjects = [] self.transformable_mobjects = [] self.moving_vectors = [] self.transformable_labels = [] self.moving_mobjects = [] self.t_matrix = np.array(self.t_matrix) self.background_plane = NumberPlane( **self.background_plane_kwargs ) if self.show_coordinates: self.background_plane.add_coordinates() if self.include_background_plane: self.add_background_mobject(self.background_plane) if self.include_foreground_plane: self.plane = NumberPlane(**self.foreground_plane_kwargs) self.add_transformable_mobject(self.plane) if self.show_basis_vectors: self.basis_vectors = self.get_basis_vectors( i_hat_color=self.i_hat_color, j_hat_color=self.j_hat_color, ) self.moving_vectors += list(self.basis_vectors) self.i_hat, self.j_hat = self.basis_vectors self.add(self.basis_vectors) def add_special_mobjects(self, mob_list, *mobs_to_add): """ Adds mobjects to a separate list that can be tracked, if these mobjects have some extra importance. Parameters ---------- mob_list (list) The special list to which you want to add these mobjects. *mobs_to_add (Mobject) The mobjects to add. """ for mobject in mobs_to_add: if mobject not in mob_list: mob_list.append(mobject) self.add(mobject) def add_background_mobject(self, *mobjects): """ Adds the mobjects to the special list self.background_mobjects. Parameters ---------- *mobjects (Mobject) The mobjects to add to the list. """ self.add_special_mobjects(self.background_mobjects, *mobjects) # TODO, this conflicts with Scene.add_fore def add_foreground_mobject(self, *mobjects): """ Adds the mobjects to the special list self.foreground_mobjects. Parameters ---------- *mobjects (Mobject) The mobjects to add to the list """ self.add_special_mobjects(self.foreground_mobjects, *mobjects) def add_transformable_mobject(self, *mobjects): """ Adds the mobjects to the special list self.transformable_mobjects. Parameters ---------- *mobjects (Mobject) The mobjects to add to the list. """ self.add_special_mobjects(self.transformable_mobjects, *mobjects) def add_moving_mobject(self, mobject, target_mobject=None): """ Adds the mobject to the special list self.moving_mobject, and adds a property to the mobject called mobject.target, which keeps track of what the mobject will move to or become etc. Parameters ---------- mobject (Mobject) The mobjects to add to the list target_mobject (Mobject) What the moving_mobject goes to, etc. """ mobject.target = target_mobject self.add_special_mobjects(self.moving_mobjects, mobject) def get_unit_square(self, color=YELLOW, opacity=0.3, stroke_width=3): """ Returns a unit square for the current NumberPlane. """ square = self.square = Rectangle( color=color, width=self.plane.get_x_unit_size(), height=self.plane.get_y_unit_size(), stroke_color=color, stroke_width=stroke_width, fill_color=color, fill_opacity=opacity ) square.move_to(self.plane.coords_to_point(0, 0), DL) return square def add_unit_square(self, animate=False, **kwargs): """ Adds a unit square to the scene via self.get_unit_square. Parameters ---------- animate (bool) Whether or not to animate the addition with DrawBorderThenFill. **kwargs Any valid keyword arguments of self.get_unit_square() Returns ------- Square The unit square. """ square = self.get_unit_square(**kwargs) if animate: self.play( DrawBorderThenFill(square), Animation(Group(*self.moving_vectors)) ) self.add_transformable_mobject(square) self.bring_to_front(*self.moving_vectors) self.square = square return self def add_vector(self, vector, color=YELLOW, **kwargs): """ Adds a vector to the scene, and puts it in the special list self.moving_vectors. Parameters ---------- vector Union(Arrow,list,tuple,np.ndarray) It can be a pre-made graphical vector, or the coordinates of one. color (str) The string of the hex color of the vector. This is only taken into consideration if 'vector' is not an Arrow. Defaults to YELLOW. **kwargs Any valid keyword argument of VectorScene.add_vector. Returns ------- Arrow The arrow representing the vector. """ vector = VectorScene.add_vector( self, vector, color=color, **kwargs ) self.moving_vectors.append(vector) return vector def write_vector_coordinates(self, vector, **kwargs): """ Returns a column matrix indicating the vector coordinates, after writing them to the screen, and adding them to the special list self.foreground_mobjects Parameters ---------- vector (Arrow) The arrow representing the vector. **kwargs Any valid keyword arguments of VectorScene.write_vector_coordinates Returns ------- Matrix The column matrix representing the vector. """ coords = VectorScene.write_vector_coordinates(self, vector, **kwargs) self.add_foreground_mobject(coords) return coords def add_transformable_label( self, vector, label, transformation_name="L", new_label=None, **kwargs): """ Method for creating, and animating the addition of a transformable label for the vector. Parameters ---------- vector (Vector) The vector for which the label must be added. label (TexMobject,str) The TexMobject/string of the label. new_label (TexMobject,str,None) What the label should display after a Linear Transformation **kwargs Any valid keyword argument of get_vector_label Returns ------- TexMobject The TexMobject of the label. """ label_mob = self.label_vector(vector, label, **kwargs) if new_label: label_mob.target_text = new_label else: label_mob.target_text = "%s(%s)" % ( transformation_name, label_mob.get_tex_string() ) label_mob.vector = vector label_mob.kwargs = kwargs if "animate" in label_mob.kwargs: label_mob.kwargs.pop("animate") self.transformable_labels.append(label_mob) return label_mob def add_title(self, title, scale_factor=1.5, animate=False): """ Adds a title, after scaling it, adding a background rectangle, moving it to the top and adding it to foreground_mobjects adding it as a local variable of self. Returns the Scene. Parameters ---------- title (str,TexMobject,TextMobject) What the title should be. scale_factor (int,float=1.5) How much the title should be scaled by. animate (bool=False) Whether or not to animate the addition. Returns ------- LinearTransformationScene The scene with the title added to it. """ if not isinstance(title, Mobject): title = TextMobject(title).scale(scale_factor) title.to_edge(UP) title.add_background_rectangle() if animate: self.play(Write(title)) self.add_foreground_mobject(title) self.title = title return self def get_matrix_transformation(self, matrix): """ Returns a function corresponding to the linear transformation represented by the matrix passed. Parameters ---------- matrix (np.ndarray, list, tuple) The matrix. """ return self.get_transposed_matrix_transformation(np.array(matrix).T) def get_transposed_matrix_transformation(self, transposed_matrix): """ Returns a function corresponding to the linear transformation represented by the transposed matrix passed. Parameters ---------- matrix (np.ndarray, list, tuple) The matrix. """ transposed_matrix = np.array(transposed_matrix) if transposed_matrix.shape == (2, 2): new_matrix = np.identity(3) new_matrix[:2, :2] = transposed_matrix transposed_matrix = new_matrix elif transposed_matrix.shape != (3, 3): raise Exception("Matrix has bad dimensions") return lambda point: np.dot(point, transposed_matrix) def get_piece_movement(self, pieces): """ This method returns an animation that moves an arbitrary mobject in "pieces" to its corresponding .target value. If self.leave_ghost_vectors is True, ghosts of the original positions/mobjects are left on screen Parameters ---------- pieces (Union[list, tuple, np.array]) The pieces for which the movement must be shown. Returns ------- Animation The animation of the movement. """ start = VGroup(*pieces) target = VGroup(*[mob.target for mob in pieces]) if self.leave_ghost_vectors: self.add(start.copy().fade(0.7)) return Transform(start, target, lag_ratio=0) def get_moving_mobject_movement(self, func): """ This method returns an animation that moves a mobject in "self.moving_mobjects" to its corresponding .target value. func is a function that determines where the .target goes. Parameters ---------- func (function) The function that determines where the .target of the moving mobject goes. Returns ------- Animation The animation of the movement. """ for m in self.moving_mobjects: if m.target is None: m.target = m.copy() target_point = func(m.get_center()) m.target.move_to(target_point) return self.get_piece_movement(self.moving_mobjects) def get_vector_movement(self, func): """ This method returns an animation that moves a mobject in "self.moving_vectors" to its corresponding .target value. func is a function that determines where the .target goes. Parameters ---------- func (function) The function that determines where the .target of the moving mobject goes. Returns ------- Animation The animation of the movement. """ for v in self.moving_vectors: v.target = Vector(func(v.get_end()), color=v.get_color()) norm = get_norm(v.target.get_end()) if norm < 0.1: v.target.get_tip().scale_in_place(norm) return self.get_piece_movement(self.moving_vectors) def get_transformable_label_movement(self): """ This method returns an animation that moves all labels in "self.transformable_labels" to its corresponding .target . Returns ------- Animation The animation of the movement. """ for l in self.transformable_labels: l.target = self.get_vector_label( l.vector.target, l.target_text, **l.kwargs ) return self.get_piece_movement(self.transformable_labels) def apply_matrix(self, matrix, **kwargs): """ Applies the transformation represented by the given matrix to the number plane, and each vector/similar mobject on it. Parameters ---------- matrix (Union[np.ndarray, list, tuple]) The matrix. **kwargs Any valid keyword argument of self.apply_transposed_matrix() """ self.apply_transposed_matrix(np.array(matrix).T, **kwargs) def apply_inverse(self, matrix, **kwargs): """ This method applies the linear transformation represented by the inverse of the passed matrix to the number plane, and each vector/similar mobject on it. Parameters ---------- matrix (Union[np.ndarray, list, tuple]) The matrix whose inverse is to be applied. **kwargs Any valid keyword argument of self.apply_matrix() """ self.apply_matrix(np.linalg.inv(matrix), **kwargs) def apply_transposed_matrix(self, transposed_matrix, **kwargs): """ Applies the transformation represented by the given transposed matrix to the number plane, and each vector/similar mobject on it. Parameters ---------- matrix (Union[np.ndarray, list, tuple]) The matrix. **kwargs Any valid keyword argument of self.apply_function() """ func = self.get_transposed_matrix_transformation(transposed_matrix) if "path_arc" not in kwargs: net_rotation = np.mean([ angle_of_vector(func(RIGHT)), angle_of_vector(func(UP)) - np.pi / 2 ]) kwargs["path_arc"] = net_rotation self.apply_function(func, **kwargs) def apply_inverse_transpose(self, t_matrix, **kwargs): """ Applies the inverse of the transformation represented by the given transposed matrix to the number plane and each vector/similar mobject on it. Parameters ---------- matrix (Union[np.ndarray, list, tuple]) The matrix. **kwargs Any valid keyword argument of self.apply_transposed_matrix() """ t_inv = np.linalg.inv(np.array(t_matrix).T).T self.apply_transposed_matrix(t_inv, **kwargs) def apply_nonlinear_transformation(self, function, **kwargs): """ Applies the non-linear transformation represented by the given function to the number plane and each vector/similar mobject on it. Parameters ---------- function (Function) The function. **kwargs Any valid keyword argument of self.apply_function() """ self.plane.prepare_for_nonlinear_transform() self.apply_function(function, **kwargs) def apply_function(self, function, added_anims=[], **kwargs): """ Applies the given function to each of the mobjects in self.transformable_mobjects, and plays the animation showing this. Parameters ---------- function (Function) The function that affects each point of each mobject in self.transformable_mobjects. added_anims (list) Any other animations that need to be played simulataneously with this. **kwargs Any valid keyword argument of a self.play() call. """ if "run_time" not in kwargs: kwargs["run_time"] = 3 anims = [ ApplyPointwiseFunction(function, t_mob) for t_mob in self.transformable_mobjects ] + [ self.get_vector_movement(function), self.get_transformable_label_movement(), self.get_moving_mobject_movement(function), ] + [ Animation(f_mob) for f_mob in self.foreground_mobjects ] + added_anims self.play(*anims, **kwargs)