LinearTransformationScene¶

Qualified name: manim.scene.vector\_space\_scene.LinearTransformationScene

class LinearTransformationScene(include_background_plane=True, include_foreground_plane=True, background_plane_kwargs=None, foreground_plane_kwargs=None, show_coordinates=False, show_basis_vectors=True, basis_vector_stroke_width=6, i_hat_color=ManimColor('#83C167'), j_hat_color=ManimColor('#FC6255'), leave_ghost_vectors=False, **kwargs)[source]¶

Bases: VectorScene

This scene contains special methods that make it especially suitable for showing linear transformations.

Parameters:

include_background_plane (bool) – Whether or not to include the background plane in the scene.
include_foreground_plane (bool) – Whether or not to include the foreground plane in the scene.
background_plane_kwargs (dict[str, Any] | None) – Parameters to be passed to NumberPlane to adjust the background plane.
foreground_plane_kwargs (dict[str, Any] | None) – Parameters to be passed to NumberPlane to adjust the foreground plane.
show_coordinates (bool) – Whether or not to include the coordinates for the background plane.
show_basis_vectors (bool) – Whether to show the basis x_axis -> i_hat and y_axis -> j_hat vectors.
basis_vector_stroke_width (float) – The stroke_width of the basis vectors.
i_hat_color (ParsableManimColor) – The color of the i_hat vector.
j_hat_color (ParsableManimColor) – The color of the j_hat vector.
leave_ghost_vectors (bool) – Indicates the previous position of the basis vectors following a transformation.
kwargs (Any)

Examples

Example: LinearTransformationSceneExample ¶

from manim import *

class LinearTransformationSceneExample(LinearTransformationScene):
    def __init__(self, **kwargs):
        LinearTransformationScene.__init__(
            self,
            show_coordinates=True,
            leave_ghost_vectors=True,
            **kwargs
        )

    def construct(self):
        matrix = [[1, 1], [0, 1]]
        self.apply_matrix(matrix)
        self.wait()

class LinearTransformationSceneExample(LinearTransformationScene):
    def __init__(self, **kwargs):
        LinearTransformationScene.__init__(
            self,
            show_coordinates=True,
            leave_ghost_vectors=True,
            **kwargs
        )

    def construct(self):
        matrix = [[1, 1], [0, 1]]
        self.apply_matrix(matrix)
        self.wait()

Methods

`add_background_mobject`	Adds the mobjects to the special list self.background_mobjects.
`add_foreground_mobject`	Adds the mobjects to the special list self.foreground_mobjects.
`add_moving_mobject`	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.
`add_special_mobjects`	Adds mobjects to a separate list that can be tracked, if these mobjects have some extra importance.
`add_title`	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.
`add_transformable_label`	Method for creating, and animating the addition of a transformable label for the vector.
`add_transformable_mobject`	Adds the mobjects to the special list self.transformable_mobjects.
`add_unit_square`	Adds a unit square to the scene via self.get_unit_square.
`add_vector`	Adds a vector to the scene, and puts it in the special list self.moving_vectors.
`apply_function`	Applies the given function to each of the mobjects in self.transformable_mobjects, and plays the animation showing this.
`apply_inverse`	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.
`apply_inverse_transpose`	Applies the inverse of the transformation represented by the given transposed matrix to the number plane and each vector/similar mobject on it.
`apply_matrix`	Applies the transformation represented by the given matrix to the number plane, and each vector/similar mobject on it.
`apply_nonlinear_transformation`	Applies the non-linear transformation represented by the given function to the number plane and each vector/similar mobject on it.
`apply_transposed_matrix`	Applies the transformation represented by the given transposed matrix to the number plane, and each vector/similar mobject on it.
`get_ghost_vectors`	Returns all ghost vectors ever added to `self`.
`get_matrix_transformation`	Returns a function corresponding to the linear transformation represented by the matrix passed.
`get_moving_mobject_movement`	This method returns an animation that moves a mobject in "self.moving_mobjects" to its corresponding .target value.
`get_piece_movement`	This method returns an animation that moves an arbitrary mobject in "pieces" to its corresponding .target value.
`get_transformable_label_movement`	This method returns an animation that moves all labels in "self.transformable_labels" to its corresponding .target .
`get_transposed_matrix_transformation`	Returns a function corresponding to the linear transformation represented by the transposed matrix passed.
`get_unit_square`	Returns a unit square for the current NumberPlane.
`get_vector_movement`	This method returns an animation that moves a mobject in "self.moving_vectors" to its corresponding .target value.
`setup`	This is meant to be implemented by any scenes which are commonly subclassed, and have some common setup involved before the construct method is called.
`update_default_configs`
`write_vector_coordinates`	Returns a column matrix indicating the vector coordinates, after writing them to the screen, and adding them to the special list self.foreground_mobjects

Attributes

`camera`
`time`	The time since the start of the scene.

add_background_mobject(*mobjects)[source]¶

Adds the mobjects to the special list self.background_mobjects.

Parameters:: *mobjects (Mobject) – The mobjects to add to the list.
Return type:: None

add_foreground_mobject(*mobjects)[source]¶

Adds the mobjects to the special list self.foreground_mobjects.

Parameters:: *mobjects (Mobject) – The mobjects to add to the list
Return type:: None

add_moving_mobject(mobject, target_mobject=None)[source]¶

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 | None) – What the moving_mobject goes to, etc.

Return type:

None

add_special_mobjects(mob_list, *mobs_to_add)[source]¶

Adds mobjects to a separate list that can be tracked, if these mobjects have some extra importance.

Parameters:

mob_list (list[Mobject]) – The special list to which you want to add these mobjects.
*mobs_to_add (Mobject) – The mobjects to add.

Return type:

None

add_title(title, scale_factor=1.5, animate=False)[source]¶

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 | MathTex | Tex) – What the title should be.
scale_factor (float) – How much the title should be scaled by.
animate (bool) – Whether or not to animate the addition.

Returns:

The scene with the title added to it.

Return type:

LinearTransformationScene

add_transformable_label(vector, label, transformation_name='L', new_label=None, **kwargs)[source]¶

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 (MathTex | str) – The MathTex/string of the label.
transformation_name (str | MathTex) – The name to give the transformation as a label.
new_label (str | MathTex | None) – What the label should display after a Linear Transformation
**kwargs (Any) – Any valid keyword argument of get_vector_label

Returns:

The MathTex of the label.

Return type:

MathTex

add_transformable_mobject(*mobjects)[source]¶

Adds the mobjects to the special list self.transformable_mobjects.

Parameters:: *mobjects (Mobject) – The mobjects to add to the list.
Return type:: None

add_unit_square(animate=False, **kwargs)[source]¶

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) – Any valid keyword arguments of self.get_unit_square()

Returns:

The unit square.

Return type:

Square

add_vector(vector, color=ManimColor('#FFFF00'), animate=False, **kwargs)[source]¶

Adds a vector to the scene, and puts it in the special list self.moving_vectors.

Parameters:

vector (Arrow | list | tuple | ndarray) – It can be a pre-made graphical vector, or the coordinates of one.
color (ParsableManimColor) – 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) – Any valid keyword argument of VectorScene.add_vector.
animate (bool)
**kwargs

Returns:

The arrow representing the vector.

Return type:

Arrow

apply_function(function, added_anims=[], **kwargs)[source]¶

Applies the given function to each of the mobjects in self.transformable_mobjects, and plays the animation showing this.

Parameters:

function (MappingFunction) – The function that affects each point of each mobject in self.transformable_mobjects.
added_anims (list[Animation]) – Any other animations that need to be played simultaneously with this.
**kwargs (Any) – Any valid keyword argument of a self.play() call.

Return type:

None

apply_inverse(matrix, **kwargs)[source]¶

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 (ndarray | list | tuple) – The matrix whose inverse is to be applied.
**kwargs (Any) – Any valid keyword argument of self.apply_matrix()

Return type:

None

apply_inverse_transpose(t_matrix, **kwargs)[source]¶

Applies the inverse of the transformation represented by the given transposed matrix to the number plane and each vector/similar mobject on it.

Parameters:

t_matrix (ndarray | list | tuple) – The matrix.
**kwargs (Any) – Any valid keyword argument of self.apply_transposed_matrix()

Return type:

None

apply_matrix(matrix, **kwargs)[source]¶

Applies the transformation represented by the given matrix to the number plane, and each vector/similar mobject on it.

Parameters:

matrix (ndarray | list | tuple) – The matrix.
**kwargs (Any) – Any valid keyword argument of self.apply_transposed_matrix()

Return type:

None

apply_nonlinear_transformation(function, **kwargs)[source]¶

Applies the non-linear transformation represented by the given function to the number plane and each vector/similar mobject on it.

Parameters:

function (Callable[[ndarray], ndarray]) – The function.
**kwargs (Any) – Any valid keyword argument of self.apply_function()

Return type:

None

apply_transposed_matrix(transposed_matrix, **kwargs)[source]¶

Applies the transformation represented by the given transposed matrix to the number plane, and each vector/similar mobject on it.

Parameters:

transposed_matrix (ndarray | list | tuple) – The matrix.
**kwargs (Any) – Any valid keyword argument of self.apply_function()

Return type:

None

get_ghost_vectors()[source]¶

Returns all ghost vectors ever added to self. Each element is a VGroup of two ghost vectors.

Return type:: VGroup

get_matrix_transformation(matrix)[source]¶

Returns a function corresponding to the linear transformation represented by the matrix passed.

Parameters:: matrix (ndarray | list | tuple) – The matrix.
Return type:: Callable[[TypeAliasForwardRef(‘~manim.typing.Point3D’)], TypeAliasForwardRef(‘~manim.typing.Point3D’)]

get_moving_mobject_movement(func)[source]¶

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 (MappingFunction) – The function that determines where the .target of the moving mobject goes.
Returns:: The animation of the movement.
Return type:: Animation

get_piece_movement(pieces)[source]¶

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 (Iterable[Mobject]) – The pieces for which the movement must be shown.
Returns:: The animation of the movement.
Return type:: Animation

get_transformable_label_movement()[source]¶

This method returns an animation that moves all labels in “self.transformable_labels” to its corresponding .target .

Returns:: The animation of the movement.
Return type:: Animation

get_transposed_matrix_transformation(transposed_matrix)[source]¶

Returns a function corresponding to the linear transformation represented by the transposed matrix passed.

Parameters:: transposed_matrix (ndarray | list | tuple) – The matrix.
Return type:: Callable[[TypeAliasForwardRef(‘~manim.typing.Point3D’)], TypeAliasForwardRef(‘~manim.typing.Point3D’)]

get_unit_square(color=ManimColor('#FFFF00'), opacity=0.3, stroke_width=3)[source]¶

Returns a unit square for the current NumberPlane.

Parameters:

color (TypeAliasForwardRef('~manim.utils.color.core.ParsableManimColor') | Iterable[TypeAliasForwardRef('~manim.utils.color.core.ParsableManimColor')]) – The string of the hex color code of the color wanted.
opacity (float) – The opacity of the square
stroke_width (float) – The stroke_width in pixels of the border of the square

Return type:

Square

get_vector_movement(func)[source]¶

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 (MappingFunction) – The function that determines where the .target of the moving mobject goes.
Returns:: The animation of the movement.
Return type:: Animation

setup()[source]¶

This is meant to be implemented by any scenes which are commonly subclassed, and have some common setup involved before the construct method is called.

Return type:: None

write_vector_coordinates(vector, **kwargs)[source]¶

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 (Vector) – The arrow representing the vector.
**kwargs (Any) – Any valid keyword arguments of VectorScene.write_vector_coordinates

Returns:

The column matrix representing the vector.

Return type:

Matrix