""" This module provides access to math operations. [NOTE] Classes, methods and attributes that accept vectors also accept other numeric sequences, such as tuples, lists. The mathutils module provides the following classes: * Color, * Euler, * Matrix, * Quaternion, * Vector, mathutils.geometry.rst mathutils.bvhtree.rst mathutils.kdtree.rst mathutils.interpolate.rst mathutils.noise.rst :maxdepth: 1 :caption: Submodules ```../examples/mathutils.0.py``` """ import typing import collections.abc import typing_extensions import numpy.typing as npt from . import bvhtree as bvhtree from . import geometry as geometry from . import interpolate as interpolate from . import kdtree as kdtree from . import noise as noise class Color: """This object gives access to Colors in Blender.Most colors returned by Blender APIs are in scene linear color space, as defined by the OpenColorIO configuration. The notable exception is user interface theming colors, which are in sRGB color space.""" b: float """ Blue color channel.""" g: float """ Green color channel.""" h: float """ HSV Hue component in [0, 1].""" hsv: tuple[float, float, float] """ HSV Values in [0, 1].""" is_frozen: bool """ True when this object has been frozen (read-only).""" is_valid: bool """ True when the owner of this data is valid.""" is_wrapped: bool """ True when this object wraps external data (read-only).""" owner: typing.Any """ The item this is wrapping or None (read-only).""" r: float """ Red color channel.""" s: float """ HSV Saturation component in [0, 1].""" v: float """ HSV Value component in [0, 1].""" def copy(self) -> typing_extensions.Self: """Returns a copy of this color. :return: A copy of the color. """ def freeze(self) -> typing_extensions.Self: """Make this object immutable.After this the object can be hashed, used in dictionaries & sets. :return: An instance of this object. """ def from_aces_to_scene_linear(self) -> typing_extensions.Self: """Convert from ACES2065-1 linear to scene linear color space. :return: A color in scene linear color space. """ def from_acescg_to_scene_linear(self) -> typing_extensions.Self: """Convert from ACEScg linear to scene linear color space. :return: A color in scene linear color space. """ def from_rec2020_linear_to_scene_linear(self) -> typing_extensions.Self: """Convert from Rec.2020 linear color space to scene linear color space. :return: A color in scene linear color space. """ def from_rec709_linear_to_scene_linear(self) -> typing_extensions.Self: """Convert from Rec.709 linear color space to scene linear color space. :return: A color in scene linear color space. """ def from_scene_linear_to_aces(self) -> typing_extensions.Self: """Convert from scene linear to ACES2065-1 linear color space. :return: A color in ACES2065-1 linear color space. """ def from_scene_linear_to_acescg(self) -> typing_extensions.Self: """Convert from scene linear to ACEScg linear color space. :return: A color in ACEScg linear color space. """ def from_scene_linear_to_rec2020_linear(self) -> typing_extensions.Self: """Convert from scene linear to Rec.2020 linear color space. :return: A color in Rec.2020 linear color space. """ def from_scene_linear_to_rec709_linear(self) -> typing_extensions.Self: """Convert from scene linear to Rec.709 linear color space. :return: A color in Rec.709 linear color space. """ def from_scene_linear_to_srgb(self) -> typing_extensions.Self: """Convert from scene linear to sRGB color space. :return: A color in sRGB color space. """ def from_scene_linear_to_xyz_d65(self) -> typing_extensions.Self: """Convert from scene linear to CIE XYZ (Illuminant D65) color space. :return: A color in XYZ color space. """ def from_srgb_to_scene_linear(self) -> typing_extensions.Self: """Convert from sRGB to scene linear color space. :return: A color in scene linear color space. """ def from_xyz_d65_to_scene_linear(self) -> typing_extensions.Self: """Convert from CIE XYZ (Illuminant D65) to scene linear color space. :return: A color in scene linear color space. """ def __init__(self, rgb: collections.abc.Sequence[float] = (0.0, 0.0, 0.0)) -> None: """ :param rgb: """ def __get__(self, instance, owner) -> typing_extensions.Self: """ :param instance: :param owner: :return: """ def __set__( self, instance, value: collections.abc.Sequence[float] | typing_extensions.Self ) -> None: """ :param instance: :param value: """ def __add__( self, other: collections.abc.Sequence[float] | typing_extensions.Self ) -> typing_extensions.Self: """ :param other: :return: """ def __sub__( self, other: collections.abc.Sequence[float] | typing_extensions.Self ) -> typing_extensions.Self: """ :param other: :return: """ def __mul__(self, other: float) -> typing_extensions.Self: """ :param other: :return: """ def __truediv__(self, other: float) -> typing_extensions.Self: """ :param other: :return: """ def __radd__( self, other: collections.abc.Sequence[float] | typing_extensions.Self ) -> typing_extensions.Self: """ :param other: :return: """ def __rsub__( self, other: collections.abc.Sequence[float] | typing_extensions.Self ) -> typing_extensions.Self: """ :param other: :return: """ def __rmul__(self, other: float) -> typing_extensions.Self: """ :param other: :return: """ def __rtruediv__(self, other: float) -> typing_extensions.Self: """ :param other: :return: """ def __iadd__( self, other: collections.abc.Sequence[float] | typing_extensions.Self ) -> typing_extensions.Self: """ :param other: :return: """ def __isub__( self, other: collections.abc.Sequence[float] | typing_extensions.Self ) -> typing_extensions.Self: """ :param other: :return: """ def __imul__(self, other: float) -> typing_extensions.Self: """ :param other: :return: """ def __itruediv__(self, other: float) -> typing_extensions.Self: """ :param other: :return: """ @typing.overload def __getitem__(self, key: int) -> float: """ :param key: :return: """ @typing.overload def __getitem__(self, key: slice) -> tuple[float, ...]: """ :param key: :return: """ @typing.overload def __setitem__(self, key: int, value: float) -> None: """ :param key: :param value: """ @typing.overload def __setitem__( self, key: slice, value: collections.abc.Iterable[float] | Color ) -> None: """ :param key: :param value: """ class Euler: """This object gives access to Eulers in Blender.`Euler angles `__ on Wikipedia.""" is_frozen: bool """ True when this object has been frozen (read-only).""" is_valid: bool """ True when the owner of this data is valid.""" is_wrapped: bool """ True when this object wraps external data (read-only).""" order: typing.Literal["XYZ", "XZY", "YXZ", "YZX", "ZXY", "ZYX"] """ Euler rotation order.""" owner: typing.Any """ The item this is wrapping or None (read-only).""" x: float """ Euler axis angle in radians.""" y: float """ Euler axis angle in radians.""" z: float """ Euler axis angle in radians.""" def copy(self) -> typing_extensions.Self: """Returns a copy of this euler. :return: A copy of the euler. """ def freeze(self) -> typing_extensions.Self: """Make this object immutable.After this the object can be hashed, used in dictionaries & sets. :return: An instance of this object. """ def make_compatible( self, other: collections.abc.Sequence[float] | typing_extensions.Self, /, ) -> None: """Make this euler compatible with another, so interpolating between them works as intended. :param other: Other euler rotation. """ def rotate( self, other: Matrix | Quaternion | collections.abc.Sequence[collections.abc.Sequence[float]] | collections.abc.Sequence[float] | typing_extensions.Self, /, ) -> None: """Rotates the euler by another mathutils value. :param other: rotation component of mathutils value """ def rotate_axis( self, axis: typing.Literal["X", "Y", "Z"], angle: float, /, ) -> None: """Rotates the euler a certain amount, wrapping the result to produce a unique euler rotation (no 720 degree pitches). :param axis: An axis string. :param angle: angle in radians. """ def to_matrix(self) -> Matrix: """Return a matrix representation of the euler. :return: A 3x3 rotation matrix representation of the euler. """ def to_quaternion(self) -> Quaternion: """Return a quaternion representation of the euler. :return: Quaternion representation of the euler. """ def zero(self) -> None: """Set all values to zero.""" def __init__( self, angles: collections.abc.Sequence[float] = (0.0, 0.0, 0.0), order: str = "XYZ", ) -> None: """ :param angles: :param order: """ def __get__(self, instance, owner) -> typing_extensions.Self: """ :param instance: :param owner: :return: """ def __set__( self, instance, value: collections.abc.Sequence[float] | typing_extensions.Self ) -> None: """ :param instance: :param value: """ @typing.overload def __getitem__(self, key: int) -> float: """ :param key: :return: """ @typing.overload def __getitem__(self, key: slice) -> tuple[float, ...]: """ :param key: :return: """ @typing.overload def __setitem__(self, key: int, value: float) -> None: """ :param key: :param value: """ @typing.overload def __setitem__( self, key: slice, value: collections.abc.Iterable[float] | Euler ) -> None: """ :param key: :param value: """ class Matrix: """This object gives access to Matrices in Blender, supporting square and rectangular matrices from 2x2 up to 4x4. """ col: MatrixAccess """ Access the matrix by columns (read-only).""" is_frozen: bool """ True when this object has been frozen (read-only).""" is_identity: bool """ True if this is an identity matrix (read-only).""" is_negative: bool """ True if this matrix results in a negative scale, 3x3 and 4x4 only, (read-only).""" is_orthogonal: bool """ True if this matrix is orthogonal, 3x3 and 4x4 only, (read-only).""" is_orthogonal_axis_vectors: bool """ True if this matrix has orthogonal axis vectors, 3x3 and 4x4 only, (read-only).""" is_valid: bool """ True when the owner of this data is valid.""" is_wrapped: bool """ True when this object wraps external data (read-only).""" median_scale: float """ The average scale applied to each axis (read-only).""" owner: typing.Any """ The item this is wrapping or None (read-only).""" row: MatrixAccess """ Access the matrix by rows (default), (read-only).""" translation: Vector """ The translation component of the matrix.""" @classmethod def Diagonal( cls, vector: collections.abc.Sequence[float], /, ) -> typing_extensions.Self: """Create a diagonal (scaling) matrix using the values from the vector. :param vector: The vector of values for the diagonal. :return: A diagonal matrix. """ @classmethod def Identity( cls, size: int, /, ) -> typing_extensions.Self: """Create an identity matrix. :param size: The size of the identity matrix to construct [2, 4]. :return: A new identity matrix. """ @classmethod def LocRotScale( cls, location: None | collections.abc.Sequence[float], rotation: Euler | None | Quaternion | collections.abc.Sequence[collections.abc.Sequence[float]] | collections.abc.Sequence[float] | typing_extensions.Self, scale: None | collections.abc.Sequence[float], /, ) -> typing_extensions.Self: """Create a matrix combining translation, rotation and scale, acting as the inverse of the decompose() method.Any of the inputs may be replaced with None if not needed. :param location: The translation component. :param rotation: The rotation component as a 3x3 matrix, quaternion, euler or None for no rotation. :param scale: The scale component. :return: Combined transformation as a 4x4 matrix. """ @classmethod def OrthoProjection( cls, axis: collections.abc.Sequence[float] | typing.Literal["X", "Y", "XY", "XZ", "YZ"], size: int, /, ) -> typing_extensions.Self: """Create a matrix to represent an orthographic projection. :param axis: An axis string, where a single axis is for a 2D matrix. Or a vector for an arbitrary axis :param size: The size of the projection matrix to construct [2, 4]. :return: A new projection matrix. """ @classmethod def Rotation( cls, angle: float, size: int, axis: collections.abc.Sequence[float] | typing.Literal["X", "Y", "Z"] | None = [], /, ) -> typing_extensions.Self: """Create a matrix representing a rotation. :param angle: The angle of rotation desired, in radians. :param size: The size of the rotation matrix to construct [2, 4]. :param axis: an axis string or a 3D Vector Object (optional when size is 2). :return: A new rotation matrix. """ @classmethod def Scale( cls, factor: float, size: int, axis: collections.abc.Sequence[float] | None = [], /, ) -> typing_extensions.Self: """Create a matrix representing a scaling. :param factor: The factor of scaling to apply. :param size: The size of the scale matrix to construct [2, 4]. :param axis: Direction to influence scale. (optional). :return: A new scale matrix. """ @classmethod def Shear( cls, plane: typing.Literal["X", "Y", "XY", "XZ", "YZ"], size: int, factor: collections.abc.Sequence[float] | float, /, ) -> typing_extensions.Self: """Create a matrix to represent a shear transformation. :param plane: An axis string, where a single axis is for a 2D matrix only. :param size: The size of the shear matrix to construct [2, 4]. :param factor: The factor of shear to apply. For a 2 size matrix use a single float. For a 3 or 4 size matrix pass a pair of floats corresponding with the plane axis. :return: A new shear matrix. """ @classmethod def Translation( cls, vector: collections.abc.Sequence[float], /, ) -> typing_extensions.Self: """Create a matrix representing a translation. :param vector: The translation vector. :return: An identity matrix with a translation. """ def adjugate(self) -> None: """Set the matrix to its adjugate.`Adjugate matrix `__ on Wikipedia.""" def adjugated(self) -> typing_extensions.Self: """Return an adjugated copy of the matrix. :return: the adjugated matrix. """ def copy(self) -> typing_extensions.Self: """Returns a copy of this matrix. :return: A copy of the matrix. """ def decompose(self) -> tuple[Vector, Quaternion, Vector]: """Return the translation, rotation, and scale components of this 4x4 matrix. :return: Tuple of translation, rotation, and scale. """ def determinant(self) -> float: """Return the determinant of a matrix.`Determinant `__ on Wikipedia. :return: Return the determinant of a matrix. """ def freeze(self) -> typing_extensions.Self: """Make this object immutable.After this the object can be hashed, used in dictionaries & sets. :return: An instance of this object. """ def identity(self) -> None: """Set the matrix to the identity matrix.`Identity matrix `__ on Wikipedia.""" def invert( self, fallback: None | collections.abc.Sequence[collections.abc.Sequence[float]] | typing_extensions.Self | None = None, /, ) -> None: """Set the matrix to its inverse.`Inverse matrix `__ on Wikipedia. :param fallback: Set the matrix to this value when the inverse cannot be calculated (instead of raising a `ValueError` exception). """ def invert_safe(self) -> None: """Set the matrix to its inverse, will never error. If degenerated (e.g. zero scale on an axis), add some epsilon to its diagonal, to get an invertible one. If tweaked matrix is still degenerated, set to the identity matrix instead.`Inverse Matrix `__ on Wikipedia. """ def inverted( self, fallback: typing.Any | None = None, /, ) -> typing.Any | typing_extensions.Self: """Return an inverted copy of the matrix. :param fallback: return this when the inverse cant be calculated (instead of raising a `ValueError`). :return: The inverted matrix or fallback when given. """ def inverted_safe(self) -> typing_extensions.Self: """Return an inverted copy of the matrix, will never error. If degenerated (e.g. zero scale on an axis), add some epsilon to its diagonal, to get an invertible one. If tweaked matrix is still degenerated, return the identity matrix instead. :return: the inverted matrix. """ def lerp( self, other: collections.abc.Sequence[collections.abc.Sequence[float]] | typing_extensions.Self, factor: float, /, ) -> typing_extensions.Self: """Returns the interpolation of two matrices. Uses polar decomposition, see "Matrix Animation and Polar Decomposition", Shoemake and Duff, 1992. :param other: value to interpolate with. :param factor: The interpolation value in [0.0, 1.0]. :return: The interpolated matrix. """ def normalize(self) -> None: """Normalize each of the matrix columns (3x3 and 4x4 only).""" def normalized(self) -> typing_extensions.Self: """Return a column normalized matrix (3x3 and 4x4 only). :return: a column normalized matrix """ def resize_4x4(self) -> None: """Resize the matrix to 4x4.""" def rotate( self, other: Euler | Quaternion | collections.abc.Sequence[collections.abc.Sequence[float]] | collections.abc.Sequence[float] | typing_extensions.Self, /, ) -> None: """Rotates the matrix by another mathutils value. :param other: rotation component of mathutils value """ def to_2x2(self) -> typing_extensions.Self: """Return a 2x2 copy of this matrix. :return: a new matrix. """ def to_3x3(self) -> typing_extensions.Self: """Return a 3x3 copy of this matrix. :return: a new matrix. """ def to_4x4(self) -> typing_extensions.Self: """Return a 4x4 copy of this matrix. :return: a new matrix. """ def to_euler( self, order: typing.Literal["XYZ", "XZY", "YXZ", "YZX", "ZXY", "ZYX"] = "XYZ", euler_compat: Euler | None | collections.abc.Sequence[float] | None = None, /, ) -> Euler: """Return an Euler representation of the rotation matrix (3x3 or 4x4 matrix only). :param order: A rotation order string. :param euler_compat: Optional euler argument the new euler will be made compatible with (no axis flipping between them). Useful for converting a series of matrices to animation curves. :return: Euler representation of the matrix. """ def to_quaternion(self) -> Quaternion: """Return a quaternion representation of the rotation matrix. :return: Quaternion representation of the rotation matrix. """ def to_scale(self) -> Vector: """Return the scale part of a 3x3 or 4x4 matrix. :return: Return the scale of a matrix. """ def to_translation(self) -> Vector: """Return the translation part of a 4x4 matrix. :return: Return the translation of a matrix. """ def transpose(self) -> None: """Set the matrix to its transpose.`Transpose `__ on Wikipedia.""" def transposed(self) -> typing_extensions.Self: """Return a new, transposed matrix. :return: a transposed matrix """ def zero(self) -> None: """Set all the matrix values to zero.""" def __init__( self, rows: collections.abc.Sequence[collections.abc.Sequence[float]] = ( (1.0, 0.0, 0.0, 0.0), (0.0, 1.0, 0.0, 0.0), (0.0, 0.0, 1.0, 0.0), (0.0, 0.0, 0.0, 1.0), ), ) -> None: """ :param rows: """ def __get__(self, instance, owner) -> typing_extensions.Self: """ :param instance: :param owner: :return: """ def __set__( self, instance, value: collections.abc.Sequence[collections.abc.Sequence[float]] | typing_extensions.Self, ) -> None: """ :param instance: :param value: """ @typing.overload def __getitem__(self, key: int) -> Vector: """ :param key: :return: """ @typing.overload def __getitem__(self, key: slice) -> tuple[Vector, ...]: """ :param key: :return: """ @typing.overload def __setitem__( self, key: int, value: Vector | collections.abc.Iterable[float] ) -> None: """ :param key: :param value: """ @typing.overload def __setitem__( self, key: slice, value: collections.abc.Iterable[Vector | collections.abc.Iterable[float]] | Matrix, ) -> None: """ :param key: :param value: """ def __len__(self) -> int: """ :return: """ def __add__( self, other: collections.abc.Sequence[collections.abc.Sequence[float]] | typing_extensions.Self, ) -> typing_extensions.Self: """ :param other: :return: """ def __sub__( self, other: collections.abc.Sequence[collections.abc.Sequence[float]] | typing_extensions.Self, ) -> typing_extensions.Self: """ :param other: :return: """ def __mul__(self, other: float) -> typing_extensions.Self: """ :param other: :return: """ @typing.overload def __matmul__( self, other: collections.abc.Sequence[collections.abc.Sequence[float]] | typing_extensions.Self, ) -> typing_extensions.Self: """ :param other: :return: """ @typing.overload def __matmul__(self, other: Vector | collections.abc.Sequence[float]) -> Vector: """ :param other: :return: """ def __radd__( self, other: collections.abc.Sequence[collections.abc.Sequence[float]] | typing_extensions.Self, ) -> typing_extensions.Self: """ :param other: :return: """ def __rsub__( self, other: collections.abc.Sequence[collections.abc.Sequence[float]] | typing_extensions.Self, ) -> typing_extensions.Self: """ :param other: :return: """ def __rmul__(self, other: float) -> typing_extensions.Self: """ :param other: :return: """ def __imul__(self, other: float) -> typing_extensions.Self: """ :param other: :return: """ class MatrixAccess: """An indexable type for accessing matrix rows or columns as `Vector` types.""" class Quaternion: """This object gives access to Quaternions in Blender.The constructor takes arguments in various forms:""" angle: float """ Angle of the quaternion.""" axis: Vector """ Quaternion axis as a vector.""" is_frozen: bool """ True when this object has been frozen (read-only).""" is_valid: bool """ True when the owner of this data is valid.""" is_wrapped: bool """ True when this object wraps external data (read-only).""" magnitude: float """ Size of the quaternion (read-only).""" owner: typing.Any """ The item this is wrapping or None (read-only).""" w: float """ Quaternion component value.""" x: float """ Quaternion component value.""" y: float """ Quaternion component value.""" z: float """ Quaternion component value.""" def conjugate(self) -> None: """Set the quaternion to its conjugate (negate x, y, z).""" def conjugated(self) -> typing_extensions.Self: """Return a new conjugated quaternion. :return: a new quaternion. """ def copy(self) -> typing_extensions.Self: """Returns a copy of this quaternion. :return: A copy of the quaternion. """ def cross( self, other: collections.abc.Sequence[float] | typing_extensions.Self, /, ) -> typing_extensions.Self: """Return the cross product of this quaternion and another. :param other: The other quaternion to perform the cross product with. :return: The cross product. """ def dot( self, other: collections.abc.Sequence[float] | typing_extensions.Self, /, ) -> float: """Return the dot product of this quaternion and another. :param other: The other quaternion to perform the dot product with. :return: The dot product. """ def freeze(self) -> typing_extensions.Self: """Make this object immutable.After this the object can be hashed, used in dictionaries & sets. :return: An instance of this object. """ def identity(self) -> None: """Set the quaternion to an identity quaternion.""" def invert(self) -> None: """Set the quaternion to its inverse.""" def inverted(self) -> typing_extensions.Self: """Return a new, inverted quaternion. :return: the inverted value. """ def make_compatible( self, other: collections.abc.Sequence[float] | typing_extensions.Self, /, ) -> None: """Make this quaternion compatible with another, so interpolating between them works as intended. :param other: The reference quaternion to make this one compatible with. """ def negate(self) -> None: """Set the quaternion to its negative.""" def normalize(self) -> None: """Normalize the quaternion.""" def normalized(self) -> typing_extensions.Self: """Return a new normalized quaternion. :return: a normalized copy. """ def rotate( self, other: Euler | Matrix | collections.abc.Sequence[collections.abc.Sequence[float]] | collections.abc.Sequence[float] | typing_extensions.Self, /, ) -> None: """Rotates the quaternion by another mathutils value. :param other: rotation component of mathutils value """ def rotation_difference( self, other: collections.abc.Sequence[float] | typing_extensions.Self, /, ) -> typing_extensions.Self: """Returns a quaternion representing the rotational difference. :param other: second quaternion. :return: the rotational difference between the two quat rotations. """ def slerp( self, other: collections.abc.Sequence[float] | typing_extensions.Self, factor: float, /, ) -> typing_extensions.Self: """Returns the interpolation of two quaternions. :param other: value to interpolate with. :param factor: The interpolation value in [0.0, 1.0]. :return: The interpolated rotation. """ def to_axis_angle(self) -> tuple[Vector, float]: """Return the axis, angle representation of the quaternion. :return: Axis, angle. """ def to_euler( self, order: typing.Literal["XYZ", "XZY", "YXZ", "YZX", "ZXY", "ZYX"] = "XYZ", euler_compat: Euler | None | collections.abc.Sequence[float] | None = None, /, ) -> Euler: """Return Euler representation of the quaternion. :param order: Rotation order. :param euler_compat: Optional euler argument the new euler will be made compatible with (no axis flipping between them). Useful for converting a series of quaternions to animation curves. :return: Euler representation of the quaternion. """ def to_exponential_map(self) -> Vector: """Return the exponential map representation of the quaternion.This representation consists of the rotation axis multiplied by the rotation angle. Such a representation is useful for interpolation between multiple orientations.To convert back to a quaternion, pass it to the `Quaternion` constructor. :return: 3D exponential map. """ def to_matrix(self) -> Matrix: """Return a matrix representation of the quaternion. :return: A 3x3 rotation matrix representation of the quaternion. """ def to_swing_twist( self, axis: typing.Literal["X", "Y", "Z"], /, ) -> tuple[Quaternion, float]: """Split the rotation into a swing quaternion with the specified axis fixed at zero, and the remaining twist rotation angle. :param axis: Twist axis as a string. :return: Swing, twist angle. """ def __init__( self, seq: Vector | collections.abc.Sequence[float] = (1.0, 0.0, 0.0, 0.0), angle: float = 0.0, ) -> None: """ :param seq: :param angle: """ def __get__(self, instance, owner) -> typing_extensions.Self: """ :param instance: :param owner: :return: """ def __set__( self, instance, value: collections.abc.Sequence[float] | typing_extensions.Self ) -> None: """ :param instance: :param value: """ def __len__(self) -> int: """ :return: """ @typing.overload def __getitem__(self, key: int) -> float: """ :param key: :return: """ @typing.overload def __getitem__(self, key: slice) -> tuple[float, ...]: """ :param key: :return: """ @typing.overload def __setitem__(self, key: int, value: float) -> None: """ :param key: :param value: """ @typing.overload def __setitem__( self, key: slice, value: collections.abc.Iterable[float] | Quaternion ) -> None: """ :param key: :param value: """ def __add__( self, other: collections.abc.Sequence[float] | typing_extensions.Self ) -> typing_extensions.Self: """ :param other: :return: """ def __sub__( self, other: collections.abc.Sequence[float] | typing_extensions.Self ) -> typing_extensions.Self: """ :param other: :return: """ def __mul__( self, other: collections.abc.Sequence[float] | float | typing_extensions.Self ) -> typing_extensions.Self: """ :param other: :return: """ @typing.overload def __matmul__(self, other: typing_extensions.Self) -> typing_extensions.Self: """ :param other: :return: """ @typing.overload def __matmul__(self, other: Vector) -> Vector: """ :param other: :return: """ def __radd__( self, other: collections.abc.Sequence[float] | typing_extensions.Self ) -> typing_extensions.Self: """ :param other: :return: """ def __rsub__( self, other: collections.abc.Sequence[float] | typing_extensions.Self ) -> typing_extensions.Self: """ :param other: :return: """ def __rmul__( self, other: collections.abc.Sequence[float] | float | typing_extensions.Self ) -> typing_extensions.Self: """ :param other: :return: """ def __imul__( self, other: collections.abc.Sequence[float] | float | typing_extensions.Self ) -> typing_extensions.Self: """ :param other: :return: """ class Vector: """This object gives access to Vectors in Blender.""" is_frozen: bool """ True when this object has been frozen (read-only).""" is_valid: bool """ True when the owner of this data is valid.""" is_wrapped: bool """ True when this object wraps external data (read-only).""" length: float """ Vector Length.""" length_squared: float """ Vector length squared (v.dot(v)).""" magnitude: float """ Vector Length.""" owner: typing.Any """ The item this is wrapping or None (read-only).""" w: float """ Vector W axis (4D Vectors only).""" ww: typing_extensions.Self www: typing_extensions.Self wwww: typing_extensions.Self wwwx: typing_extensions.Self wwwy: typing_extensions.Self wwwz: typing_extensions.Self wwx: typing_extensions.Self wwxw: typing_extensions.Self wwxx: typing_extensions.Self wwxy: typing_extensions.Self wwxz: typing_extensions.Self wwy: typing_extensions.Self wwyw: typing_extensions.Self wwyx: typing_extensions.Self wwyy: typing_extensions.Self wwyz: typing_extensions.Self wwz: typing_extensions.Self wwzw: typing_extensions.Self wwzx: typing_extensions.Self wwzy: typing_extensions.Self wwzz: typing_extensions.Self wx: typing_extensions.Self wxw: typing_extensions.Self wxww: typing_extensions.Self wxwx: typing_extensions.Self wxwy: typing_extensions.Self wxwz: typing_extensions.Self wxx: typing_extensions.Self wxxw: typing_extensions.Self wxxx: typing_extensions.Self wxxy: typing_extensions.Self wxxz: typing_extensions.Self wxy: typing_extensions.Self wxyw: typing_extensions.Self wxyx: typing_extensions.Self wxyy: typing_extensions.Self wxyz: typing_extensions.Self wxz: typing_extensions.Self wxzw: typing_extensions.Self wxzx: typing_extensions.Self wxzy: typing_extensions.Self wxzz: typing_extensions.Self wy: typing_extensions.Self wyw: typing_extensions.Self wyww: typing_extensions.Self wywx: typing_extensions.Self wywy: typing_extensions.Self wywz: typing_extensions.Self wyx: typing_extensions.Self wyxw: typing_extensions.Self wyxx: typing_extensions.Self wyxy: typing_extensions.Self wyxz: typing_extensions.Self wyy: typing_extensions.Self wyyw: typing_extensions.Self wyyx: typing_extensions.Self wyyy: typing_extensions.Self wyyz: typing_extensions.Self wyz: typing_extensions.Self wyzw: typing_extensions.Self wyzx: typing_extensions.Self wyzy: typing_extensions.Self wyzz: typing_extensions.Self wz: typing_extensions.Self wzw: typing_extensions.Self wzww: typing_extensions.Self wzwx: typing_extensions.Self wzwy: typing_extensions.Self wzwz: typing_extensions.Self wzx: typing_extensions.Self wzxw: typing_extensions.Self wzxx: typing_extensions.Self wzxy: typing_extensions.Self wzxz: typing_extensions.Self wzy: typing_extensions.Self wzyw: typing_extensions.Self wzyx: typing_extensions.Self wzyy: typing_extensions.Self wzyz: typing_extensions.Self wzz: typing_extensions.Self wzzw: typing_extensions.Self wzzx: typing_extensions.Self wzzy: typing_extensions.Self wzzz: typing_extensions.Self x: float """ Vector X axis.""" xw: typing_extensions.Self xww: typing_extensions.Self xwww: typing_extensions.Self xwwx: typing_extensions.Self xwwy: typing_extensions.Self xwwz: typing_extensions.Self xwx: typing_extensions.Self xwxw: typing_extensions.Self xwxx: typing_extensions.Self xwxy: typing_extensions.Self xwxz: typing_extensions.Self xwy: typing_extensions.Self xwyw: typing_extensions.Self xwyx: typing_extensions.Self xwyy: typing_extensions.Self xwyz: typing_extensions.Self xwz: typing_extensions.Self xwzw: typing_extensions.Self xwzx: typing_extensions.Self xwzy: typing_extensions.Self xwzz: typing_extensions.Self xx: typing_extensions.Self xxw: typing_extensions.Self xxww: typing_extensions.Self xxwx: typing_extensions.Self xxwy: typing_extensions.Self xxwz: typing_extensions.Self xxx: typing_extensions.Self xxxw: typing_extensions.Self xxxx: typing_extensions.Self xxxy: typing_extensions.Self xxxz: typing_extensions.Self xxy: typing_extensions.Self xxyw: typing_extensions.Self xxyx: typing_extensions.Self xxyy: typing_extensions.Self xxyz: typing_extensions.Self xxz: typing_extensions.Self xxzw: typing_extensions.Self xxzx: typing_extensions.Self xxzy: typing_extensions.Self xxzz: typing_extensions.Self xy: typing_extensions.Self xyw: typing_extensions.Self xyww: typing_extensions.Self xywx: typing_extensions.Self xywy: typing_extensions.Self xywz: typing_extensions.Self xyx: typing_extensions.Self xyxw: typing_extensions.Self xyxx: typing_extensions.Self xyxy: typing_extensions.Self xyxz: typing_extensions.Self xyy: typing_extensions.Self xyyw: typing_extensions.Self xyyx: typing_extensions.Self xyyy: typing_extensions.Self xyyz: typing_extensions.Self xyz: typing_extensions.Self xyzw: typing_extensions.Self xyzx: typing_extensions.Self xyzy: typing_extensions.Self xyzz: typing_extensions.Self xz: typing_extensions.Self xzw: typing_extensions.Self xzww: typing_extensions.Self xzwx: typing_extensions.Self xzwy: typing_extensions.Self xzwz: typing_extensions.Self xzx: typing_extensions.Self xzxw: typing_extensions.Self xzxx: typing_extensions.Self xzxy: typing_extensions.Self xzxz: typing_extensions.Self xzy: typing_extensions.Self xzyw: typing_extensions.Self xzyx: typing_extensions.Self xzyy: typing_extensions.Self xzyz: typing_extensions.Self xzz: typing_extensions.Self xzzw: typing_extensions.Self xzzx: typing_extensions.Self xzzy: typing_extensions.Self xzzz: typing_extensions.Self y: float """ Vector Y axis.""" yw: typing_extensions.Self yww: typing_extensions.Self ywww: typing_extensions.Self ywwx: typing_extensions.Self ywwy: typing_extensions.Self ywwz: typing_extensions.Self ywx: typing_extensions.Self ywxw: typing_extensions.Self ywxx: typing_extensions.Self ywxy: typing_extensions.Self ywxz: typing_extensions.Self ywy: typing_extensions.Self ywyw: typing_extensions.Self ywyx: typing_extensions.Self ywyy: typing_extensions.Self ywyz: typing_extensions.Self ywz: typing_extensions.Self ywzw: typing_extensions.Self ywzx: typing_extensions.Self ywzy: typing_extensions.Self ywzz: typing_extensions.Self yx: typing_extensions.Self yxw: typing_extensions.Self yxww: typing_extensions.Self yxwx: typing_extensions.Self yxwy: typing_extensions.Self yxwz: typing_extensions.Self yxx: typing_extensions.Self yxxw: typing_extensions.Self yxxx: typing_extensions.Self yxxy: typing_extensions.Self yxxz: typing_extensions.Self yxy: typing_extensions.Self yxyw: typing_extensions.Self yxyx: typing_extensions.Self yxyy: typing_extensions.Self yxyz: typing_extensions.Self yxz: typing_extensions.Self yxzw: typing_extensions.Self yxzx: typing_extensions.Self yxzy: typing_extensions.Self yxzz: typing_extensions.Self yy: typing_extensions.Self yyw: typing_extensions.Self yyww: typing_extensions.Self yywx: typing_extensions.Self yywy: typing_extensions.Self yywz: typing_extensions.Self yyx: typing_extensions.Self yyxw: typing_extensions.Self yyxx: typing_extensions.Self yyxy: typing_extensions.Self yyxz: typing_extensions.Self yyy: typing_extensions.Self yyyw: typing_extensions.Self yyyx: typing_extensions.Self yyyy: typing_extensions.Self yyyz: typing_extensions.Self yyz: typing_extensions.Self yyzw: typing_extensions.Self yyzx: typing_extensions.Self yyzy: typing_extensions.Self yyzz: typing_extensions.Self yz: typing_extensions.Self yzw: typing_extensions.Self yzww: typing_extensions.Self yzwx: typing_extensions.Self yzwy: typing_extensions.Self yzwz: typing_extensions.Self yzx: typing_extensions.Self yzxw: typing_extensions.Self yzxx: typing_extensions.Self yzxy: typing_extensions.Self yzxz: typing_extensions.Self yzy: typing_extensions.Self yzyw: typing_extensions.Self yzyx: typing_extensions.Self yzyy: typing_extensions.Self yzyz: typing_extensions.Self yzz: typing_extensions.Self yzzw: typing_extensions.Self yzzx: typing_extensions.Self yzzy: typing_extensions.Self yzzz: typing_extensions.Self z: float """ Vector Z axis (3D Vectors only).""" zw: typing_extensions.Self zww: typing_extensions.Self zwww: typing_extensions.Self zwwx: typing_extensions.Self zwwy: typing_extensions.Self zwwz: typing_extensions.Self zwx: typing_extensions.Self zwxw: typing_extensions.Self zwxx: typing_extensions.Self zwxy: typing_extensions.Self zwxz: typing_extensions.Self zwy: typing_extensions.Self zwyw: typing_extensions.Self zwyx: typing_extensions.Self zwyy: typing_extensions.Self zwyz: typing_extensions.Self zwz: typing_extensions.Self zwzw: typing_extensions.Self zwzx: typing_extensions.Self zwzy: typing_extensions.Self zwzz: typing_extensions.Self zx: typing_extensions.Self zxw: typing_extensions.Self zxww: typing_extensions.Self zxwx: typing_extensions.Self zxwy: typing_extensions.Self zxwz: typing_extensions.Self zxx: typing_extensions.Self zxxw: typing_extensions.Self zxxx: typing_extensions.Self zxxy: typing_extensions.Self zxxz: typing_extensions.Self zxy: typing_extensions.Self zxyw: typing_extensions.Self zxyx: typing_extensions.Self zxyy: typing_extensions.Self zxyz: typing_extensions.Self zxz: typing_extensions.Self zxzw: typing_extensions.Self zxzx: typing_extensions.Self zxzy: typing_extensions.Self zxzz: typing_extensions.Self zy: typing_extensions.Self zyw: typing_extensions.Self zyww: typing_extensions.Self zywx: typing_extensions.Self zywy: typing_extensions.Self zywz: typing_extensions.Self zyx: typing_extensions.Self zyxw: typing_extensions.Self zyxx: typing_extensions.Self zyxy: typing_extensions.Self zyxz: typing_extensions.Self zyy: typing_extensions.Self zyyw: typing_extensions.Self zyyx: typing_extensions.Self zyyy: typing_extensions.Self zyyz: typing_extensions.Self zyz: typing_extensions.Self zyzw: typing_extensions.Self zyzx: typing_extensions.Self zyzy: typing_extensions.Self zyzz: typing_extensions.Self zz: typing_extensions.Self zzw: typing_extensions.Self zzww: typing_extensions.Self zzwx: typing_extensions.Self zzwy: typing_extensions.Self zzwz: typing_extensions.Self zzx: typing_extensions.Self zzxw: typing_extensions.Self zzxx: typing_extensions.Self zzxy: typing_extensions.Self zzxz: typing_extensions.Self zzy: typing_extensions.Self zzyw: typing_extensions.Self zzyx: typing_extensions.Self zzyy: typing_extensions.Self zzyz: typing_extensions.Self zzz: typing_extensions.Self zzzw: typing_extensions.Self zzzx: typing_extensions.Self zzzy: typing_extensions.Self zzzz: typing_extensions.Self @classmethod def Fill( cls, size: int, fill: float = 0.0, /, ) -> typing_extensions.Self: """Create a vector of length size with all values set to fill. :param size: The length of the vector to be created. :param fill: The value used to fill the vector. :return: A new vector. """ @classmethod def Linspace( cls, start: float, stop: float, size: int, /, ) -> typing_extensions.Self: """Create a vector of the specified size which is filled with linearly spaced values between start and stop values. :param start: The start of the range used to fill the vector. :param stop: The end of the range used to fill the vector. :param size: The size of the vector to be created. :return: A new vector. """ @classmethod def Range( cls, start: int, stop: int, step: int = 1, /, ) -> typing_extensions.Self: """Create a vector filled with a range of values.This method can also be called with a single argument, in which case the argument is interpreted as stop and start defaults to 0. :param start: The start of the range used to fill the vector. :param stop: The end of the range used to fill the vector. :param step: The step between successive values in the vector. :return: A new vector. """ @classmethod def Repeat( cls, vector: collections.abc.Sequence[float] | typing_extensions.Self, size: int, /, ) -> typing_extensions.Self: """Create a vector by repeating the values in vector until the required size is reached. :param vector: The vector to draw values from. :param size: The size of the vector to be created. :return: A new vector. """ def angle( self, other: collections.abc.Sequence[float] | typing_extensions.Self, fallback: typing.Any | None = None, /, ) -> float | typing.Any: """Return the angle between two vectors. :param other: another vector to compare the angle with :param fallback: return this when the angle cant be calculated (zero length vector), (instead of raising a `ValueError`). :return: angle in radians or fallback when given """ def angle_signed( self, other: collections.abc.Sequence[float] | typing_extensions.Self, fallback: typing.Any | None = None, /, ) -> float | typing.Any: """Return the signed angle between two 2D vectors (clockwise is positive). :param other: another vector to compare the angle with :param fallback: return this when the angle cant be calculated (zero length vector), (instead of raising a `ValueError`). :return: angle in radians or fallback when given """ def copy(self) -> typing_extensions.Self: """Returns a copy of this vector. :return: A copy of the vector. """ def cross( self, other: collections.abc.Sequence[float] | typing_extensions.Self, /, ) -> float | typing_extensions.Self: """Return the cross product of this vector and another. :param other: The other vector to perform the cross product with. :return: The cross product as a vector or a float when 2D vectors are used. """ def dot( self, other: collections.abc.Sequence[float] | typing_extensions.Self, /, ) -> float: """Return the dot product of this vector and another. :param other: The other vector to perform the dot product with. :return: The dot product. """ def freeze(self) -> typing_extensions.Self: """Make this object immutable.After this the object can be hashed, used in dictionaries & sets. :return: An instance of this object. """ def lerp( self, other: collections.abc.Sequence[float] | typing_extensions.Self, factor: float, /, ) -> typing_extensions.Self: """Returns the interpolation of two vectors. :param other: value to interpolate with. :param factor: The interpolation value in [0.0, 1.0]. :return: The interpolated vector. """ def negate(self) -> None: """Set all values to their negative.""" def normalize(self) -> None: """Normalize the vector, making the length of the vector always 1.0.""" def normalized(self) -> typing_extensions.Self: """Return a new, normalized vector. :return: a normalized copy of the vector """ def orthogonal(self) -> typing_extensions.Self: """Return a perpendicular vector. :return: a new vector 90 degrees from this vector. """ def project( self, other: collections.abc.Sequence[float] | typing_extensions.Self, /, ) -> typing_extensions.Self: """Return the projection of this vector onto the other. :param other: second vector. :return: the parallel projection vector """ def reflect( self, mirror: collections.abc.Sequence[float] | typing_extensions.Self, /, ) -> typing_extensions.Self: """Return the reflection vector from the mirror argument. :param mirror: This vector could be a normal from the reflecting surface. :return: The reflected vector matching the size of this vector. """ def resize( self, size: int, /, ) -> None: """Resize the vector to have size number of elements. :param size: The new size of the vector. """ def resize_2d(self) -> None: """Resize the vector to 2D (x, y).""" def resize_3d(self) -> None: """Resize the vector to 3D (x, y, z).""" def resize_4d(self) -> None: """Resize the vector to 4D (x, y, z, w).""" def resized( self, size: int, /, ) -> typing_extensions.Self: """Return a resized copy of the vector with size number of elements. :param size: The new size of the vector. :return: A new vector. """ def rotate( self, other: Euler | Matrix | Quaternion | collections.abc.Sequence[collections.abc.Sequence[float]] | collections.abc.Sequence[float], /, ) -> None: """Rotate the vector by a rotation value. :param other: rotation component of mathutils value """ def rotation_difference( self, other: collections.abc.Sequence[float] | typing_extensions.Self, /, ) -> Quaternion: """Returns a quaternion representing the rotational difference between this vector and another. :param other: second vector. :return: the rotational difference between the two vectors. """ def slerp( self, other: collections.abc.Sequence[float] | typing_extensions.Self, factor: float, fallback: typing.Any | None = None, /, ) -> typing_extensions.Self: """Returns the interpolation of two non-zero vectors (spherical coordinates). :param other: value to interpolate with. :param factor: The interpolation value typically in [0.0, 1.0]. :param fallback: return this when the vector cant be calculated (zero length vector or direct opposites), (instead of raising a `ValueError`). :return: The interpolated vector. """ def to_2d(self) -> typing_extensions.Self: """Return a 2d copy of the vector. :return: a new vector """ def to_3d(self) -> typing_extensions.Self: """Return a 3d copy of the vector. :return: a new vector """ def to_4d(self) -> typing_extensions.Self: """Return a 4d copy of the vector. :return: a new vector """ def to_track_quat( self, track: typing.Literal["X", "Y", "Z", "-X", "-Y", "-Z"] = "Z", up: typing.Literal["X", "Y", "Z"] = "Y", /, ) -> Quaternion: """Return a quaternion rotation from the vector and the track and up axis. :param track: Track axis string. :param up: Up axis string. :return: rotation from the vector and the track and up axis. """ def to_tuple( self, precision: int = -1, /, ) -> tuple[float, ...]: """Return this vector as a tuple with a given precision. :param precision: The number to round the value to in [-1, 21]. :return: the values of the vector rounded by precision """ def zero(self) -> None: """Set all values to zero.""" def __init__(self, seq: collections.abc.Sequence[float] = (0.0, 0.0, 0.0)) -> None: """ :param seq: """ def __get__(self, instance, owner) -> typing_extensions.Self: """ :param instance: :param owner: :return: """ def __set__( self, instance, value: collections.abc.Sequence[float] | typing_extensions.Self ) -> None: """ :param instance: :param value: """ def __len__(self) -> int: """ :return: """ @typing.overload def __getitem__(self, key: int) -> float: """ :param key: :return: """ @typing.overload def __getitem__(self, key: slice) -> tuple[float, ...]: """ :param key: :return: """ @typing.overload def __setitem__(self, key: int, value: float) -> None: """ :param key: :param value: """ @typing.overload def __setitem__( self, key: slice, value: collections.abc.Iterable[float] | Vector ) -> None: """ :param key: :param value: """ def __neg__(self) -> typing_extensions.Self: """ :return: """ def __add__( self, other: collections.abc.Sequence[float] | typing_extensions.Self ) -> typing_extensions.Self: """ :param other: :return: """ def __sub__( self, other: collections.abc.Sequence[float] | typing_extensions.Self ) -> typing_extensions.Self: """ :param other: :return: """ @typing.overload def __mul__(self, other: float) -> typing_extensions.Self: """ :param other: :return: """ @typing.overload def __mul__( self, other: collections.abc.Sequence[float] | typing_extensions.Self ) -> typing_extensions.Self: """ :param other: :return: """ def __truediv__(self, other: float) -> typing_extensions.Self: """ :param other: :return: """ @typing.overload def __matmul__( self, other: collections.abc.Sequence[float] | typing_extensions.Self ) -> float: """ :param other: :return: """ @typing.overload def __matmul__( self, other: Matrix | collections.abc.Sequence[collections.abc.Sequence[float]] ) -> typing_extensions.Self: """ :param other: :return: """ def __radd__( self, other: collections.abc.Sequence[float] | typing_extensions.Self ) -> typing_extensions.Self: """ :param other: :return: """ def __rsub__( self, other: collections.abc.Sequence[float] | typing_extensions.Self ) -> typing_extensions.Self: """ :param other: :return: """ def __rmul__(self, other: float) -> typing_extensions.Self: """ :param other: :return: """ def __rtruediv__(self, other: float) -> typing_extensions.Self: """ :param other: :return: """ def __iadd__( self, other: collections.abc.Sequence[float] | typing_extensions.Self ) -> typing_extensions.Self: """ :param other: :return: """ def __isub__( self, other: collections.abc.Sequence[float] | typing_extensions.Self ) -> typing_extensions.Self: """ :param other: :return: """ def __imul__(self, other: float) -> typing_extensions.Self: """ :param other: :return: """ def __itruediv__(self, other: float) -> typing_extensions.Self: """ :param other: :return: """