Math Types & Utilities (mathutils)

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,

Submodules

import mathutils
from math import radians

vec = mathutils.Vector((1.0, 2.0, 3.0))

mat_rot = mathutils.Matrix.Rotation(radians(90.0), 4, 'X')
mat_trans = mathutils.Matrix.Translation(vec)

mat = mat_trans @ mat_rot
mat.invert()

mat3 = mat.to_3x3()
quat1 = mat.to_quaternion()
quat2 = mat3.to_quaternion()

quat_diff = quat1.rotation_difference(quat2)

print(quat_diff.angle)

class mathutils.Color(rgb)

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.

Parameters: rgb (3d vector) – (r, g, b) color values

import mathutils

# color values are represented as RGB values from 0 - 1, this is blue
col = mathutils.Color((0.0, 0.0, 1.0))

# as well as r/g/b attribute access you can adjust them by h/s/v
col.s *= 0.5

# you can access its components by attribute or index
print("Color R:", col.r)
print("Color G:", col[1])
print("Color B:", col[-1])
print("Color HSV: %.2f, %.2f, %.2f", col[:])


# components of an existing color can be set
col[:] = 0.0, 0.5, 1.0

# components of an existing color can use slice notation to get a tuple
print("Values: %f, %f, %f" % col[:])

# colors can be added and subtracted
col += mathutils.Color((0.25, 0.0, 0.0))

# Color can be multiplied, in this example color is scaled to 0-255
# can printed as integers
print("Color: %d, %d, %d" % (col * 255.0)[:])

# This example prints the color as hexadecimal
print("Hexadecimal: %.2x%.2x%.2x" % (int(col.r * 255), int(col.g * 255), int(col.b * 255)))

copy()

Returns a copy of this color.

Returns: A copy of the color.
Return type: Color

Note

use this to get a copy of a wrapped color with no reference to the original data.

freeze()

Make this object immutable.

After this the object can be hashed, used in dictionaries & sets.

Returns: An instance of this object.

from_aces_to_scene_linear()

Convert from ACES2065-1 linear to scene linear color space.

Returns: A color in scene linear color space.
Return type: Color

from_rec709_linear_to_scene_linear()

Convert from Rec.709 linear color space to scene linear color space.

Returns: A color in scene linear color space.
Return type: Color

from_scene_linear_to_aces()

Convert from scene linear to ACES2065-1 linear color space.

Returns: A color in ACES2065-1 linear color space.
Return type: Color

from_scene_linear_to_rec709_linear()

Convert from scene linear to Rec.709 linear color space.

Returns: A color in Rec.709 linear color space.
Return type: Color

from_scene_linear_to_srgb()

Convert from scene linear to sRGB color space.

Returns: A color in sRGB color space.
Return type: Color

from_scene_linear_to_xyz_d65()

Convert from scene linear to CIE XYZ (Illuminant D65) color space.

Returns: A color in XYZ color space.
Return type: Color

from_srgb_to_scene_linear()

Convert from sRGB to scene linear color space.

Returns: A color in scene linear color space.
Return type: Color

from_xyz_d65_to_scene_linear()

Convert from CIE XYZ (Illuminant D65) to scene linear color space.

Returns: A color in scene linear color space.
Return type: Color

b

Blue color channel.

Type: float

g

Green color channel.

Type: float

h

HSV Hue component in [0, 1].

Type: float

hsv

HSV Values in [0, 1].

Type: float triplet

is_frozen

True when this object has been frozen (read-only).

Type: boolean

is_valid

True when the owner of this data is valid.

Type: boolean

is_wrapped

True when this object wraps external data (read-only).

Type: boolean

owner: The item this is wrapping or None (read-only).

r

Red color channel.

Type: float

s

HSV Saturation component in [0, 1].

Type: float

v

HSV Value component in [0, 1].

Type: float

class mathutils.Euler(angles, order='XYZ')

This object gives access to Eulers in Blender.

See also

Euler angles on Wikipedia.

Parameters

angles (3d vector) – Three angles, in radians.
order (str) – Optional order of the angles, a permutation of XYZ.

import mathutils
import math

# create a new euler with default axis rotation order
eul = mathutils.Euler((0.0, math.radians(45.0), 0.0), 'XYZ')

# rotate the euler
eul.rotate_axis('Z', math.radians(10.0))

# you can access its components by attribute or index
print("Euler X", eul.x)
print("Euler Y", eul[1])
print("Euler Z", eul[-1])

# components of an existing euler can be set
eul[:] = 1.0, 2.0, 3.0

# components of an existing euler can use slice notation to get a tuple
print("Values: %f, %f, %f" % eul[:])

# the order can be set at any time too
eul.order = 'ZYX'

# eulers can be used to rotate vectors
vec = mathutils.Vector((0.0, 0.0, 1.0))
vec.rotate(eul)

# often its useful to convert the euler into a matrix so it can be used as
# transformations with more flexibility
mat_rot = eul.to_matrix()
mat_loc = mathutils.Matrix.Translation((2.0, 3.0, 4.0))
mat = mat_loc @ mat_rot.to_4x4()

copy()

Returns a copy of this euler.

Returns: A copy of the euler.
Return type: Euler

Note

use this to get a copy of a wrapped euler with no reference to the original data.

freeze()

Make this object immutable.

After this the object can be hashed, used in dictionaries & sets.

Returns: An instance of this object.

make_compatible(other): Make this euler compatible with another, so interpolating between them works as intended.

Note

the rotation order is not taken into account for this function.

rotate(other)

Rotates the euler by another mathutils value.

Parameters: other (Euler, Quaternion or Matrix) – rotation component of mathutils value

rotate_axis(axis, angle)

Rotates the euler a certain amount and returning a unique euler rotation (no 720 degree pitches).

Parameters

axis (string) – single character in [‘X, ‘Y’, ‘Z’].
angle (float) – angle in radians.

to_matrix()

Return a matrix representation of the euler.

Returns: A 3x3 rotation matrix representation of the euler.
Return type: Matrix

to_quaternion()

Return a quaternion representation of the euler.

Returns: Quaternion representation of the euler.
Return type: Quaternion

zero(): Set all values to zero.

is_frozen

True when this object has been frozen (read-only).

Type: boolean

is_valid

True when the owner of this data is valid.

Type: boolean

is_wrapped

True when this object wraps external data (read-only).

Type: boolean

order

Euler rotation order.

Type: string in [‘XYZ’, ‘XZY’, ‘YXZ’, ‘YZX’, ‘ZXY’, ‘ZYX’]

owner: The item this is wrapping or None (read-only).

x

Euler axis angle in radians.

Type: float

y

Euler axis angle in radians.

Type: float

z

Euler axis angle in radians.

Type: float

class mathutils.Matrix([rows])

This object gives access to Matrices in Blender, supporting square and rectangular matrices from 2x2 up to 4x4.

Parameters: rows (2d number sequence) – Sequence of rows. When omitted, a 4x4 identity matrix is constructed.

import mathutils
import math

# create a location matrix
mat_loc = mathutils.Matrix.Translation((2.0, 3.0, 4.0))

# create an identitiy matrix
mat_sca = mathutils.Matrix.Scale(0.5, 4, (0.0, 0.0, 1.0))

# create a rotation matrix
mat_rot = mathutils.Matrix.Rotation(math.radians(45.0), 4, 'X')

# combine transformations
mat_out = mat_loc @ mat_rot @ mat_sca
print(mat_out)

# extract components back out of the matrix as two vectors and a quaternion
loc, rot, sca = mat_out.decompose()
print(loc, rot, sca)

# recombine extracted components
mat_out2 = mathutils.Matrix.LocRotScale(loc, rot, sca)
print(mat_out2)

# it can also be useful to access components of a matrix directly
mat = mathutils.Matrix()
mat[0][0], mat[1][0], mat[2][0] = 0.0, 1.0, 2.0

mat[0][0:3] = 0.0, 1.0, 2.0

# each item in a matrix is a vector so vector utility functions can be used
mat[0].xyz = 0.0, 1.0, 2.0

classmethod Diagonal(vector)

Create a diagonal (scaling) matrix using the values from the vector.

Parameters: vector (Vector) – The vector of values for the diagonal.
Returns: A diagonal matrix.
Return type: Matrix

classmethod Identity(size)

Create an identity matrix.

Parameters: size (int) – The size of the identity matrix to construct [2, 4].
Returns: A new identity matrix.
Return type: Matrix

classmethod LocRotScale(location, rotation, scale)

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.

Parameters

location (Vector or None) – The translation component.
rotation (3x3 Matrix, Quaternion, Euler or None) – The rotation component.
scale (Vector or None) – The scale component.

Returns

Combined transformation matrix.

Return type

4x4 Matrix

# Compute local object transformation matrix:
if obj.rotation_mode == 'QUATERNION':
    matrix = mathutils.Matrix.LocRotScale(obj.location, obj.rotation_quaternion, obj.scale)
else:
    matrix = mathutils.Matrix.LocRotScale(obj.location, obj.rotation_euler, obj.scale)

classmethod OrthoProjection(axis, size)

Create a matrix to represent an orthographic projection.

Parameters

axis (string or Vector) – Can be any of the following: [‘X’, ‘Y’, ‘XY’, ‘XZ’, ‘YZ’], where a single axis is for a 2D matrix. Or a vector for an arbitrary axis
size (int) – The size of the projection matrix to construct [2, 4].

Returns

A new projection matrix.

Return type

Matrix

classmethod Rotation(angle, size, axis)

Create a matrix representing a rotation.

Parameters

angle (float) – The angle of rotation desired, in radians.
size (int) – The size of the rotation matrix to construct [2, 4].
axis (string or Vector) – a string in [‘X’, ‘Y’, ‘Z’] or a 3D Vector Object (optional when size is 2).

Returns

A new rotation matrix.

Return type

Matrix

classmethod Scale(factor, size, axis)

Create a matrix representing a scaling.

Parameters

factor (float) – The factor of scaling to apply.
size (int) – The size of the scale matrix to construct [2, 4].
axis (Vector) – Direction to influence scale. (optional).

Returns

A new scale matrix.

Return type

Matrix

classmethod Shear(plane, size, factor)

Create a matrix to represent an shear transformation.

Parameters

plane (string) – Can be any of the following: [‘X’, ‘Y’, ‘XY’, ‘XZ’, ‘YZ’], where a single axis is for a 2D matrix only.
size (int) – The size of the shear matrix to construct [2, 4].
factor (float or float pair) – The factor of shear to apply. For a 3 or 4 size matrix pass a pair of floats corresponding with the plane axis.

Returns

A new shear matrix.

Return type

Matrix

classmethod Translation(vector)

Create a matrix representing a translation.

Parameters: vector (Vector) – The translation vector.
Returns: An identity matrix with a translation.
Return type: Matrix

adjugate()

Set the matrix to its adjugate.

Raises: ValueError – if the matrix cannot be adjugate.

See also

Adjugate matrix on Wikipedia.

adjugated()

Return an adjugated copy of the matrix.

Returns: the adjugated matrix.
Return type: Matrix
Raises: ValueError – if the matrix cannot be adjugated

copy()

Returns a copy of this matrix.

Returns: an instance of itself
Return type: Matrix

decompose()

Return the translation, rotation, and scale components of this matrix.

Returns: tuple of translation, rotation, and scale
Return type: (Vector, Quaternion, Vector)

determinant()

Return the determinant of a matrix.

Returns: Return the determinant of a matrix.
Return type: float

See also

Determinant on Wikipedia.

freeze()

Make this object immutable.

After this the object can be hashed, used in dictionaries & sets.

Returns: An instance of this object.

identity(): Set the matrix to the identity matrix.

Note

An object with a location and rotation of zero, and a scale of one will have an identity matrix.

See also

Identity matrix on Wikipedia.

invert(fallback=None)

Set the matrix to its inverse.

Parameters: fallback (Matrix) – Set the matrix to this value when the inverse cannot be calculated (instead of raising a ValueError exception).

See also

Inverse matrix on Wikipedia.

invert_safe(): 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.

See also

Inverse Matrix on Wikipedia.

inverted(fallback=None)

Return an inverted copy of the matrix.

Parameters: fallback (any) – return this when the inverse can’t be calculated (instead of raising a ValueError).
Returns: the inverted matrix or fallback when given.
Return type: Matrix

inverted_safe()

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.

Returns: the inverted matrix.
Return type: Matrix

lerp(other, factor)

Returns the interpolation of two matrices. Uses polar decomposition, see “Matrix Animation and Polar Decomposition”, Shoemake and Duff, 1992.

Parameters

other (Matrix) – value to interpolate with.
factor (float) – The interpolation value in [0.0, 1.0].

Returns

The interpolated matrix.

Return type

Matrix

normalize(): Normalize each of the matrix columns.

normalized()

Return a column normalized matrix

Returns: a column normalized matrix
Return type: Matrix

resize_4x4(): Resize the matrix to 4x4.

rotate(other)

Rotates the matrix by another mathutils value.

Parameters: other (Euler, Quaternion or Matrix) – rotation component of mathutils value

Note

If any of the columns are not unit length this may not have desired results.

to_2x2()

Return a 2x2 copy of this matrix.

Returns: a new matrix.
Return type: Matrix

to_3x3()

Return a 3x3 copy of this matrix.

Returns: a new matrix.
Return type: Matrix

to_4x4()

Return a 4x4 copy of this matrix.

Returns: a new matrix.
Return type: Matrix

to_euler(order, euler_compat)

Return an Euler representation of the rotation matrix (3x3 or 4x4 matrix only).

Parameters

order (string) – Optional rotation order argument in [‘XYZ’, ‘XZY’, ‘YXZ’, ‘YZX’, ‘ZXY’, ‘ZYX’].
euler_compat (Euler) – 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.

Returns

Euler representation of the matrix.

Return type

Euler

to_quaternion()

Return a quaternion representation of the rotation matrix.

Returns: Quaternion representation of the rotation matrix.
Return type: Quaternion

to_scale()

Return the scale part of a 3x3 or 4x4 matrix.

Returns: Return the scale of a matrix.
Return type: Vector

Note

This method does not return a negative scale on any axis because it is not possible to obtain this data from the matrix alone.

to_translation()

Return the translation part of a 4 row matrix.

Returns: Return the translation of a matrix.
Return type: Vector

transpose(): Set the matrix to its transpose.

See also

Transpose on Wikipedia.

transposed()

Return a new, transposed matrix.

Returns: a transposed matrix
Return type: Matrix

zero()

Set all the matrix values to zero.

Return type: Matrix

col

Access the matrix by columns, 3x3 and 4x4 only, (read-only).

Type: Matrix Access

is_frozen

True when this object has been frozen (read-only).

Type: boolean

is_negative

True if this matrix results in a negative scale, 3x3 and 4x4 only, (read-only).

Type: bool

is_orthogonal

True if this matrix is orthogonal, 3x3 and 4x4 only, (read-only).

Type: bool

is_orthogonal_axis_vectors

True if this matrix has got orthogonal axis vectors, 3x3 and 4x4 only, (read-only).

Type: bool

is_valid

True when the owner of this data is valid.

Type: boolean

is_wrapped

True when this object wraps external data (read-only).

Type: boolean

median_scale

The average scale applied to each axis (read-only).

Type: float

owner: The item this is wrapping or None (read-only).

row

Access the matrix by rows (default), (read-only).

Type: Matrix Access

translation

The translation component of the matrix.

Type: Vector

class mathutils.Quaternion([seq[, angle]])

This object gives access to Quaternions in Blender.

Parameters

seq (Vector) – size 3 or 4
angle (float) – rotation angle, in radians

The constructor takes arguments in various forms:

(), no args: Create an identity quaternion
(wxyz): Create a quaternion from a (w, x, y, z) vector.
(exponential_map): Create a quaternion from a 3d exponential map vector.

See also

to_exponential_map()
(axis, angle): Create a quaternion representing a rotation of angle radians over axis.

See also

to_axis_angle()

import mathutils
import math

# a new rotation 90 degrees about the Y axis
quat_a = mathutils.Quaternion((0.7071068, 0.0, 0.7071068, 0.0))

# passing values to Quaternion's directly can be confusing so axis, angle
# is supported for initializing too
quat_b = mathutils.Quaternion((0.0, 1.0, 0.0), math.radians(90.0))

print("Check quaternions match", quat_a == quat_b)

# like matrices, quaternions can be multiplied to accumulate rotational values
quat_a = mathutils.Quaternion((0.0, 1.0, 0.0), math.radians(90.0))
quat_b = mathutils.Quaternion((0.0, 0.0, 1.0), math.radians(45.0))
quat_out = quat_a @ quat_b

# print the quat, euler degrees for mere mortals and (axis, angle)
print("Final Rotation:")
print(quat_out)
print("%.2f, %.2f, %.2f" % tuple(math.degrees(a) for a in quat_out.to_euler()))
print("(%.2f, %.2f, %.2f), %.2f" % (quat_out.axis[:] +
                                    (math.degrees(quat_out.angle), )))

# multiple rotations can be interpolated using the exponential map
quat_c = mathutils.Quaternion((1.0, 0.0, 0.0), math.radians(15.0))
exp_avg = (quat_a.to_exponential_map() +
           quat_b.to_exponential_map() +
           quat_c.to_exponential_map()) / 3.0
quat_avg = mathutils.Quaternion(exp_avg)
print("Average rotation:")
print(quat_avg)

conjugate(): Set the quaternion to its conjugate (negate x, y, z).

conjugated()

Return a new conjugated quaternion.

Returns: a new quaternion.
Return type: Quaternion

copy()

Returns a copy of this quaternion.

Returns: A copy of the quaternion.
Return type: Quaternion

Note

use this to get a copy of a wrapped quaternion with no reference to the original data.

cross(other)

Return the cross product of this quaternion and another.

Parameters: other (Quaternion) – The other quaternion to perform the cross product with.
Returns: The cross product.
Return type: Quaternion

dot(other)

Return the dot product of this quaternion and another.

Parameters: other (Quaternion) – The other quaternion to perform the dot product with.
Returns: The dot product.
Return type: float

freeze()

Make this object immutable.

After this the object can be hashed, used in dictionaries & sets.

Returns: An instance of this object.

identity()

Set the quaternion to an identity quaternion.

Return type: Quaternion

invert(): Set the quaternion to its inverse.

inverted()

Return a new, inverted quaternion.

Returns: the inverted value.
Return type: Quaternion

make_compatible(other): Make this quaternion compatible with another, so interpolating between them works as intended.

negate()

Set the quaternion to its negative.

Return type: Quaternion

normalize(): Normalize the quaternion.

normalized()

Return a new normalized quaternion.

Returns: a normalized copy.
Return type: Quaternion

rotate(other)

Rotates the quaternion by another mathutils value.

Parameters: other (Euler, Quaternion or Matrix) – rotation component of mathutils value

rotation_difference(other)

Returns a quaternion representing the rotational difference.

Parameters: other (Quaternion) – second quaternion.
Returns: the rotational difference between the two quat rotations.
Return type: Quaternion

slerp(other, factor)

Returns the interpolation of two quaternions.

Parameters

other (Quaternion) – value to interpolate with.
factor (float) – The interpolation value in [0.0, 1.0].

Returns

The interpolated rotation.

Return type

Quaternion

to_axis_angle()

Return the axis, angle representation of the quaternion.

Returns: axis, angle.
Return type: (Vector, float) pair

to_euler(order, euler_compat)

Return Euler representation of the quaternion.

Parameters

order (string) – Optional rotation order argument in [‘XYZ’, ‘XZY’, ‘YXZ’, ‘YZX’, ‘ZXY’, ‘ZYX’].
euler_compat (Euler) – 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.

Returns

Euler representation of the quaternion.

Return type

Euler

to_exponential_map()

Return the exponential map representation of the quaternion.

This representation consist of the rotation axis multiplied by the rotation angle. Such a representation is useful for interpolation between multiple orientations.

Returns: exponential map.
Return type: Vector of size 3

To convert back to a quaternion, pass it to the Quaternion constructor.

to_matrix()

Return a matrix representation of the quaternion.

Returns: A 3x3 rotation matrix representation of the quaternion.
Return type: Matrix

to_swing_twist(axis)

Split the rotation into a swing quaternion with the specified axis fixed at zero, and the remaining twist rotation angle.

Parameters: axis – twist axis as a string in [‘X’, ‘Y’, ‘Z’]
Returns: swing, twist angle.
Return type: (Quaternion, float) pair

angle

Angle of the quaternion.

Type: float

axis

Quaternion axis as a vector.

Type: Vector

is_frozen

True when this object has been frozen (read-only).

Type: boolean

is_valid

True when the owner of this data is valid.

Type: boolean

is_wrapped

True when this object wraps external data (read-only).

Type: boolean

magnitude

Size of the quaternion (read-only).

Type: float

owner: The item this is wrapping or None (read-only).

w

Quaternion axis value.

Type: float

x

Quaternion axis value.

Type: float

y

Quaternion axis value.

Type: float

z

Quaternion axis value.

Type: float

class mathutils.Vector(seq)

This object gives access to Vectors in Blender.

Parameters: seq (sequence of numbers) – Components of the vector, must be a sequence of at least two

import mathutils

# zero length vector
vec = mathutils.Vector((0.0, 0.0, 1.0))

# unit length vector
vec_a = vec.normalized()

vec_b = mathutils.Vector((0.0, 1.0, 2.0))

vec2d = mathutils.Vector((1.0, 2.0))
vec3d = mathutils.Vector((1.0, 0.0, 0.0))
vec4d = vec_a.to_4d()

# other mathutuls types
quat = mathutils.Quaternion()
matrix = mathutils.Matrix()

# Comparison operators can be done on Vector classes:

# (In)equality operators == and != test component values, e.g. 1,2,3 != 3,2,1
vec_a == vec_b
vec_a != vec_b

# Ordering operators >, >=, > and <= test vector length.
vec_a > vec_b
vec_a >= vec_b
vec_a < vec_b
vec_a <= vec_b


# Math can be performed on Vector classes
vec_a + vec_b
vec_a - vec_b
vec_a @ vec_b
vec_a * 10.0
matrix @ vec_a
quat @ vec_a
-vec_a


# You can access a vector object like a sequence
x = vec_a[0]
len(vec)
vec_a[:] = vec_b
vec_a[:] = 1.0, 2.0, 3.0
vec2d[:] = vec3d[:2]


# Vectors support 'swizzle' operations
# See https://en.wikipedia.org/wiki/Swizzling_(computer_graphics)
vec.xyz = vec.zyx
vec.xy = vec4d.zw
vec.xyz = vec4d.wzz
vec4d.wxyz = vec.yxyx

classmethod Fill(size, fill=0.0)

Create a vector of length size with all values set to fill.

Parameters

size (int) – The length of the vector to be created.
fill (float) – The value used to fill the vector.

classmethod Linspace(start, stop, size)

Create a vector of the specified size which is filled with linearly spaced values between start and stop values.

Parameters

start (int) – The start of the range used to fill the vector.
stop (int) – The end of the range used to fill the vector.
size (int) – The size of the vector to be created.

classmethod Range(start, stop, step=1)

Create a filled with a range of values.

Parameters

start (int) – The start of the range used to fill the vector.
stop (int) – The end of the range used to fill the vector.
step (int) – The step between successive values in the vector.

classmethod Repeat(vector, size)

Create a vector by repeating the values in vector until the required size is reached.

Parameters

tuple (mathutils.Vector) – The vector to draw values from.
size (int) – The size of the vector to be created.

angle(other, fallback=None)

Return the angle between two vectors.

Parameters

other (Vector) – another vector to compare the angle with
fallback (any) – return this when the angle can’t be calculated (zero length vector), (instead of raising a ValueError).

Returns

angle in radians or fallback when given

Return type

float

angle_signed(other, fallback)

Return the signed angle between two 2D vectors (clockwise is positive).

Parameters

other (Vector) – another vector to compare the angle with
fallback (any) – return this when the angle can’t be calculated (zero length vector), (instead of raising a ValueError).

Returns

angle in radians or fallback when given

Return type

float

copy()

Returns a copy of this vector.

Returns: A copy of the vector.
Return type: Vector

Note

use this to get a copy of a wrapped vector with no reference to the original data.

cross(other)

Return the cross product of this vector and another.

Parameters: other (Vector) – The other vector to perform the cross product with.
Returns: The cross product.
Return type: Vector or float when 2D vectors are used

Note

both vectors must be 2D or 3D

dot(other)

Return the dot product of this vector and another.

Parameters: other (Vector) – The other vector to perform the dot product with.
Returns: The dot product.
Return type: float

freeze()

Make this object immutable.

After this the object can be hashed, used in dictionaries & sets.

Returns: An instance of this object.

lerp(other, factor)

Returns the interpolation of two vectors.

Parameters

other (Vector) – value to interpolate with.
factor (float) – The interpolation value in [0.0, 1.0].

Returns

The interpolated vector.

Return type

Vector

negate(): Set all values to their negative.

normalize(): Normalize the vector, making the length of the vector always 1.0.

Warning

Normalizing a vector where all values are zero has no effect.

Note

Normalize works for vectors of all sizes, however 4D Vectors w axis is left untouched.

normalized()

Return a new, normalized vector.

Returns: a normalized copy of the vector
Return type: Vector

orthogonal()

Return a perpendicular vector.

Returns: a new vector 90 degrees from this vector.
Return type: Vector

Note

the axis is undefined, only use when any orthogonal vector is acceptable.

project(other)

Return the projection of this vector onto the other.

Parameters: other (Vector) – second vector.
Returns: the parallel projection vector
Return type: Vector

reflect(mirror)

Return the reflection vector from the mirror argument.

Parameters: mirror (Vector) – This vector could be a normal from the reflecting surface.
Returns: The reflected vector matching the size of this vector.
Return type: Vector

resize(size=3): Resize the vector to have size number of elements.

resize_2d(): Resize the vector to 2D (x, y).

resize_3d(): Resize the vector to 3D (x, y, z).

resize_4d(): Resize the vector to 4D (x, y, z, w).

resized(size=3)

Return a resized copy of the vector with size number of elements.

Returns: a new vector
Return type: Vector

rotate(other)

Rotate the vector by a rotation value.

Note

2D vectors are a special case that can only be rotated by a 2x2 matrix.

Parameters: other (Euler, Quaternion or Matrix) – rotation component of mathutils value

rotation_difference(other)

Returns a quaternion representing the rotational difference between this vector and another.

Parameters: other (Vector) – second vector.
Returns: the rotational difference between the two vectors.
Return type: Quaternion

Note

2D vectors raise an AttributeError.

slerp(other, factor, fallback=None)

Returns the interpolation of two non-zero vectors (spherical coordinates).

Parameters

other (Vector) – value to interpolate with.
factor (float) – The interpolation value typically in [0.0, 1.0].
fallback (any) – return this when the vector can’t be calculated (zero length vector or direct opposites), (instead of raising a ValueError).

Returns

The interpolated vector.

Return type

Vector

to_2d()

Return a 2d copy of the vector.

Returns: a new vector
Return type: Vector

to_3d()

Return a 3d copy of the vector.

Returns: a new vector
Return type: Vector

to_4d()

Return a 4d copy of the vector.

Returns: a new vector
Return type: Vector

to_track_quat(track, up)

Return a quaternion rotation from the vector and the track and up axis.

Parameters

track (string) – Track axis in [‘X’, ‘Y’, ‘Z’, ‘-X’, ‘-Y’, ‘-Z’].
up (string) – Up axis in [‘X’, ‘Y’, ‘Z’].

Returns

rotation from the vector and the track and up axis.

Return type

Quaternion

to_tuple(precision=- 1)

Return this vector as a tuple with.

Parameters: precision (int) – The number to round the value to in [-1, 21].
Returns: the values of the vector rounded by precision
Return type: tuple

zero(): Set all values to zero.

is_frozen

True when this object has been frozen (read-only).

Type: boolean

is_valid

True when the owner of this data is valid.

Type: boolean

is_wrapped

True when this object wraps external data (read-only).

Type: boolean

length

Vector Length.

Type: float

length_squared

Vector length squared (v.dot(v)).

Type: float

magnitude

Vector Length.

Type: float

owner: The item this is wrapping or None (read-only).

w

Vector W axis (4D Vectors only).

Type: float

ww: Undocumented, consider contributing.

www: Undocumented, consider contributing.

wwww: Undocumented, consider contributing.

wwwx: Undocumented, consider contributing.

wwwy: Undocumented, consider contributing.

wwwz: Undocumented, consider contributing.

wwx: Undocumented, consider contributing.

wwxw: Undocumented, consider contributing.

wwxx: Undocumented, consider contributing.

wwxy: Undocumented, consider contributing.

wwxz: Undocumented, consider contributing.

wwy: Undocumented, consider contributing.

wwyw: Undocumented, consider contributing.

wwyx: Undocumented, consider contributing.

wwyy: Undocumented, consider contributing.

wwyz: Undocumented, consider contributing.

wwz: Undocumented, consider contributing.

wwzw: Undocumented, consider contributing.

wwzx: Undocumented, consider contributing.

wwzy: Undocumented, consider contributing.

wwzz: Undocumented, consider contributing.

wx: Undocumented, consider contributing.

wxw: Undocumented, consider contributing.

wxww: Undocumented, consider contributing.

wxwx: Undocumented, consider contributing.

wxwy: Undocumented, consider contributing.

wxwz: Undocumented, consider contributing.

wxx: Undocumented, consider contributing.

wxxw: Undocumented, consider contributing.

wxxx: Undocumented, consider contributing.

wxxy: Undocumented, consider contributing.

wxxz: Undocumented, consider contributing.

wxy: Undocumented, consider contributing.

wxyw: Undocumented, consider contributing.

wxyx: Undocumented, consider contributing.

wxyy: Undocumented, consider contributing.

wxyz: Undocumented, consider contributing.

wxz: Undocumented, consider contributing.

wxzw: Undocumented, consider contributing.

wxzx: Undocumented, consider contributing.

wxzy: Undocumented, consider contributing.

wxzz: Undocumented, consider contributing.

wy: Undocumented, consider contributing.

wyw: Undocumented, consider contributing.

wyww: Undocumented, consider contributing.

wywx: Undocumented, consider contributing.

wywy: Undocumented, consider contributing.

wywz: Undocumented, consider contributing.

wyx: Undocumented, consider contributing.

wyxw: Undocumented, consider contributing.

wyxx: Undocumented, consider contributing.

wyxy: Undocumented, consider contributing.

wyxz: Undocumented, consider contributing.

wyy: Undocumented, consider contributing.

wyyw: Undocumented, consider contributing.

wyyx: Undocumented, consider contributing.

wyyy: Undocumented, consider contributing.

wyyz: Undocumented, consider contributing.

wyz: Undocumented, consider contributing.

wyzw: Undocumented, consider contributing.

wyzx: Undocumented, consider contributing.

wyzy: Undocumented, consider contributing.

wyzz: Undocumented, consider contributing.

wz: Undocumented, consider contributing.

wzw: Undocumented, consider contributing.

wzww: Undocumented, consider contributing.

wzwx: Undocumented, consider contributing.

wzwy: Undocumented, consider contributing.

wzwz: Undocumented, consider contributing.

wzx: Undocumented, consider contributing.

wzxw: Undocumented, consider contributing.

wzxx: Undocumented, consider contributing.

wzxy: Undocumented, consider contributing.

wzxz: Undocumented, consider contributing.

wzy: Undocumented, consider contributing.

wzyw: Undocumented, consider contributing.

wzyx: Undocumented, consider contributing.

wzyy: Undocumented, consider contributing.

wzyz: Undocumented, consider contributing.

wzz: Undocumented, consider contributing.

wzzw: Undocumented, consider contributing.

wzzx: Undocumented, consider contributing.

wzzy: Undocumented, consider contributing.

wzzz: Undocumented, consider contributing.

x

Vector X axis.

Type: float

xw: Undocumented, consider contributing.

xww: Undocumented, consider contributing.

xwww: Undocumented, consider contributing.

xwwx: Undocumented, consider contributing.

xwwy: Undocumented, consider contributing.

xwwz: Undocumented, consider contributing.

xwx: Undocumented, consider contributing.

xwxw: Undocumented, consider contributing.

xwxx: Undocumented, consider contributing.

xwxy: Undocumented, consider contributing.

xwxz: Undocumented, consider contributing.

xwy: Undocumented, consider contributing.

xwyw: Undocumented, consider contributing.

xwyx: Undocumented, consider contributing.

xwyy: Undocumented, consider contributing.

xwyz: Undocumented, consider contributing.

xwz: Undocumented, consider contributing.

xwzw: Undocumented, consider contributing.

xwzx: Undocumented, consider contributing.

xwzy: Undocumented, consider contributing.

xwzz: Undocumented, consider contributing.

xx: Undocumented, consider contributing.

xxw: Undocumented, consider contributing.

xxww: Undocumented, consider contributing.

xxwx: Undocumented, consider contributing.

xxwy: Undocumented, consider contributing.

xxwz: Undocumented, consider contributing.

xxx: Undocumented, consider contributing.

xxxw: Undocumented, consider contributing.

xxxx: Undocumented, consider contributing.

xxxy: Undocumented, consider contributing.

xxxz: Undocumented, consider contributing.

xxy: Undocumented, consider contributing.

xxyw: Undocumented, consider contributing.

xxyx: Undocumented, consider contributing.

xxyy: Undocumented, consider contributing.

xxyz: Undocumented, consider contributing.

xxz: Undocumented, consider contributing.

xxzw: Undocumented, consider contributing.

xxzx: Undocumented, consider contributing.

xxzy: Undocumented, consider contributing.

xxzz: Undocumented, consider contributing.

xy: Undocumented, consider contributing.

xyw: Undocumented, consider contributing.

xyww: Undocumented, consider contributing.

xywx: Undocumented, consider contributing.

xywy: Undocumented, consider contributing.

xywz: Undocumented, consider contributing.

xyx: Undocumented, consider contributing.

xyxw: Undocumented, consider contributing.

xyxx: Undocumented, consider contributing.

xyxy: Undocumented, consider contributing.

xyxz: Undocumented, consider contributing.

xyy: Undocumented, consider contributing.

xyyw: Undocumented, consider contributing.

xyyx: Undocumented, consider contributing.

xyyy: Undocumented, consider contributing.

xyyz: Undocumented, consider contributing.

xyz: Undocumented, consider contributing.

xyzw: Undocumented, consider contributing.

xyzx: Undocumented, consider contributing.

xyzy: Undocumented, consider contributing.

xyzz: Undocumented, consider contributing.

xz: Undocumented, consider contributing.

xzw: Undocumented, consider contributing.

xzww: Undocumented, consider contributing.

xzwx: Undocumented, consider contributing.

xzwy: Undocumented, consider contributing.

xzwz: Undocumented, consider contributing.

xzx: Undocumented, consider contributing.

xzxw: Undocumented, consider contributing.

xzxx: Undocumented, consider contributing.

xzxy: Undocumented, consider contributing.

xzxz: Undocumented, consider contributing.

xzy: Undocumented, consider contributing.

xzyw: Undocumented, consider contributing.

xzyx: Undocumented, consider contributing.

xzyy: Undocumented, consider contributing.

xzyz: Undocumented, consider contributing.

xzz: Undocumented, consider contributing.

xzzw: Undocumented, consider contributing.

xzzx: Undocumented, consider contributing.

xzzy: Undocumented, consider contributing.

xzzz: Undocumented, consider contributing.

y

Vector Y axis.

Type: float

yw: Undocumented, consider contributing.

yww: Undocumented, consider contributing.

ywww: Undocumented, consider contributing.

ywwx: Undocumented, consider contributing.

ywwy: Undocumented, consider contributing.

ywwz: Undocumented, consider contributing.

ywx: Undocumented, consider contributing.

ywxw: Undocumented, consider contributing.

ywxx: Undocumented, consider contributing.

ywxy: Undocumented, consider contributing.

ywxz: Undocumented, consider contributing.

ywy: Undocumented, consider contributing.

ywyw: Undocumented, consider contributing.

ywyx: Undocumented, consider contributing.

ywyy: Undocumented, consider contributing.

ywyz: Undocumented, consider contributing.

ywz: Undocumented, consider contributing.

ywzw: Undocumented, consider contributing.

ywzx: Undocumented, consider contributing.

ywzy: Undocumented, consider contributing.

ywzz: Undocumented, consider contributing.

yx: Undocumented, consider contributing.

yxw: Undocumented, consider contributing.

yxww: Undocumented, consider contributing.

yxwx: Undocumented, consider contributing.

yxwy: Undocumented, consider contributing.

yxwz: Undocumented, consider contributing.

yxx: Undocumented, consider contributing.

yxxw: Undocumented, consider contributing.

yxxx: Undocumented, consider contributing.

yxxy: Undocumented, consider contributing.

yxxz: Undocumented, consider contributing.

yxy: Undocumented, consider contributing.

yxyw: Undocumented, consider contributing.

yxyx: Undocumented, consider contributing.

yxyy: Undocumented, consider contributing.

yxyz: Undocumented, consider contributing.

yxz: Undocumented, consider contributing.

yxzw: Undocumented, consider contributing.

yxzx: Undocumented, consider contributing.

yxzy: Undocumented, consider contributing.

yxzz: Undocumented, consider contributing.

yy: Undocumented, consider contributing.

yyw: Undocumented, consider contributing.

yyww: Undocumented, consider contributing.

yywx: Undocumented, consider contributing.

yywy: Undocumented, consider contributing.

yywz: Undocumented, consider contributing.

yyx: Undocumented, consider contributing.

yyxw: Undocumented, consider contributing.

yyxx: Undocumented, consider contributing.

yyxy: Undocumented, consider contributing.

yyxz: Undocumented, consider contributing.

yyy: Undocumented, consider contributing.

yyyw: Undocumented, consider contributing.

yyyx: Undocumented, consider contributing.

yyyy: Undocumented, consider contributing.

yyyz: Undocumented, consider contributing.

yyz: Undocumented, consider contributing.

yyzw: Undocumented, consider contributing.

yyzx: Undocumented, consider contributing.

yyzy: Undocumented, consider contributing.

yyzz: Undocumented, consider contributing.

yz: Undocumented, consider contributing.

yzw: Undocumented, consider contributing.

yzww: Undocumented, consider contributing.

yzwx: Undocumented, consider contributing.

yzwy: Undocumented, consider contributing.

yzwz: Undocumented, consider contributing.

yzx: Undocumented, consider contributing.

yzxw: Undocumented, consider contributing.

yzxx: Undocumented, consider contributing.

yzxy: Undocumented, consider contributing.

yzxz: Undocumented, consider contributing.

yzy: Undocumented, consider contributing.

yzyw: Undocumented, consider contributing.

yzyx: Undocumented, consider contributing.

yzyy: Undocumented, consider contributing.

yzyz: Undocumented, consider contributing.

yzz: Undocumented, consider contributing.

yzzw: Undocumented, consider contributing.

yzzx: Undocumented, consider contributing.

yzzy: Undocumented, consider contributing.

yzzz: Undocumented, consider contributing.

z

Vector Z axis (3D Vectors only).

Type: float

zw: Undocumented, consider contributing.

zww: Undocumented, consider contributing.

zwww: Undocumented, consider contributing.

zwwx: Undocumented, consider contributing.

zwwy: Undocumented, consider contributing.

zwwz: Undocumented, consider contributing.

zwx: Undocumented, consider contributing.

zwxw: Undocumented, consider contributing.

zwxx: Undocumented, consider contributing.

zwxy: Undocumented, consider contributing.

zwxz: Undocumented, consider contributing.

zwy: Undocumented, consider contributing.

zwyw: Undocumented, consider contributing.

zwyx: Undocumented, consider contributing.

zwyy: Undocumented, consider contributing.

zwyz: Undocumented, consider contributing.

zwz: Undocumented, consider contributing.

zwzw: Undocumented, consider contributing.

zwzx: Undocumented, consider contributing.

zwzy: Undocumented, consider contributing.

zwzz: Undocumented, consider contributing.

zx: Undocumented, consider contributing.

zxw: Undocumented, consider contributing.

zxww: Undocumented, consider contributing.

zxwx: Undocumented, consider contributing.

zxwy: Undocumented, consider contributing.

zxwz: Undocumented, consider contributing.

zxx: Undocumented, consider contributing.

zxxw: Undocumented, consider contributing.

zxxx: Undocumented, consider contributing.

zxxy: Undocumented, consider contributing.

zxxz: Undocumented, consider contributing.

zxy: Undocumented, consider contributing.

zxyw: Undocumented, consider contributing.

zxyx: Undocumented, consider contributing.

zxyy: Undocumented, consider contributing.

zxyz: Undocumented, consider contributing.

zxz: Undocumented, consider contributing.

zxzw: Undocumented, consider contributing.

zxzx: Undocumented, consider contributing.

zxzy: Undocumented, consider contributing.

zxzz: Undocumented, consider contributing.

zy: Undocumented, consider contributing.

zyw: Undocumented, consider contributing.

zyww: Undocumented, consider contributing.

zywx: Undocumented, consider contributing.

zywy: Undocumented, consider contributing.

zywz: Undocumented, consider contributing.

zyx: Undocumented, consider contributing.

zyxw: Undocumented, consider contributing.

zyxx: Undocumented, consider contributing.

zyxy: Undocumented, consider contributing.

zyxz: Undocumented, consider contributing.

zyy: Undocumented, consider contributing.

zyyw: Undocumented, consider contributing.

zyyx: Undocumented, consider contributing.

zyyy: Undocumented, consider contributing.

zyyz: Undocumented, consider contributing.

zyz: Undocumented, consider contributing.

zyzw: Undocumented, consider contributing.

zyzx: Undocumented, consider contributing.

zyzy: Undocumented, consider contributing.

zyzz: Undocumented, consider contributing.

zz: Undocumented, consider contributing.

zzw: Undocumented, consider contributing.

zzww: Undocumented, consider contributing.

zzwx: Undocumented, consider contributing.

zzwy: Undocumented, consider contributing.

zzwz: Undocumented, consider contributing.

zzx: Undocumented, consider contributing.

zzxw: Undocumented, consider contributing.

zzxx: Undocumented, consider contributing.

zzxy: Undocumented, consider contributing.

zzxz: Undocumented, consider contributing.

zzy: Undocumented, consider contributing.

zzyw: Undocumented, consider contributing.

zzyx: Undocumented, consider contributing.

zzyy: Undocumented, consider contributing.

zzyz: Undocumented, consider contributing.

zzz: Undocumented, consider contributing.

zzzw: Undocumented, consider contributing.

zzzx: Undocumented, consider contributing.

zzzy: Undocumented, consider contributing.

zzzz: Undocumented, consider contributing.