Math Types & Utilities (mathutils)

This module provides access to matrices, eulers, quaternions and vectors.

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

This object gives access to Colors in Blender.

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.

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_wrapped

True when this object wraps external data (readonly).

Type :boolean
owner

The item this is wrapping or None (readonly).

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

This object gives access to Eulers in Blender.

import mathutils

# todo
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.

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 a 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 roation 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_wrapped

True when this object wraps external data (readonly).

Type :boolean
order

Euler rotation order.

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

The item this is wrapping or None (readonly).

x

Euler X axis in radians.

Type :float
y

Euler Y axis in radians.

Type :float
z

Euler Z axis in radians.

Type :float
class mathutils.Matrix

This object gives access to Matrices in Blender.

import mathutils

# todo
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 corrasponding 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
copy()

Returns a copy of this matrix.

Returns:an instance of itself
Return type:Matrix
decompose()

Return the location, rotaion and scale components of this matrix.

Returns:loc, rot, scale triple.
Return type:(Vector, Quaternion, Vector)
determinant()

Return the determinant of a matrix.

Returns:Return a the determinant of a matrix.
Return type:float
identity()

Set the matrix to the identity matrix.

Note

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

invert()

Set the matrix to its inverse.

inverted()

Return an inverted copy of the matrix.

Returns:the inverted matrix.
Return type:Matrix
lerp(other, factor)

Returns the interpolation of two matricies.

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

The interpolated rotation.

Return type:

Matrix

resize_4x4()

Resize the matrix to 4x4.

rotate(other)

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

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

Note

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

to_translation()

Return a the translation part of a 4 row matrix.

Returns:Return a the translation of a matrix.
Return type:Vector
transpose()

Set the matrix to its transpose.

transposed()

Return a new, transposed matrix.

Returns:a transposed matrix
Return type:Matrix
zero()

Set all the matrix values to zero.

Returns:an instance of itself
Return type:Matrix
col_size

The column size of the matrix (readonly).

Type :int
is_negative

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

Type :bool
is_orthogonal

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

Type :bool
is_wrapped

True when this object wraps external data (readonly).

Type :boolean
median_scale

The average scale applied to each axis (readonly).

Type :float
owner

The item this is wrapping or None (readonly).

row_size

The row size of the matrix (readonly).

Type :int
class mathutils.Quaternion

This object gives access to Quaternions in Blender.

import mathutils

# todo
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:Quaternion
identity()

Set the quaternion to an identity quaternion.

Returns:an instance of itself.
Return type:Quaternion
invert()

Set the quaternion to its inverse.

inverted()

Return a new, inverted quaternion.

Returns:the inverted value.
Return type:Quaternion
negate()

Set the quaternion to its negative.

Returns:an instance of itself.
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 a by another mathutils value.

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

Return a matrix representation of the quaternion.

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

angle of the quaternion.

Type :float
axis

quaternion axis as a vector.

Type :Vector
is_wrapped

True when this object wraps external data (readonly).

Type :boolean
magnitude

Size of the quaternion (readonly).

Type :float
owner

The item this is wrapping or None (readonly).

w

Quaternion W value.

Type :float
x

Quaternion X axis.

Type :float
y

Quaternion Y axis.

Type :float
z

Quaternion Z axis.

Type :float
class mathutils.Vector

This object gives access to Vectors in Blender.

import mathutils

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

# unit length vector
vec_a = vec.copy().normalize()

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:

# greater and less then test vector length.
vec_a > vec_b
vec_a >= vec_b
vec_a < vec_b
vec_a <= vec_b

# ==, != test vector values e.g. 1,2,3 != 3,2,1 even if they are the same length
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 * vec_b
-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 http://en.wikipedia.org/wiki/Swizzling_(computer_graphics)
vec.xyz = vec.zyx
vec.xy = vec4d.zw
vec.xyz = vec4d.wzz
vec4d.wxyz = vec.yxyx
angle(other, fallback)

Return the angle between two vectors.

Parameters:
  • other (Vector) – another vector to compare the angle with
  • fallback (any) – return this value when the angle cant be calculated (zero length vector)
Returns:

angle in radians or fallback when given

Return type:

float

Note

Zero length vectors raise an AttributeError.

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

Note

both vectors must be 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:Vector
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 rotation.

Return type:

Vector

negate()

Set all values to their negative.

Returns:an instance of itself
Return type:Vector
normalize()

Normalize the vector, making the length of the vector always 1.0.

Warning

Normalizing a vector where all values are zero results in all axis having a nan value (not a number).

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
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_2d()

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

Returns:an instance of itself
Return type:Vector
resize_3d()

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

Returns:an instance of itself
Return type:Vector
resize_4d()

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

Returns:an instance of itself
Return type:Vector
rotate(other)

Return vector by a rotation value.

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

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_wrapped

True when this object wraps external data (readonly).

Type :boolean
length

Vector Length.

Type :float
magnitude

Vector Length.

Type :float
owner

The item this is wrapping or None (readonly).

w

Vector W axis (4D Vectors only).

Type :float
ww

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x

Vector X axis.

Type :float
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y

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Type :float
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yzww

Undocumented (contribute)

yzwx

Undocumented (contribute)

yzwy

Undocumented (contribute)

yzwz

Undocumented (contribute)

yzx

Undocumented (contribute)

yzxw

Undocumented (contribute)

yzxx

Undocumented (contribute)

yzxy

Undocumented (contribute)

yzxz

Undocumented (contribute)

yzy

Undocumented (contribute)

yzyw

Undocumented (contribute)

yzyx

Undocumented (contribute)

yzyy

Undocumented (contribute)

yzyz

Undocumented (contribute)

yzz

Undocumented (contribute)

yzzw

Undocumented (contribute)

yzzx

Undocumented (contribute)

yzzy

Undocumented (contribute)

yzzz

Undocumented (contribute)

z

Vector Z axis (3D Vectors only).

Type :float
zw

Undocumented (contribute)

zww

Undocumented (contribute)

zwww

Undocumented (contribute)

zwwx

Undocumented (contribute)

zwwy

Undocumented (contribute)

zwwz

Undocumented (contribute)

zwx

Undocumented (contribute)

zwxw

Undocumented (contribute)

zwxx

Undocumented (contribute)

zwxy

Undocumented (contribute)

zwxz

Undocumented (contribute)

zwy

Undocumented (contribute)

zwyw

Undocumented (contribute)

zwyx

Undocumented (contribute)

zwyy

Undocumented (contribute)

zwyz

Undocumented (contribute)

zwz

Undocumented (contribute)

zwzw

Undocumented (contribute)

zwzx

Undocumented (contribute)

zwzy

Undocumented (contribute)

zwzz

Undocumented (contribute)

zx

Undocumented (contribute)

zxw

Undocumented (contribute)

zxww

Undocumented (contribute)

zxwx

Undocumented (contribute)

zxwy

Undocumented (contribute)

zxwz

Undocumented (contribute)

zxx

Undocumented (contribute)

zxxw

Undocumented (contribute)

zxxx

Undocumented (contribute)

zxxy

Undocumented (contribute)

zxxz

Undocumented (contribute)

zxy

Undocumented (contribute)

zxyw

Undocumented (contribute)

zxyx

Undocumented (contribute)

zxyy

Undocumented (contribute)

zxyz

Undocumented (contribute)

zxz

Undocumented (contribute)

zxzw

Undocumented (contribute)

zxzx

Undocumented (contribute)

zxzy

Undocumented (contribute)

zxzz

Undocumented (contribute)

zy

Undocumented (contribute)

zyw

Undocumented (contribute)

zyww

Undocumented (contribute)

zywx

Undocumented (contribute)

zywy

Undocumented (contribute)

zywz

Undocumented (contribute)

zyx

Undocumented (contribute)

zyxw

Undocumented (contribute)

zyxx

Undocumented (contribute)

zyxy

Undocumented (contribute)

zyxz

Undocumented (contribute)

zyy

Undocumented (contribute)

zyyw

Undocumented (contribute)

zyyx

Undocumented (contribute)

zyyy

Undocumented (contribute)

zyyz

Undocumented (contribute)

zyz

Undocumented (contribute)

zyzw

Undocumented (contribute)

zyzx

Undocumented (contribute)

zyzy

Undocumented (contribute)

zyzz

Undocumented (contribute)

zz

Undocumented (contribute)

zzw

Undocumented (contribute)

zzww

Undocumented (contribute)

zzwx

Undocumented (contribute)

zzwy

Undocumented (contribute)

zzwz

Undocumented (contribute)

zzx

Undocumented (contribute)

zzxw

Undocumented (contribute)

zzxx

Undocumented (contribute)

zzxy

Undocumented (contribute)

zzxz

Undocumented (contribute)

zzy

Undocumented (contribute)

zzyw

Undocumented (contribute)

zzyx

Undocumented (contribute)

zzyy

Undocumented (contribute)

zzyz

Undocumented (contribute)

zzz

Undocumented (contribute)

zzzw

Undocumented (contribute)

zzzx

Undocumented (contribute)

zzzy

Undocumented (contribute)

zzzz

Undocumented (contribute)

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Property Definitions (bpy.props)

Next topic

Geometry Utilities (mathutils.geometry)