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.

See also

<http://en.wikipedia.org/wiki/Identity_matrix>

invert()¶: Set the matrix to its inverse.

See also

<http://en.wikipedia.org/wiki/Inverse_matrix>

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.

See also

<http://en.wikipedia.org/wiki/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

length_squared¶

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

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¶: Undocumented (contribute)

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x¶

Vector X axis.

Type :	float

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y¶

Vector Y axis.

Type :	float

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yyyz¶: Undocumented (contribute)

yyz¶: Undocumented (contribute)

yyzw¶: Undocumented (contribute)

yyzx¶: Undocumented (contribute)

yyzy¶: Undocumented (contribute)

yyzz¶: Undocumented (contribute)

yz¶: Undocumented (contribute)

yzw¶: Undocumented (contribute)

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)

Math Types & Utilities (mathutils)¶

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