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.

Submodules:

The mathutils module provides the following classes:

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)

Color

class mathutils.Color(rgb)

This object gives access to Colors in Blender.

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 hexidecimal
print("Hexidecimal: %.2x%.2x%.2x" % (col * 255.0)[:])
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.
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_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

Euler

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

This object gives access to Eulers in Blender.

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 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_frozen

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

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

Matrix

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 ommitted, 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
loc, rot, sca = mat_out.decompose()
print(loc, rot, sca)

# 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 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 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.

Note

When the matrix cannot be adjugated a ValueError exception is raised.

See also

Adjugate matrix <https://en.wikipedia.org/wiki/Adjugate_matrix> on Wikipedia.

adjugated()

Return an adjugated copy of the matrix.

Returns:the adjugated matrix.
Return type:Matrix

Note

When the matrix cant be adjugated a ValueError exception is raised.

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:trans, rot, scale triple.
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 <https://en.wikipedia.org/wiki/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 <https://en.wikipedia.org/wiki/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 <https://en.wikipedia.org/wiki/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 <https://en.wikipedia.org/wiki/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.

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_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 <https://en.wikipedia.org/wiki/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 matix by colums, 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_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 matix by rows (default), (read-only).

Type:Matrix Access
translation

The translation component of the matrix.

Type:Vector

Quaternion

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.

(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 mear 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:Quaternion
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
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
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_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

Vector

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 * 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 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=0, 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:Vector
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.

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_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

www

Undocumented

wwww

Undocumented

wwwx

Undocumented

wwwy

Undocumented

wwwz

Undocumented

wwx

Undocumented

wwxw

Undocumented

wwxx

Undocumented

wwxy

Undocumented

wwxz

Undocumented

wwy

Undocumented

wwyw

Undocumented

wwyx

Undocumented

wwyy

Undocumented

wwyz

Undocumented

wwz

Undocumented

wwzw

Undocumented

wwzx

Undocumented

wwzy

Undocumented

wwzz

Undocumented

wx

Undocumented

wxw

Undocumented

wxww

Undocumented

wxwx

Undocumented

wxwy

Undocumented

wxwz

Undocumented

wxx

Undocumented

wxxw

Undocumented

wxxx

Undocumented

wxxy

Undocumented

wxxz

Undocumented

wxy

Undocumented

wxyw

Undocumented

wxyx

Undocumented

wxyy

Undocumented

wxyz

Undocumented

wxz

Undocumented

wxzw

Undocumented

wxzx

Undocumented

wxzy

Undocumented

wxzz

Undocumented

wy

Undocumented

wyw

Undocumented

wyww

Undocumented

wywx

Undocumented

wywy

Undocumented

wywz

Undocumented

wyx

Undocumented

wyxw

Undocumented

wyxx

Undocumented

wyxy

Undocumented

wyxz

Undocumented

wyy

Undocumented

wyyw

Undocumented

wyyx

Undocumented

wyyy

Undocumented

wyyz

Undocumented

wyz

Undocumented

wyzw

Undocumented

wyzx

Undocumented

wyzy

Undocumented

wyzz

Undocumented

wz

Undocumented

wzw

Undocumented

wzww

Undocumented

wzwx

Undocumented

wzwy

Undocumented

wzwz

Undocumented

wzx

Undocumented

wzxw

Undocumented

wzxx

Undocumented

wzxy

Undocumented

wzxz

Undocumented

wzy

Undocumented

wzyw

Undocumented

wzyx

Undocumented

wzyy

Undocumented

wzyz

Undocumented

wzz

Undocumented

wzzw

Undocumented

wzzx

Undocumented

wzzy

Undocumented

wzzz

Undocumented

x

Vector X axis.

Type:float
xw

Undocumented

xww

Undocumented

xwww

Undocumented

xwwx

Undocumented

xwwy

Undocumented

xwwz

Undocumented

xwx

Undocumented

xwxw

Undocumented

xwxx

Undocumented

xwxy

Undocumented

xwxz

Undocumented

xwy

Undocumented

xwyw

Undocumented

xwyx

Undocumented

xwyy

Undocumented

xwyz

Undocumented

xwz

Undocumented

xwzw

Undocumented

xwzx

Undocumented

xwzy

Undocumented

xwzz

Undocumented

xx

Undocumented

xxw

Undocumented

xxww

Undocumented

xxwx

Undocumented

xxwy

Undocumented

xxwz

Undocumented

xxx

Undocumented

xxxw

Undocumented

xxxx

Undocumented

xxxy

Undocumented

xxxz

Undocumented

xxy

Undocumented

xxyw

Undocumented

xxyx

Undocumented

xxyy

Undocumented

xxyz

Undocumented

xxz

Undocumented

xxzw

Undocumented

xxzx

Undocumented

xxzy

Undocumented

xxzz

Undocumented

xy

Undocumented

xyw

Undocumented

xyww

Undocumented

xywx

Undocumented

xywy

Undocumented

xywz

Undocumented

xyx

Undocumented

xyxw

Undocumented

xyxx

Undocumented

xyxy

Undocumented

xyxz

Undocumented

xyy

Undocumented

xyyw

Undocumented

xyyx

Undocumented

xyyy

Undocumented

xyyz

Undocumented

xyz

Undocumented

xyzw

Undocumented

xyzx

Undocumented

xyzy

Undocumented

xyzz

Undocumented

xz

Undocumented

xzw

Undocumented

xzww

Undocumented

xzwx

Undocumented

xzwy

Undocumented

xzwz

Undocumented

xzx

Undocumented

xzxw

Undocumented

xzxx

Undocumented

xzxy

Undocumented

xzxz

Undocumented

xzy

Undocumented

xzyw

Undocumented

xzyx

Undocumented

xzyy

Undocumented

xzyz

Undocumented

xzz

Undocumented

xzzw

Undocumented

xzzx

Undocumented

xzzy

Undocumented

xzzz

Undocumented

y

Vector Y axis.

Type:float
yw

Undocumented

yww

Undocumented

ywww

Undocumented

ywwx

Undocumented

ywwy

Undocumented

ywwz

Undocumented

ywx

Undocumented

ywxw

Undocumented

ywxx

Undocumented

ywxy

Undocumented

ywxz

Undocumented

ywy

Undocumented

ywyw

Undocumented

ywyx

Undocumented

ywyy

Undocumented

ywyz

Undocumented

ywz

Undocumented

ywzw

Undocumented

ywzx

Undocumented

ywzy

Undocumented

ywzz

Undocumented

yx

Undocumented

yxw

Undocumented

yxww

Undocumented

yxwx

Undocumented

yxwy

Undocumented

yxwz

Undocumented

yxx

Undocumented

yxxw

Undocumented

yxxx

Undocumented

yxxy

Undocumented

yxxz

Undocumented

yxy

Undocumented

yxyw

Undocumented

yxyx

Undocumented

yxyy

Undocumented

yxyz

Undocumented

yxz

Undocumented

yxzw

Undocumented

yxzx

Undocumented

yxzy

Undocumented

yxzz

Undocumented

yy

Undocumented

yyw

Undocumented

yyww

Undocumented

yywx

Undocumented

yywy

Undocumented

yywz

Undocumented

yyx

Undocumented

yyxw

Undocumented

yyxx

Undocumented

yyxy

Undocumented

yyxz

Undocumented

yyy

Undocumented

yyyw

Undocumented

yyyx

Undocumented

yyyy

Undocumented

yyyz

Undocumented

yyz

Undocumented

yyzw

Undocumented

yyzx

Undocumented

yyzy

Undocumented

yyzz

Undocumented

yz

Undocumented

yzw

Undocumented

yzww

Undocumented

yzwx

Undocumented

yzwy

Undocumented

yzwz

Undocumented

yzx

Undocumented

yzxw

Undocumented

yzxx

Undocumented

yzxy

Undocumented

yzxz

Undocumented

yzy

Undocumented

yzyw

Undocumented

yzyx

Undocumented

yzyy

Undocumented

yzyz

Undocumented

yzz

Undocumented

yzzw

Undocumented

yzzx

Undocumented

yzzy

Undocumented

yzzz

Undocumented

z

Vector Z axis (3D Vectors only).

Type:float
zw

Undocumented

zww

Undocumented

zwww

Undocumented

zwwx

Undocumented

zwwy

Undocumented

zwwz

Undocumented

zwx

Undocumented

zwxw

Undocumented

zwxx

Undocumented

zwxy

Undocumented

zwxz

Undocumented

zwy

Undocumented

zwyw

Undocumented

zwyx

Undocumented

zwyy

Undocumented

zwyz

Undocumented

zwz

Undocumented

zwzw

Undocumented

zwzx

Undocumented

zwzy

Undocumented

zwzz

Undocumented

zx

Undocumented

zxw

Undocumented

zxww

Undocumented

zxwx

Undocumented

zxwy

Undocumented

zxwz

Undocumented

zxx

Undocumented

zxxw

Undocumented

zxxx

Undocumented

zxxy

Undocumented

zxxz

Undocumented

zxy

Undocumented

zxyw

Undocumented

zxyx

Undocumented

zxyy

Undocumented

zxyz

Undocumented

zxz

Undocumented

zxzw

Undocumented

zxzx

Undocumented

zxzy

Undocumented

zxzz

Undocumented

zy

Undocumented

zyw

Undocumented

zyww

Undocumented

zywx

Undocumented

zywy

Undocumented

zywz

Undocumented

zyx

Undocumented

zyxw

Undocumented

zyxx

Undocumented

zyxy

Undocumented

zyxz

Undocumented

zyy

Undocumented

zyyw

Undocumented

zyyx

Undocumented

zyyy

Undocumented

zyyz

Undocumented

zyz

Undocumented

zyzw

Undocumented

zyzx

Undocumented

zyzy

Undocumented

zyzz

Undocumented

zz

Undocumented

zzw

Undocumented

zzww

Undocumented

zzwx

Undocumented

zzwy

Undocumented

zzwz

Undocumented

zzx

Undocumented

zzxw

Undocumented

zzxx

Undocumented

zzxy

Undocumented

zzxz

Undocumented

zzy

Undocumented

zzyw

Undocumented

zzyx

Undocumented

zzyy

Undocumented

zzyz

Undocumented

zzz

Undocumented

zzzw

Undocumented

zzzx

Undocumented

zzzy

Undocumented

zzzz

Undocumented