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:
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 (Sequence[float]) – (red, green, blue) color values where (0, 0, 0) is black & (1, 1, 1) is white.
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}".format(*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}".format(*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}".format(*(int(c) for c in (col * 255.0)))) # This example prints the color as hexadecimal print("Hexadecimal: {:02x}{:02x}{:02x}".format(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:
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:
- 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:
- 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:
- 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:
- from_scene_linear_to_srgb()¶
Convert from scene linear to sRGB color space.
- Returns:
A color in sRGB color space.
- Return type:
- 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:
- from_srgb_to_scene_linear()¶
Convert from sRGB to scene linear color space.
- Returns:
A color in scene linear color space.
- Return type:
- 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:
- 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:
bool
- is_valid¶
True when the owner of this data is valid.
- Type:
bool
- is_wrapped¶
True when this object wraps external data (read-only).
- Type:
bool
- 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 (Sequence[float]) – (X, Y, Z) 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}".format(*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:
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
|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 (str) – 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:
- to_quaternion()¶
Return a quaternion representation of the euler.
- Returns:
Quaternion representation of the euler.
- Return type:
- zero()¶
Set all values to zero.
- is_frozen¶
True when this object has been frozen (read-only).
- Type:
bool
- is_valid¶
True when the owner of this data is valid.
- Type:
bool
- is_wrapped¶
True when this object wraps external data (read-only).
- Type:
bool
- order¶
Euler rotation order.
- Type:
str 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 (Sequence[Sequence[float]]) – 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.
- 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:
- 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
| None) – The translation component.rotation (
Matrix
|Quaternion
|Euler
| None) – The rotation component as a 3x3 matrix, quaternion, euler or None for no rotation.scale (
Vector
| None) – The scale component.
- Returns:
Combined transformation as a 4x4 matrix.
- Return type:
# 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.
- classmethod Rotation(angle, size, axis)¶
Create a matrix representing a rotation.
- classmethod Scale(factor, size, axis)¶
Create a matrix representing a scaling.
- classmethod Shear(plane, size, factor)¶
Create a matrix to represent an shear transformation.
- Parameters:
plane (str) – 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 | Sequence[float]) – The factor of shear to apply. For a 2 size matrix use a single float. For a 3 or 4 size matrix pass a pair of floats corresponding with the plane axis.
- Returns:
A new shear matrix.
- Return type:
- classmethod Translation(vector)¶
Create a matrix representing a translation.
- 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:
- Raises:
ValueError – if the matrix cannot be adjugated
- decompose()¶
Return the translation, rotation, and scale components of this matrix.
- Returns:
Tuple of translation, rotation, and scale.
- Return type:
tuple[
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 aValueError
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
| Any
- 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:
- lerp(other, factor)¶
Returns the interpolation of two matrices. Uses polar decomposition, see “Matrix Animation and Polar Decomposition”, Shoemake and Duff, 1992.
- normalize()¶
Normalize each of the matrix columns.
Note
for 4x4 matrices, the 4th column (translation) is left untouched.
- normalized()¶
Return a column normalized matrix
- Returns:
a column normalized matrix
- Return type:
Note
for 4x4 matrices, the 4th column (translation) is left untouched.
- resize_4x4()¶
Resize the matrix to 4x4.
- rotate(other)¶
Rotates the matrix by another mathutils value.
- Parameters:
other (
Euler
|Quaternion
|Matrix
) – rotation component of mathutils value
Note
If any of the columns are not unit length this may not have desired results.
- to_euler(order, euler_compat)¶
Return an Euler representation of the rotation matrix (3x3 or 4x4 matrix only).
- Parameters:
order (str) – 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:
- to_quaternion()¶
Return a quaternion representation of the rotation matrix.
- Returns:
Quaternion representation of the rotation matrix.
- Return type:
- to_scale()¶
Return the scale part of a 3x3 or 4x4 matrix.
- Returns:
Return the scale of a matrix.
- Return type:
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:
- zero()¶
Set all the matrix values to zero.
- 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:
bool
- is_identity¶
True if this is an identity matrix (read-only).
- Type:
bool
- 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:
bool
- is_wrapped¶
True when this object wraps external data (read-only).
- Type:
bool
- 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
- class mathutils.Quaternion([seq[, angle]])¶
This object gives access to Quaternions in Blender.
- Parameters:
seq (
Vector
) – size 3 or 4angle (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
- (axis, angle)
Create a quaternion representing a rotation of angle radians over axis.
See also
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}".format(*(math.degrees(a) for a in quat_out.to_euler()))) print("({:.2f}, {:.2f}, {:.2f}), {:.2f}".format(*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:
- copy()¶
Returns a copy of this quaternion.
- Returns:
A copy of the quaternion.
- Return type:
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:
- 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.
- invert()¶
Set the quaternion to its inverse.
- inverted()¶
Return a new, inverted quaternion.
- Returns:
the inverted value.
- Return type:
- make_compatible(other)¶
Make this quaternion compatible with another, so interpolating between them works as intended.
- negate()¶
Set the quaternion to its negative.
- normalize()¶
Normalize the quaternion.
- normalized()¶
Return a new normalized quaternion.
- Returns:
a normalized copy.
- Return type:
- rotate(other)¶
Rotates the quaternion by another mathutils value.
- Parameters:
other (
Euler
|Quaternion
|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:
- 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:
- to_axis_angle()¶
Return the axis, angle representation of the quaternion.
- Returns:
Axis, angle.
- Return type:
tuple[
Vector
, float]
- to_euler(order, euler_compat)¶
Return Euler representation of the quaternion.
- Parameters:
order (str) – 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:
- 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:
- 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 (str) – Twist axis as a string in [‘X’, ‘Y’, ‘Z’].
- Returns:
Swing, twist angle.
- Return type:
tuple[
Quaternion
, float]
- angle¶
Angle of the quaternion.
- Type:
float
- is_frozen¶
True when this object has been frozen (read-only).
- Type:
bool
- is_valid¶
True when the owner of this data is valid.
- Type:
bool
- is_wrapped¶
True when this object wraps external data (read-only).
- Type:
bool
- 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[float]) – 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:
vector (
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 withfallback (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 | Any
- angle_signed(other, fallback)¶
Return the signed angle between two 2D vectors (clockwise is positive).
- Parameters:
other (
Vector
) – another vector to compare the angle withfallback (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 | Any
- copy()¶
Returns a copy of this vector.
- Returns:
A copy of the vector.
- Return type:
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 as a vector or a float when 2D vectors are used.
- Return type:
Vector
| float
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.
- 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:
- orthogonal()¶
Return a perpendicular vector.
- Returns:
a new vector 90 degrees from this vector.
- Return type:
Note
the axis is undefined, only use when any orthogonal vector is acceptable.
- project(other)¶
Return the projection of this vector onto the other.
- reflect(mirror)¶
Return the reflection vector from the mirror argument.
- 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:
- 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
|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:
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:
- to_track_quat(track, up)¶
Return a quaternion rotation from the vector and the track and up axis.
- Parameters:
track (str) – Track axis in [‘X’, ‘Y’, ‘Z’, ‘-X’, ‘-Y’, ‘-Z’].
up (str) – Up axis in [‘X’, ‘Y’, ‘Z’].
- Returns:
rotation from the vector and the track and up axis.
- Return type:
- 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[float]
- zero()¶
Set all values to zero.
- is_frozen¶
True when this object has been frozen (read-only).
- Type:
bool
- is_valid¶
True when the owner of this data is valid.
- Type:
bool
- is_wrapped¶
True when this object wraps external data (read-only).
- Type:
bool
- 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
- x¶
Vector X axis.
- Type:
float
- y¶
Vector Y axis.
- Type:
float
- z¶
Vector Z axis (3D Vectors only).
- Type:
float