# Math Types & Utilities (mathutils)

This module provides access to the math classes:

- `Color`,
- `Euler`,
- `Matrix`,
- `Quaternion`,
- `Vector`,

Note

Classes, methods and attributes that accept vectors also accept other numeric sequences, such as tuples, lists.

    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.

  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

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

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 cant be adjugated a `ValueError` exception is raised.

    See also

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

  `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 location, rotation 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 the determinant of a matrix.
    Return type: | float

    See also

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

  `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 zero location and rotation, a scale of one, will have an identity matrix.

    See also

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

  `invert`(fallback=None)

    Set the matrix to its inverse.

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

    See also

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

  `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

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

  `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 negative a 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

    <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.

    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

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

  This object gives access to Quaternions in Blender.

  Parameters: | seq (`Vector`) – size 3 or 4 angle (float) – rotation angle, in radians

  The constructor takes arguments in various forms:

  (), no args
    Create an identity quaternion
  (wxyz)
    Create a quaternion from a `(w, x, y, z)` vector.
  (exponential_map)

    Create a quaternion from a 3d exponential map vector.

    See also

    `to_exponential_map()`

  (axis, angle)

    Create a quaternion representing a rotation of angle radians over axis.

    See also

    `to_axis_angle()`

      import mathutils
      import math

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

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

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

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

      # print the quat, euler degrees for 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

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 http://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`

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  `wwxy`

    Undocumented

  `wwxz`

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  `wwy`

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  `wwyw`

    Undocumented

  `wwyx`

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  `wwyy`

    Undocumented

  `wwyz`

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  `wwz`

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  `wwzw`

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  `wwzx`

    Undocumented

  `wwzy`

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  `wwzz`

    Undocumented

  `wx`

    Undocumented

  `wxw`

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  `wxww`

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  `wxwx`

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  `wxwy`

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  `wxwz`

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  `wxx`

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  `wxxw`

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  `wxxx`

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  `wxxy`

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  `wxxz`

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  `wxy`

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  `wxyw`

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  `wxyx`

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  `wxyy`

    Undocumented

  `wxyz`

    Undocumented

  `wxz`

    Undocumented

  `wxzw`

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  `wxzx`

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  `wxzy`

    Undocumented

  `wxzz`

    Undocumented

  `wy`

    Undocumented

  `wyw`

    Undocumented

  `wyww`

    Undocumented

  `wywx`

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  `wywy`

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  `wywz`

    Undocumented

  `wyx`

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  `wyxw`

    Undocumented

  `wyxx`

    Undocumented

  `wyxy`

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  `wyxz`

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  `wyy`

    Undocumented

  `wyyw`

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  `wyyx`

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  `wyyy`

    Undocumented

  `wyyz`

    Undocumented

  `wyz`

    Undocumented

  `wyzw`

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  `wyzx`

    Undocumented

  `wyzy`

    Undocumented

  `wyzz`

    Undocumented

  `wz`

    Undocumented

  `wzw`

    Undocumented

  `wzww`

    Undocumented

  `wzwx`

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  `wzwy`

    Undocumented

  `wzwz`

    Undocumented

  `wzx`

    Undocumented

  `wzxw`

    Undocumented

  `wzxx`

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  `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`

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  `xwxz`

    Undocumented

  `xwy`

    Undocumented

  `xwyw`

    Undocumented

  `xwyx`

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  `xwyy`

    Undocumented

  `xwyz`

    Undocumented

  `xwz`

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  `xwzw`

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  `xwzx`

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  `xwzy`

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  `xwzz`

    Undocumented

  `xx`

    Undocumented

  `xxw`

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  `xxww`

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  `xxwx`

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  `xxwy`

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  `xxwz`

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  `xxx`

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  `xxxw`

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  `xxxx`

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  `xxxy`

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  `xxxz`

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  `xxy`

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  `xxyw`

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  `xxyx`

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  `xxyy`

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  `xxyz`

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  `xxz`

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  `xxzw`

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  `xxzx`

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  `xxzy`

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  `xxzz`

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  `xy`

    Undocumented

  `xyw`

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  `xyww`

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  `xywx`

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  `xywy`

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  `xywz`

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  `xyx`

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  `xyxw`

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  `xyxx`

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  `xyxy`

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  `xyxz`

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  `xyy`

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  `xyyw`

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  `xyyx`

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  `xyyy`

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  `xyyz`

    Undocumented

  `xyz`

    Undocumented

  `xyzw`

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  `xyzx`

    Undocumented

  `xyzy`

    Undocumented

  `xyzz`

    Undocumented

  `xz`

    Undocumented

  `xzw`

    Undocumented

  `xzww`

    Undocumented

  `xzwx`

    Undocumented

  `xzwy`

    Undocumented

  `xzwz`

    Undocumented

  `xzx`

    Undocumented

  `xzxw`

    Undocumented

  `xzxx`

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  `xzxy`

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  `xzxz`

    Undocumented

  `xzy`

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  `xzyw`

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  `xzyx`

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  `xzyy`

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  `xzyz`

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  `xzz`

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  `xzzw`

    Undocumented

  `xzzx`

    Undocumented

  `xzzy`

    Undocumented

  `xzzz`

    Undocumented

  `y`

    Vector Y axis.

    Type: | float

  `yw`

    Undocumented

  `yww`

    Undocumented

  `ywww`

    Undocumented

  `ywwx`

    Undocumented

  `ywwy`

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  `ywwz`

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  `ywx`

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  `ywxw`

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  `ywxx`

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  `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`

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  `yxwz`

    Undocumented

  `yxx`

    Undocumented

  `yxxw`

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  `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`

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  `yyyx`

    Undocumented

  `yyyy`

    Undocumented

  `yyyz`

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  `yyz`

    Undocumented

  `yyzw`

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  `yyzx`

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  `yyzy`

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  `yyzz`

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  `yz`

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  `yzw`

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  `yzww`

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  `yzwx`

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  `yzwy`

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  `yzwz`

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  `yzx`

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  `yzxw`

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  `yzy`

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  `yzyw`

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  `yzyy`

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  `yzyz`

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  `yzz`

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  `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`

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  `zxwz`

    Undocumented

  `zxx`

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  `zxxw`

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  `zxxx`

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  `zxxy`

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  `zxxz`

    Undocumented

  `zxy`

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  `zxyw`

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  `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`

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  `zzxy`

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  `zzxz`

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  `zzy`

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  `zzyw`

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  `zzyy`

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  `zzz`

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  `zzzz`

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