Documentation for mathutils.

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+# Blender.Mathutils module and its subtypes
+
+"""
+The Blender.Mathutils submodule.
+
+Mathutils
+=========
+
+This module provides access to matrices, eulers, quaternions and vectors.
+
+Example::
+  import Blender
+  from Blender import Mathutils
+  from Blender.Mathutils import *
+
+  vec = Vector([1,2,3])
+  mat = RotationMatrix(90, 4, 'x')
+  matT = TranslationMatrix(vec)
+
+  matTotal = mat * matT
+  matTotal.invert()
+
+  mat3 = matTotal.rotationPart
+  quat1 = mat.toQuat()
+  quat2 = mat3.toQuat()
+
+  angle = DifferenceQuats(quat1, quat2)
+  print angle  
+"""
+
+def Rand (high = 1, low = 0):
+  """
+  Return a random number within a range.
+  High and low represent the range from which the random
+  number must return its result.
+  @type high: float
+  @param high: The upper range.
+  @type low: float
+  @param low: The lower range.
+  """
+
+def Vector (list = None):
+  """
+  Create a new Vector object from a list.
+  @type list: PyList of float or int
+  @param list: The list of values for the Vector object.
+  Must be 2, 3, or 4 values.
+  @rtype: Vector object.
+  @return: It depends wheter a parameter was passed:
+      - (list): Vector object initialized with the given values;
+      - ():     An empty 3 dimensional vector.
+  """
+
+def CopyVec(vector):
+  """
+  Create a copy of the Vector object.
+  @type vector: Vector object.
+  @param vector: A 2d,3d or 4d vector to be copied.
+  @rtype: Vector object.
+  @return: A new vector object which is a copy of the one passed in.
+  """
+
+def CrossVecs(vec1, vec2):
+  """
+  Return the cross product of two vectors.
+  @type vec1: Vector object.
+  @param vec1: A 3d vector.
+  @type vec2: Vector object.
+  @param vec2: A 3d vector.
+  @rtype: Vector object.
+  @return: A new vector representing the cross product of
+  the two vectors.
+  """
+
+def DotVecs(vec1, vec2):
+  """
+  Return the dot product of two vectors.
+  @type vec1: Vector object.
+  @param vec1: A 2d,3d or 4d vector.
+  @type vec2: Vector object.
+  @param vec2: A 2d,3d or 4d vector.
+  @rtype: float
+  @return: Return the scalar product of vector muliplication.
+  """
+
+def AngleBetweenVecs(vec1, vec2):
+  """
+  Return the angle between two vectors.
+  @type vec1: Vector object.
+  @param vec1: A 2d or 3d vector.
+  @type vec2: Vector object.
+  @param vec2: A 2d or 3d vector.
+  @rtype: float
+  @return: The angle between the vectors in degrees.
+  """
+
+def MidpointVecs(vec1, vec2):
+  """
+  Return a vector to the midpoint between two vectors.
+  @type vec1: Vector object.
+  @param vec1: A 2d,3d or 4d vector.
+  @type vec2: Vector object.
+  @param vec2: A 2d,3d or 4d vector.
+  @rtype: Vector object
+  @return: The vector to the midpoint.
+  """
+
+def VecMultMat(vec, mat):
+  """
+  Multiply a vector and matrix (pre-multiply)
+  Vector size and matrix column size must equal.
+  @type vec: Vector object.
+  @param vec: A 2d,3d or 4d vector.
+  @type mat: Matrix object.
+  @param mat: A 2d,3d or 4d matrix.
+  @rtype: Vector object
+  @return: The row vector that results from the muliplication.
+  """
+
+def ProjectVecs(vec1, vec2):
+  """  
+  Return the projection of vec1 onto vec2.
+  @type vec1: Vector object.
+  @param vec1: A 2d,3d or 4d vector.
+  @type vec2: Vector object.
+  @param vec2: A 2d,3d or 4d vector.
+  @rtype: Vector object
+  @return: The parallel projection vector.
+  """
+
+def Matrix(list1 = None, list2 = None, list3 = None, list4 = None):
+  """  
+  Create a new matrix object from intialized values.
+  @type list1: PyList of int/float
+  @param list1: A 2d,3d or 4d list.
+  @type list2: PyList of int/float
+  @param list2: A 2d,3d or 4d list.
+  @type list3: PyList of int/float
+  @param list3: A 2d,3d or 4d list.
+  @type list4: PyList of int/float
+  @param list4: A 2d,3d or 4d list.
+  @rtype: New matrix object.
+  @return: It depends wheter a parameter was passed:
+      - (list1, etc.): Matrix object initialized with the given values;
+      - ():     An empty 3 dimensional matrix.
+  """
+
+def RotationMatrix(angle, matSize, axisFlag, axis):
+  """  
+  Create a matrix representing a rotation.
+  @type angle: float
+  @param angle: The angle of rotation desired.
+  @type matSize: int
+  @param matSize: The size of the rotation matrix to construct.
+  Can be 2d, 3d, or 4d.
+  @type axisFlag: string (optional)
+  @param axisFlag: Possible values:
+       - "x - x-axis rotation"
+       - "y - y-axis rotation"
+       - "z - z-axis rotation"
+       - "r - arbitrary rotation around vector"
+  @type axis: Vector object. (optional)
+  @param axis: The arbitrary axis of rotation used with "R"
+  @rtype: Matrix object.
+  @return: A new rotation matrix.
+  """
+
+def TranslationMatrix(vector):
+  """  
+  Create a matrix representing a translation
+  @type vector: Vector object
+  @param vector: The translation vector
+  @rtype: Matrix object.
+  @return: An identity matrix with a translation.
+  """
+
+def ScaleMatrix(factor, matSize, axis):
+  """  
+  Create a matrix representing a scaling.
+  @type factor: float
+  @param factor: The factor of scaling to apply.
+  @type matSize: int
+  @param matSize: The size of the scale matrix to construct.
+  Can be 2d, 3d, or 4d.
+  @type axis: Vector object.  (optional)
+  @param axis: Direction to influence scale.
+  @rtype: Matrix object.
+  @return: A new scale matrix.
+  """
+
+def OrthoProjectionMatrix(plane, matSize, axis):
+  """  
+  Create a matrix to represent an orthographic projection
+  @type plane: string
+  @param plane: Can be any of the following:
+       - "x - x projection (2D)"
+       - "y - y projection (2D)"
+       - "xy - xy projection"
+       - "xz - xz projection"
+       - "yz - yz projection"
+       - "r - arbitrary projection plane"
+  @type matSize: int
+  @param matSize: The size of the projection matrix to construct.
+  Can be 2d, 3d, or 4d.
+  @type axis: Vector object. (optional)
+  @param axis: Arbitrary perpendicular plane vector.
+  @rtype: Matrix object.
+  @return: A new projeciton matrix.
+  """
+
+def ShearMatrix(plane, factor, matSize):
+  """  
+  Create a matrix to represent an orthographic projection
+  @type plane: string
+  @param plane: Can be any of the following:
+       - "x - x shear (2D)"
+       - "y - y shear (2D)"
+       - "xy - xy shear"
+       - "xz - xz shear"
+       - "yz - yz shear"
+  @type factor: float
+  @param factor: The factor of shear to apply.
+  @type matSize: int
+  @param matSize: The size of the projection matrix to construct.
+  Can be 2d, 3d, or 4d.
+  @rtype: Matrix object.
+  @return: A new shear matrix.
+  """
+
+def CopyMat(matrix):
+  """
+  Create a copy of the Matrix object.
+  @type matrix: Matrix object.
+  @param matrix: A 2d,3d or 4d matrix to be copied.
+  @rtype: Matrix object.
+  @return: A new matrix object which is a copy of the one passed in.
+  """
+
+def MatMultVec(mat, vec):
+  """
+  Multiply a matrix and a vector (post-multiply)
+  Vector size and matrix row size must equal.
+  @type vec: Vector object.
+  @param vec: A 2d,3d or 4d vector.
+  @type mat: Matrix object.
+  @param mat: A 2d,3d or 4d matrix.
+  @rtype: Vector object
+  @return: The column vector that results from the muliplication.
+  """
+
+def Quaternion(list = None, angle = None):
+  """  
+  Create a new matrix object from intialized values.
+  @type list: PyList of int/float
+  @param list: A 3d or 4d list to intialize quaternion.
+  4d if intializing, 3d if will be used as an axis of rotation.
+  @type angle: float (optional)
+  @param angle: An arbitrary rotation amount around 'list'.
+  List is used as an axis of rotation in this case.
+  @rtype: New quaternion object.
+  @return: It depends wheter a parameter was passed:
+      - (list/angle): Quaternion object initialized with the given values;
+      - ():     An identity 4 dimensional quaternion.
+  """
+
+def CopyQuat(quaternion):
+  """
+  Create a copy of the Quaternion object.
+  @type quaternion: Quaternion object.
+  @param quaternion: Quaternion to be copied.
+  @rtype: Quaternion object.
+  @return: A new quaternion object which is a copy of the one passed in.
+  """
+
+def CrossQuats(quat1, quat2):
+  """
+  Return the cross product of two quaternions.
+  @type quat1: Quaternion object.
+  @param quat1: Quaternion.
+  @type quat2: Quaternion object.
+  @param quat2: Quaternion.
+  @rtype: Quaternion object.
+  @return: A new quaternion representing the cross product of
+  the two quaternions.
+  """
+
+def DotQuats(quat1, quat2):
+  """
+  Return the dot product of two quaternions.
+  @type quat1: Quaternion object.
+  @param quat1: Quaternion.
+  @type quat2: Quaternion object.
+  @param quat2: Quaternion.
+  @rtype: float
+  @return: Return the scalar product of quaternion muliplication.
+  """
+
+def DifferenceQuats(quat1, quat2):
+  """
+  Returns a quaternion represting the rotational difference.
+  @type quat1: Quaternion object.
+  @param quat1: Quaternion.
+  @type quat2: Quaternion object.
+  @param quat2: Quaternion.
+  @rtype: Quaternion object
+  @return: Return a quaternion which which represents the rotational
+  difference between the two quat rotations.
+  """
+
+def Slerp(quat1, quat2, factor):
+  """
+  Returns the interpolation of two quaternions.
+  @type quat1: Quaternion object.
+  @param quat1: Quaternion.
+  @type quat2: Quaternion object.
+  @param quat2: Quaternion.
+  @type factor: float
+  @param factor: The interpolation value
+  @rtype: Quaternion object
+  @return: The interpolated rotation.
+  """
+
+def Euler(list = None):
+  """
+  Create a new euler object.
+  @type list: PyList of float/int
+  @param list: 3d list to initalize euler
+  @rtype: Euler object
+  @return: Euler representing heading, pitch, bank.
+  Values are in degrees.
+  """
+
+def CopyEuler(euler):
+  """
+  Create a new euler object.
+  @type euler: Euler object
+  @param euler: The euler to copy
+  @rtype: Euler object
+  @return: A copy of the euler object passed in.
+  """
+
+def RotateEuler(euler, angle, axis):
+  """
+  Roatate a euler by an amount in degrees around an axis.
+  @type euler: Euler object
+  @param euler: Euler to rotate.
+  @type angle: float
+  @param angle: The amount of rotation in degrees
+  @type axis: string
+  @param axis: axis to rotate around:
+       - "x"
+       - "y"
+       - "z"
+  """
+
+class Vector:
+  """
+  The Vector object
+  =================
+    This object gives access to Vectors in Blender.
+  @cvar x: The x value.
+  @cvar y: The y value.
+  @cvar z: The z value (if any).
+  @cvar w: The w value (if any).
+  @cvar length: The magnitude of the vector.
+  """
+
+  def zero():
+    """
+    Set all values to zero.
+    """
+
+  def normalize():
+    """
+    Normalize the vector.
+    """
+
+  def negate():
+    """
+    Set all values to their negative.
+    """
+
+  def resize2D():
+    """
+    Resize the vector to 2d.
+    """
+
+  def resize3D():
+    """
+    Resize the vector to 3d.
+    """
+
+  def resize4D():
+    """
+    Resize the vector to 4d.
+    """
+
+class Euler:
+  """
+  The Euler object
+  ================
+    This object gives access to Eulers in Blender.
+  @cvar x: The heading value in degrees.
+  @cvar y: The pitch value in degrees.
+  @cvar z: The roll value in degrees.
+  """
+
+  def zero():
+    """
+    Set all values to zero.
+    """
+
+  def unique():
+    """
+    Calculate a unique rotation for this euler.
+    """
+
+  def toMatrix():
+    """
+    Return a matrix representation of the euler.
+    @rtype: Matrix object
+    @return: A roation matrix representation of the euler.
+
+    """
+
+  def toQuat():
+    """
+    Return a quaternion representation of the euler.
+    @rtype: Quaternion object
+    @return: Quaternion representation of the euler.
+
+    """
+
+class Quaternion:
+  """
+  The Quaternion object
+  =====================
+    This object gives access to Quaternions in Blender.
+  @cvar w: The w value.
+  @cvar x: The x value.
+  @cvar y: The y value.
+  @cvar z: The z value.
+  @cvar magnitude: The magnitude of the quaternion.
+  @cvar axis: Vector representing the axis of rotation.
+  @cvar angle: A scalar representing the amount of rotation
+  in degrees.
+  """
+
+  def identity():
+    """
+    Set the quaternion to the identity quaternion.
+    """
+
+  def negate():
+    """
+    Set the quaternion to it's negative.
+    """
+
+  def conjugate():
+    """
+    Set the quaternion to it's conjugate.
+    """
+
+  def inverse():
+    """
+    Set the quaternion to it's inverse
+    """
+
+  def normalize():
+    """
+    Normalize the quaternion.
+    """
+
+  def toEuler():
+    """
+    Return Euler representation of the quaternion.
+    @rtype: Euler object
+    @return: Euler representation of the quaternion.
+
+    """
+  
+  def toMatrix():
+    """
+    Return a matrix representation of the quaternion.
+    @rtype: Matrix object
+    @return: A rotation matrix representation of the quaternion.
+
+    """
+
+class Matrix:
+  """
+  The Matrix Object
+  =================
+    This object gives access to Matrices in Blender.
+  @cvar rowsize: The row size of the matrix.
+  @cvar colsize: The column size of the matrix.
+  """
+
+  def zero():
+    """
+    Set all matrix values to 0.
+    """
+
+  def identity():
+    """
+    Set the matrix to the identity matrix.
+    """
+
+  def transpose():
+    """
+    Set the matrix to it's transpose.
+    """
+
+  def determinant():
+    """
+    Return a the determinant of a matrix.
+    @rtype: int
+    @return: Return a the determinant of a matrix.
+
+    """
+
+  def inverse():
+    """
+    Set the matrix to it's inverse.
+    """
+
+  def rotationPart():
+    """
+    Return the 3d rotation matrix.
+    @rtype: Matrix object.
+    @return: Return the 3d rotation matrix.
+
+    """
+
+  def translationPart():
+    """
+    Return a the translation part of a 4 row matrix.
+    @rtype: Vector object.
+    @return: Return a the translation of a matrix.
+
+    """
+
+  def resize4x4():
+    """
+    Resize the matrix to by 4x4
+    """
+  
+  def toEuler():
+    """
+    Return a euler representing the rotation matrix.
+    @rtype: Euler object
+    @return: Return a euler representing the rotation matrix.
+
+    """
+
+  def toQuat():
+    """
+    Return a quaternion representation the rotation matrix
+    @rtype: Quaternion object
+    @return: Quaternion representation the rotation matrix
+
+    """
+