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Blender

Module Mathutils
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Module Mathutils

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
Classes
Euler This object gives access to Eulers in Blender.
Matrix This object gives access to Matrices in Blender.
Quaternion This object gives access to Quaternions in Blender.
Vector This object gives access to Vectors in Blender.

Function Summary
float AngleBetweenVecs(vec1, vec2)
Return the angle between two vectors.
Euler object CopyEuler(euler)
Create a new euler object.
Matrix object. CopyMat(matrix)
Create a copy of the Matrix object.
Quaternion object. CopyQuat(quaternion)
Create a copy of the Quaternion object.
Vector object. CopyVec(vector)
Create a copy of the Vector object.
Quaternion object. CrossQuats(quat1, quat2)
Return the cross product of two quaternions.
Vector object. CrossVecs(vec1, vec2)
Return the cross product of two vectors.
Quaternion object DifferenceQuats(quat1, quat2)
Returns a quaternion represting the rotational difference.
float DotQuats(quat1, quat2)
Return the dot product of two quaternions.
float DotVecs(vec1, vec2)
Return the dot product of two vectors.
Vector object MatMultVec(mat, vec)
Multiply a matrix and a vector (post-multiply) Vector size and matrix row size must equal.
Vector object MidpointVecs(vec1, vec2)
Return a vector to the midpoint between two vectors.
Matrix object. OrthoProjectionMatrix(plane, matSize, axis)
Create a matrix to represent an orthographic projection
Vector object ProjectVecs(vec1, vec2)
Return the projection of vec1 onto vec2.
  Rand(high, low)
Return a random number within a range.
  RotateEuler(euler, angle, axis)
Roatate a euler by an amount in degrees around an axis.
Matrix object. RotationMatrix(angle, matSize, axisFlag, axis)
Create a matrix representing a rotation.
Matrix object. ScaleMatrix(factor, matSize, axis)
Create a matrix representing a scaling.
Matrix object. ShearMatrix(plane, factor, matSize)
Create a matrix to represent an orthographic projection
Quaternion object Slerp(quat1, quat2, factor)
Returns the interpolation of two quaternions.
Matrix object. TranslationMatrix(vector)
Create a matrix representing a translation
Vector object VecMultMat(vec, mat)
Multiply a vector and matrix (pre-multiply) Vector size and matrix column size must equal.

Function Details

AngleBetweenVecs(vec1, vec2)

Return the angle between two vectors.
Parameters:
vec1 - A 2d or 3d vector.
           (type=Vector object.)
vec2 - A 2d or 3d vector.
           (type=Vector object.)
Returns:
The angle between the vectors in degrees.
           (type=float)

CopyEuler(euler)

Create a new euler object.
Parameters:
euler - The euler to copy
           (type=Euler object)
Returns:
A copy of the euler object passed in.
           (type=Euler object)

CopyMat(matrix)

Create a copy of the Matrix object.
Parameters:
matrix - A 2d,3d or 4d matrix to be copied.
           (type=Matrix object.)
Returns:
A new matrix object which is a copy of the one passed in.
           (type=Matrix object.)

CopyQuat(quaternion)

Create a copy of the Quaternion object.
Parameters:
quaternion - Quaternion to be copied.
           (type=Quaternion object.)
Returns:
A new quaternion object which is a copy of the one passed in.
           (type=Quaternion object.)

CopyVec(vector)

Create a copy of the Vector object.
Parameters:
vector - A 2d,3d or 4d vector to be copied.
           (type=Vector object.)
Returns:
A new vector object which is a copy of the one passed in.
           (type=Vector object.)

CrossQuats(quat1, quat2)

Return the cross product of two quaternions.
Parameters:
quat1 - Quaternion.
           (type=Quaternion object.)
quat2 - Quaternion.
           (type=Quaternion object.)
Returns:
A new quaternion representing the cross product of the two quaternions.
           (type=Quaternion object.)

CrossVecs(vec1, vec2)

Return the cross product of two vectors.
Parameters:
vec1 - A 3d vector.
           (type=Vector object.)
vec2 - A 3d vector.
           (type=Vector object.)
Returns:
A new vector representing the cross product of the two vectors.
           (type=Vector object.)

DifferenceQuats(quat1, quat2)

Returns a quaternion represting the rotational difference.
Parameters:
quat1 - Quaternion.
           (type=Quaternion object.)
quat2 - Quaternion.
           (type=Quaternion object.)
Returns:
Return a quaternion which which represents the rotational difference between the two quat rotations.
           (type=Quaternion object)

DotQuats(quat1, quat2)

Return the dot product of two quaternions.
Parameters:
quat1 - Quaternion.
           (type=Quaternion object.)
quat2 - Quaternion.
           (type=Quaternion object.)
Returns:
Return the scalar product of quaternion muliplication.
           (type=float)

DotVecs(vec1, vec2)

Return the dot product of two vectors.
Parameters:
vec1 - A 2d,3d or 4d vector.
           (type=Vector object.)
vec2 - A 2d,3d or 4d vector.
           (type=Vector object.)
Returns:
Return the scalar product of vector muliplication.
           (type=float)

MatMultVec(mat, vec)

Multiply a matrix and a vector (post-multiply) Vector size and matrix row size must equal.
Parameters:
mat - A 2d,3d or 4d matrix.
           (type=Matrix object.)
vec - A 2d,3d or 4d vector.
           (type=Vector object.)
Returns:
The column vector that results from the muliplication.
           (type=Vector object)

MidpointVecs(vec1, vec2)

Return a vector to the midpoint between two vectors.
Parameters:
vec1 - A 2d,3d or 4d vector.
           (type=Vector object.)
vec2 - A 2d,3d or 4d vector.
           (type=Vector object.)
Returns:
The vector to the midpoint.
           (type=Vector object)

OrthoProjectionMatrix(plane, matSize, axis)

Create a matrix to represent an orthographic projection
Parameters:
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=string)
matSize - The size of the projection matrix to construct. Can be 2d, 3d, or 4d.
           (type=int)
axis - Arbitrary perpendicular plane vector.
           (type=Vector object. (optional))
Returns:
A new projeciton matrix.
           (type=Matrix object.)

ProjectVecs(vec1, vec2)

Return the projection of vec1 onto vec2.
Parameters:
vec1 - A 2d,3d or 4d vector.
           (type=Vector object.)
vec2 - A 2d,3d or 4d vector.
           (type=Vector object.)
Returns:
The parallel projection vector.
           (type=Vector object)

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.
Parameters:
high - The upper range.
           (type=float)
low - The lower range.
           (type=float)

RotateEuler(euler, angle, axis)

Roatate a euler by an amount in degrees around an axis.
Parameters:
euler - Euler to rotate.
           (type=Euler object)
angle - The amount of rotation in degrees
           (type=float)
axis - axis to rotate around:
  • "x"
  • "y"
  • "z"

           (type=string)

RotationMatrix(angle, matSize, axisFlag, axis)

Create a matrix representing a rotation.
Parameters:
angle - The angle of rotation desired.
           (type=float)
matSize - The size of the rotation matrix to construct. Can be 2d, 3d, or 4d.
           (type=int)
axisFlag - Possible values:
  • "x - x-axis rotation"
  • "y - y-axis rotation"
  • "z - z-axis rotation"
  • "r - arbitrary rotation around vector"

           (type=string (optional))
axis - The arbitrary axis of rotation used with "R"
           (type=Vector object. (optional))
Returns:
A new rotation matrix.
           (type=Matrix object.)

ScaleMatrix(factor, matSize, axis)

Create a matrix representing a scaling.
Parameters:
factor - The factor of scaling to apply.
           (type=float)
matSize - The size of the scale matrix to construct. Can be 2d, 3d, or 4d.
           (type=int)
axis - Direction to influence scale.
           (type=Vector object. (optional))
Returns:
A new scale matrix.
           (type=Matrix object.)

ShearMatrix(plane, factor, matSize)

Create a matrix to represent an orthographic projection
Parameters:
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=string)
factor - The factor of shear to apply.
           (type=float)
matSize - The size of the projection matrix to construct. Can be 2d, 3d, or 4d.
           (type=int)
Returns:
A new shear matrix.
           (type=Matrix object.)

Slerp(quat1, quat2, factor)

Returns the interpolation of two quaternions.
Parameters:
quat1 - Quaternion.
           (type=Quaternion object.)
quat2 - Quaternion.
           (type=Quaternion object.)
factor - The interpolation value
           (type=float)
Returns:
The interpolated rotation.
           (type=Quaternion object)

TranslationMatrix(vector)

Create a matrix representing a translation
Parameters:
vector - The translation vector
           (type=Vector object)
Returns:
An identity matrix with a translation.
           (type=Matrix object.)

VecMultMat(vec, mat)

Multiply a vector and matrix (pre-multiply) Vector size and matrix column size must equal.
Parameters:
vec - A 2d,3d or 4d vector.
           (type=Vector object.)
mat - A 2d,3d or 4d matrix.
           (type=Matrix object.)
Returns:
The row vector that results from the muliplication.
           (type=Vector object)

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