Calculate angle method.

Calculate the angle between 3 vectors representing 3 connected points.

:param v1, v2, v3: the tree points that define the angle :type v1, v2, v3: L{Vector}

:return: angle :rtype: float

Calculate dihedral angle method.

Calculate the dihedral angle between 4 vectors representing 4 connected points. The angle is in ]-pi, pi].

:param v1, v2, v3, v4: the four points that define the dihedral angle :type v1, v2, v3, v4: L{Vector}

Return angles, axis pair that corresponds to rotation matrix m.

The case where m is the identity matrix corresponds to a singularity where any rotation axis is valid. In that case, Vector([1,0,0]), is returned.

Return a (left multiplying) matrix that mirrors p onto q.

Example:

     >>> mirror=refmat(p, q)
     >>> qq=p.left_multiply(mirror)
     >>> print(q)
     >>> print(qq) 

:type p,q: L{Vector} :return: The mirror operation, a 3x3 Numeric array.

Calculate left multiplying rotation matrix.

Calculate a left multiplying rotation matrix that rotates theta rad around vector.

Example:

     >>> m=rotaxis(pi, Vector(1, 0, 0))
     >>> rotated_vector=any_vector.left_multiply(m)

:type theta: float :param theta: the rotation angle

:type vector: L{Vector} :param vector: the rotation axis

:return: The rotation matrix, a 3x3 Numeric array.

Return a (left multiplying) matrix that rotates p onto q.

Example:

     >>> r=rotmat(p, q)
     >>> print(q)
     >>> print(p.left_multiply(r))

:param p: moving vector :type p: L{Vector}

:param q: fixed vector :type q: L{Vector}

:return: rotation matrix that rotates p onto q :rtype: 3x3 Numeric array

Vector to axis method.

Return the vector between a point and the closest point on a line (ie. the perpendicular projection of the point on the line).

:type line: L{Vector} :param line: vector defining a line

:type point: L{Vector} :param point: vector defining the point