Module Vector'

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

Example:
    >>> mirror=refmat(p,q)
    >>> qq=p.left_multiply(mirror)
    >>> print q, qq # q and qq should be the same

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

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.

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, 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

Returns 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