[vtkusers] Transformation matrix for transforming one vector to another

[David Gobbi]

On Sat, Dec 31, 2011 at 8:24 AM, Donny Zimmerman
<donny.zimmerman at willowpointsoftware.com> wrote:
> If I have a plane perpendicular to one vector say {0, 1000, 0} how would I
> get the transformation matrix to transform it to be perpendicular to vector
> {975, -250, 600}. I would like to use the RotateX, RotateY, RotateZ and
> translate functions of vtkTransform to accomplish this. Any help?

This fits into the "advanced math" category, you can't do it with
any of the basic transform operations.  The solution relies on
quaternions.  Below is some code that generates the 3x3 rotation
matrix.  Finding the translation and building a 4x4 matrix is left as
an exercise for the reader.

  // Compute rotation matrix between two vectors
  double vec[3];
  vtkMath::Cross(normal1, normal2, vec);
  double costheta = vtkMath::Dot(normal1, normal2);
  double sintheta = vtkMath::Norm(vec);
  double theta = atan2(sintheta, costheta);
  if (sintheta != 0)
    {
    vec[0] /= sintheta;
    vec[1] /= sintheta;
    vec[2] /= sintheta;
    }
  // convert to quaternion
  costheta = cos(0.5*theta);
  sintheta = sin(0.5*theta);
  double quat[4];
  quat[0] = costheta;
  quat[1] = vec[0]*sintheta;
  quat[2] = vec[1]*sintheta;
  quat[3] = vec[2]*sintheta;
  // convert to matrix
  double mat[3][3];
  vtkMath::QuaternionToMatrix3x3(quat, mat);

-- David