/// <summary>
/// calcultes new translation when combining translations
///
/// Rt = Ra Rb
/// Ct = Cb
/// Tt = Ra (Cb + Tb - Ca) + Ca + Ta - Cb
///
/// for theory:
/// http://www.euclideanspace.com/maths/geometry/rotations/rotationAndTranslation/nonMatrix/index.htm
/// </summary>
/// <param name="ta">Ta = translation of transform a in absolute coordinates</param>
/// <param name="ra">Ra = rotation function of transform a in absolute coordinates</param>
/// <param name="ca">Ca = centre of rotation of transform a in absolute coordinates</param>
/// <param name="tb">Tb = translation of transform b in coordinates of transform a</param>
/// <param name="cb">Cb = centre of rotation of transform b in coordinates of transform a</param>
/// <returns>Tt total offset</returns>
public vector3D rotationOffset(vector3D ta, classRotation ra, vector3D ca, vector3D tb, vector3D cb)
{
vector3D result = new vector3D(cb);
result.add(tb);
result.sub(ca);
if (ra != null)
{
ra.transform(result);
}
result.add(ca);
result.add(ta);
result.sub(cb);
return(result);
}
/// <summary>
/// calcultes new translation when combining translations
///
/// Rt = Ra Rb
/// Ct = Cb
/// Tt = Ra (Cb + Tb - Ca) + Ca + Ta - Cb
///
/// for theory:
/// http://www.euclideanspace.com/maths/geometry/rotations/rotationAndTranslation/nonMatrix/index.htm
/// </summary>
/// <param name="ta">Ta = translation of transform a in absolute coordinates</param>
/// <param name="ra">Ra = rotation function of transform a in absolute coordinates</param>
/// <param name="ca">Ca = centre of rotation of transform a in absolute coordinates</param>
/// <param name="tb">Tb = translation of transform b in coordinates of transform a</param>
/// <param name="cb">Cb = centre of rotation of transform b in coordinates of transform a</param>
/// <returns>Tt total offset</returns>
public vector3D rotationOffset(vector3D ta, classRotation ra, vector3D ca, vector3D tb, vector3D cb)
{
vector3D result = new vector3D(cb);
result.add(tb);
result.sub(ca);
if (ra != null) ra.transform(result);
result.add(ca);
result.add(ta);
result.sub(cb);
return result;
}
