QuaternionT.hh

/*===========================================================================*\
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 *                              OpenFlipper                                  *
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/*===========================================================================*\
 *                                                                           *
 *   $Revision: 6743 $                                                       *
 *   $Author: moebius $                                                      *
 *   $Date: 2009-08-05 11:03:10 +0200 (Mi, 05. Aug 2009) $                   *
 *                                                                           *
\*===========================================================================*/



//=============================================================================
//
//  CLASS Quaternion
//
//=============================================================================

#ifndef ACG_QUATERNION_HH
#define ACG_QUATERNION_HH


//== INCLUDES =================================================================

#include "VectorT.hh"
#include "Matrix4x4T.hh"


//== NAMESPACES  ==============================================================

namespace ACG {


//== CLASS DEFINITION =========================================================


template <class Scalar>
class QuaternionT : public VectorT<Scalar,4>
{
public:

#define W Base::values_[0]
#define X Base::values_[1]
#define Y Base::values_[2]
#define Z Base::values_[3]


  typedef VectorT<Scalar,4>    Base;
  typedef QuaternionT<Scalar>  Quaternion;
  typedef VectorT<Scalar,3>    Vec3;
  typedef VectorT<Scalar,4>    Vec4;
  typedef Matrix4x4T<Scalar>   Matrix;


  QuaternionT(Scalar _w=1.0, Scalar _x=0.0, Scalar _y=0.0, Scalar _z=0.0)
    : Vec4(_w, _x, _y, _z) {}

  QuaternionT(const Vec3& _p)
    : Vec4(0, _p[0], _p[1], _p[2]) {}

  QuaternionT(const Vec4& _p)
    : Vec4(_p[0], _p[1], _p[2], _p[3]) {}

  QuaternionT(Vec3 _axis, Scalar _angle)
  {
    _axis.normalize();
    Scalar theta = 0.5 * _angle;
    Scalar sin_theta = sin(theta);
    W = cos(theta);
    X = sin_theta * _axis[0];
    Y = sin_theta * _axis[1];
    Z = sin_theta * _axis[2];
  }


  void identity() { W=1.0; X=Y=Z=0.0; }


  Quaternion conjugate() const
  { return Quaternion(W, -X, -Y, -Z); }


  Quaternion invert() const
  { return conjugate()/Base::sqrnorm(); }


  Quaternion operator*(const Quaternion& _q) const
  { return Quaternion(W*_q.W - X*_q.X - Y*_q.Y - Z*_q.Z,
                      W*_q.X + X*_q.W + Y*_q.Z - Z*_q.Y,
                      W*_q.Y - X*_q.Z + Y*_q.W + Z*_q.X,
                      W*_q.Z + X*_q.Y - Y*_q.X + Z*_q.W); }


  Quaternion& operator*=(const Quaternion& _q)
  { return *this = *this * _q; }


  Vec3 rotate(const Vec3& _v)
  { 
    Quaternion q = *this * Quaternion(_v) * conjugate();
    return Vec3(q[1], q[2], q[3]);
  }


  void axis_angle(Vec3& _axis, Scalar& _angle) const
  {
    if (fabs(W) > 0.999999)
    {
      _axis  = Vec3(1,0,0);
      _angle = 0;
    }
    else
    {
      _angle = 2.0 * acos(W);
      _axis  = Vec3(X, Y, Z).normalize();
    }
  }



  Matrix rotation_matrix() const
  {
    Scalar
      ww(W*W), xx(X*X), yy(Y*Y), zz(Z*Z), wx(W*X),
      wy(W*Y), wz(W*Z), xy(X*Y), xz(X*Z), yz(Y*Z);

    Matrix m;

    m(0,0) = ww + xx - yy - zz;
    m(1,0) = 2.0*(xy + wz);
    m(2,0) = 2.0*(xz - wy);

    m(0,1) = 2.0*(xy - wz);
    m(1,1) = ww - xx + yy - zz;
    m(2,1) = 2.0*(yz + wx);

    m(0,2) = 2.0*(xz + wy);
    m(1,2) = 2.0*(yz - wx);
    m(2,2) = ww - xx - yy + zz;

    m(0,3) = m(1,3) = m(2,3) = m(3,0) = m(3,1) = m(3,2) = 0.0;
    m(3,3) = 1.0;

    return m;
  }



  Matrix right_mult_matrix() const
  {
    Matrix m;
    m(0,0) =  W; m(0,1) = -X; m(0,2) = -Y; m(0,3) = -Z;
    m(1,0) =  X; m(1,1) =  W; m(1,2) = -Z; m(1,3) =  Y;
    m(2,0) =  Y; m(2,1) =  Z; m(2,2) =  W; m(2,3) = -X;
    m(3,0) =  Z; m(3,1) = -Y; m(3,2) =  X; m(3,3) =  W;
    return m;
  }


  Matrix left_mult_matrix() const
  {
    Matrix m;
    m(0,0) =  W; m(0,1) = -X; m(0,2) = -Y; m(0,3) = -Z;
    m(1,0) =  X; m(1,1) =  W; m(1,2) =  Z; m(1,3) = -Y;
    m(2,0) =  Y; m(2,1) = -Z; m(2,2) =  W; m(2,3) =  X;
    m(3,0) =  Z; m(3,1) =  Y; m(3,2) = -X; m(3,3) =  W;
    return m;
  }


#undef W
#undef X
#undef Y
#undef Z
};


typedef QuaternionT<float>  Quaternionf;
typedef QuaternionT<double> Quaterniond;


//=============================================================================
} // namespace ACG
//=============================================================================
#endif // ACG_QUATERNION_HH defined
//=============================================================================