/****************************************************************************

 Copyright (C) 2002-2007 Gilles Debunne (Gilles.Debunne@imag.fr)

 This file is part of the QGLViewer library.
 Version 2.2.6-3, released on August 28, 2007.

 http://artis.imag.fr/Members/Gilles.Debunne/QGLViewer

 libQGLViewer is free software; you can redistribute it and/or modify
 it under the terms of the GNU General Public License as published by
 the Free Software Foundation; either version 2 of the License, or
 (at your option) any later version.

 libQGLViewer is distributed in the hope that it will be useful,
 but WITHOUT ANY WARRANTY; without even the implied warranty of
 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
 GNU General Public License for more details.

 You should have received a copy of the GNU General Public License
 along with libQGLViewer; if not, write to the Free Software
 Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA

*****************************************************************************/

#include "AppGLWidget_quaternion.h"
#include <stdlib.h> // RAND_MAX

// All the methods are declared inline in Quaternion.h
using namespace std;

/*! Constructs a Quaternion that will rotate from the \p from direction to the \p to direction.

Note that this rotation is not uniquely defined. The selected axis is usually orthogonal to \p from
and \p to. However, this method is robust and can handle small or almost identical vectors. */
Quaternion::Quaternion(const Vec& from, const Vec& to)
{
  const float epsilon = 1E-10f;

  const float fromSqNorm = from.squaredNorm();
  const float toSqNorm   = to.squaredNorm();
  // Identity Quaternion when one vector is null
  if ((fromSqNorm < epsilon) || (toSqNorm < epsilon))
    {
      q[0]=q[1]=q[2]=0.0;
      q[3]=1.0;
    }
  else
    {
      Vec axis = cross(from, to);
      const float axisSqNorm = axis.squaredNorm();

      // Aligned vectors, pick any axis, not aligned with from or to
      if (axisSqNorm < epsilon)
	axis = from.orthogonalVec();

      double angle = asin(sqrt(axisSqNorm / (fromSqNorm * toSqNorm)));

      if (from*to < 0.0)
	angle = M_PI-angle;

      setAxisAngle(axis, angle);
    }
}

/*! Returns the image of \p v by the Quaternion inverse() rotation.

rotate() performs an inverse transformation. Same as inverse().rotate(v). */
Vec Quaternion::inverseRotate(const Vec& v) const
{
  return inverse().rotate(v);
}

/*! Returns the image of \p v by the Quaternion rotation.

See also inverseRotate() and operator*(const Quaternion&, const Vec&). */
Vec Quaternion::rotate(const Vec& v) const
{
  const double q00 = 2.0l * q[0] * q[0];
  const double q11 = 2.0l * q[1] * q[1];
  const double q22 = 2.0l * q[2] * q[2];

  const double q01 = 2.0l * q[0] * q[1];
  const double q02 = 2.0l * q[0] * q[2];
  const double q03 = 2.0l * q[0] * q[3];

  const double q12 = 2.0l * q[1] * q[2];
  const double q13 = 2.0l * q[1] * q[3];

  const double q23 = 2.0l * q[2] * q[3];

  return Vec((1.0 - q11 - q22)*v[0] + (      q01 - q23)*v[1] + (      q02 + q13)*v[2],
	     (      q01 + q23)*v[0] + (1.0 - q22 - q00)*v[1] + (      q12 - q03)*v[2],
	     (      q02 - q13)*v[0] + (      q12 + q03)*v[1] + (1.0 - q11 - q00)*v[2] );
}

/*! Set the Quaternion from a (supposedly correct) 3x3 rotation matrix.

  The matrix is expressed in European format: its three \e columns are the images by the rotation of
  the three vectors of an orthogonal basis. Note that OpenGL uses a symmetric representation for its
  matrices.

  setFromRotatedBasis() sets a Quaternion from the three axis of a rotated frame. It actually fills
  the three columns of a matrix with these rotated basis vectors and calls this method. */
void Quaternion::setFromRotationMatrix(const double m[3][3])
{
  // Compute one plus the trace of the matrix
  const double onePlusTrace = 1.0 + m[0][0] + m[1][1] + m[2][2];

  if (onePlusTrace > 1E-5)
    {
      // Direct computation
      const double s = sqrt(onePlusTrace) * 2.0;
      q[0] = (m[2][1] - m[1][2]) / s;
      q[1] = (m[0][2] - m[2][0]) / s;
      q[2] = (m[1][0] - m[0][1]) / s;
      q[3] = 0.25 * s;
    }
  else
    {
      // Computation depends on major diagonal term
      if ((m[0][0] > m[1][1])&(m[0][0] > m[2][2]))
	{ 
	  const double s = sqrt(1.0 + m[0][0] - m[1][1] - m[2][2]) * 2.0; 
	  q[0] = 0.25 * s;
	  q[1] = (m[0][1] + m[1][0]) / s; 
	  q[2] = (m[0][2] + m[2][0]) / s; 
	  q[3] = (m[1][2] - m[2][1]) / s;
	}
      else
	if (m[1][1] > m[2][2])
	  { 
	    const double s = sqrt(1.0 + m[1][1] - m[0][0] - m[2][2]) * 2.0; 
	    q[0] = (m[0][1] + m[1][0]) / s; 
	    q[1] = 0.25 * s;
	    q[2] = (m[1][2] + m[2][1]) / s; 
	    q[3] = (m[0][2] - m[2][0]) / s;
	  }
	else
	  { 
	    const double s = sqrt(1.0 + m[2][2] - m[0][0] - m[1][1]) * 2.0; 
	    q[0] = (m[0][2] + m[2][0]) / s; 
	    q[1] = (m[1][2] + m[2][1]) / s; 
	    q[2] = 0.25 * s;
	    q[3] = (m[0][1] - m[1][0]) / s;
	  }
    }
  normalize();
}

#ifndef DOXYGEN
void Quaternion::setFromRotationMatrix(const float m[3][3])
{
  cout << "setFromRotationMatrix now waits for a double[3][3] parameter" << endl;

  double mat[3][3];
  for (int i=0; i<3; ++i)
    for (int j=0; j<3; ++j)
      mat[i][j] = double(m[i][j]);

  setFromRotationMatrix(mat);
}

void Quaternion::setFromRotatedBase(const Vec& X, const Vec& Y, const Vec& Z)
{
  cout << "setFromRotatedBase is deprecated, use setFromRotatedBasis instead" << endl;
  setFromRotatedBasis(X,Y,Z);
}
#endif

/*! Sets the Quaternion from the three rotated vectors of an orthogonal basis.

  The three vectors do not have to be normalized but must be orthogonal and direct (X^Y=k*Z, with k>0).

  \code
  Quaternion q;
  q.setFromRotatedBasis(X, Y, Z);
  // Now q.rotate(Vec(1,0,0)) == X and q.inverseRotate(X) == Vec(1,0,0)
  // Same goes for Y and Z with Vec(0,1,0) and Vec(0,0,1).
  \endcode

  See also setFromRotationMatrix() and Quaternion(const Vec&, const Vec&). */
void Quaternion::setFromRotatedBasis(const Vec& X, const Vec& Y, const Vec& Z)
{
  double m[3][3];
  double normX = X.norm();
  double normY = Y.norm();
  double normZ = Z.norm();

  for (int i=0; i<3; ++i)
    {
      m[i][0] = X[i] / normX;
      m[i][1] = Y[i] / normY;
      m[i][2] = Z[i] / normZ;
    }
  
  setFromRotationMatrix(m);
}

/*! Returns the axis vector and the angle (in radians) of the rotation represented by the Quaternion.
 See the axis() and angle() documentations. */
void Quaternion::getAxisAngle(Vec& axis, float& angle) const
{
  angle = 2.0*acos(q[3]);
  axis = Vec(q[0], q[1], q[2]);
  const float sinus = axis.norm();
  if (sinus > 1E-8)
    axis /= sinus;

  if (angle > M_PI)
    {
      angle = 2.0*M_PI - angle;
      axis = -axis;
    }
}

/*! Returns the normalized axis direction of the rotation represented by the Quaternion.

It is null for an identity Quaternion. See also angle() and getAxisAngle(). */
Vec Quaternion::axis() const
{
  Vec res = Vec(q[0], q[1], q[2]);
  const float sinus = res.norm();
  if (sinus > 1E-8)
    res /= sinus;
  return (acos(q[3]) <= M_PI/2.0) ? res : -res;
}

/*! Returns the angle (in radians) of the rotation represented by the Quaternion.

 This value is always in the range [0-pi]. Larger rotational angles are obtained by inverting the
 axis() direction.

 See also axis() and getAxisAngle(). */
float Quaternion::angle() const
{
  const float angle = 2.0 * acos(q[3]);
  return (angle <= M_PI) ? angle : 2.0*M_PI - angle;
}




/*! Returns the Quaternion associated 4x4 OpenGL rotation matrix.

 Use \c glMultMatrixd(q.matrix()) to apply the rotation represented by Quaternion \c q to the
 current OpenGL matrix.

 See also getMatrix(), getRotationMatrix() and inverseMatrix().

 \attention The result is only valid until the next call to matrix(). Use it immediately (as shown
 above) or consider using getMatrix() instead.

 \attention The matrix is given in OpenGL format (row-major order) and is the transpose of the
 actual mathematical European representation. Consider using getRotationMatrix() instead. */
const GLdouble* Quaternion::matrix() const
{
  static GLdouble m[4][4];
  getMatrix(m);
  return (const GLdouble*)(m);
}

/*! Fills \p m with the OpenGL representation of the Quaternion rotation.

Use matrix() if you do not need to store this matrix and simply want to alter the current OpenGL
matrix. See also getInverseMatrix() and Frame::getMatrix(). */
void Quaternion::getMatrix(GLdouble m[4][4]) const
{
  const double q00 = 2.0l * q[0] * q[0];
  const double q11 = 2.0l * q[1] * q[1];
  const double q22 = 2.0l * q[2] * q[2];

  const double q01 = 2.0l * q[0] * q[1];
  const double q02 = 2.0l * q[0] * q[2];
  const double q03 = 2.0l * q[0] * q[3];

  const double q12 = 2.0l * q[1] * q[2];
  const double q13 = 2.0l * q[1] * q[3];

  const double q23 = 2.0l * q[2] * q[3];

  m[0][0] = 1.0l - q11 - q22;
  m[1][0] =        q01 - q23;
  m[2][0] =        q02 + q13;

  m[0][1] =        q01 + q23;
  m[1][1] = 1.0l - q22 - q00;
  m[2][1] =        q12 - q03;

  m[0][2] =        q02 - q13;
  m[1][2] =        q12 + q03;
  m[2][2] = 1.0l - q11 - q00;

  m[0][3] = 0.0l;
  m[1][3] = 0.0l;
  m[2][3] = 0.0l;

  m[3][0] = 0.0l;
  m[3][1] = 0.0l;
  m[3][2] = 0.0l;
  m[3][3] = 1.0l;
}

/*! Same as getMatrix(), but with a \c GLdouble[16] parameter. See also getInverseMatrix() and Frame::getMatrix(). */
void Quaternion::getMatrix(GLdouble m[16]) const
{
  static GLdouble mat[4][4];
  getMatrix(mat);
  int count = 0;
  for (int i=0; i<4; ++i)
    for (int j=0; j<4; ++j)
      m[count++] = mat[i][j];
}

/*! Fills \p m with the 3x3 rotation matrix associated with the Quaternion.

  See also getInverseRotationMatrix().

  \attention \p m uses the European mathematical representation of the rotation matrix. Use matrix()
  and getMatrix() to retrieve the OpenGL transposed version. */
void Quaternion::getRotationMatrix(float m[3][3]) const
{
  static GLdouble mat[4][4];
  getMatrix(mat);
  for (int i=0; i<3; ++i)
    for (int j=0; j<3; ++j)
      // Beware of transposition
      m[i][j] = mat[j][i];
}

/*! Returns the associated 4x4 OpenGL \e inverse rotation matrix. This is simply the matrix() of the
  inverse().

  \attention The result is only valid until the next call to inverseMatrix(). Use it immediately (as
  in \c glMultMatrixd(q.inverseMatrix())) or use getInverseMatrix() instead.

  \attention The matrix is given in OpenGL format (row-major order) and is the transpose of the
  actual mathematical European representation. Consider using getInverseRotationMatrix() instead. */
const GLdouble* Quaternion::inverseMatrix() const
{
  static GLdouble m[4][4];
  getInverseMatrix(m);
  return (const GLdouble*)(m);
}

/*! Fills \p m with the OpenGL matrix corresponding to the inverse() rotation.

Use inverseMatrix() if you do not need to store this matrix and simply want to alter the current
OpenGL matrix. See also getMatrix(). */
void Quaternion::getInverseMatrix(GLdouble m[4][4]) const
{
  inverse().getMatrix(m);
}

/*! Same as getInverseMatrix(), but with a \c GLdouble[16] parameter. See also getMatrix(). */
void Quaternion::getInverseMatrix(GLdouble m[16]) const
{
  inverse().getMatrix(m);
}

/*! \p m is set to the 3x3 \e inverse rotation matrix associated with the Quaternion.

 \attention This is the classical mathematical rotation matrix. The OpenGL format uses its
 transposed version. See inverseMatrix() and getInverseMatrix(). */
void Quaternion::getInverseRotationMatrix(float m[3][3]) const
{
  static GLdouble mat[4][4];
  getInverseMatrix(mat);
  for (int i=0; i<3; ++i)
    for (int j=0; j<3; ++j)
      // Beware of transposition
      m[i][j] = mat[j][i];
}


/*! Returns the slerp interpolation of Quaternions \p a and \p b, at time \p t.

 \p t should range in [0,1]. Result is \p a when \p t=0 and \p b when \p t=1.

 When \p allowFlip is \c true (default) the slerp interpolation will always use the "shortest path"
 between the Quaternions' orientations, by "flipping" the source Quaternion if needed (see
 negate()). */
Quaternion Quaternion::slerp(const Quaternion& a, const Quaternion& b, float t, bool allowFlip)
{
  float cosAngle = Quaternion::dot(a, b);

  float c1, c2;
  // Linear interpolation for close orientations
  if ((1.0 - fabs(cosAngle)) < 0.01)
    {
      c1 = 1.0 - t;
      c2 = t;
    }
  else
    {
      // Spherical interpolation
      float angle    = acos(fabs(cosAngle));
      float sinAngle = sin(angle);
      c1 = sin(angle * (1.0 - t)) / sinAngle;
      c2 = sin(angle * t) / sinAngle;
    }

  // Use the shortest path
  if (allowFlip && (cosAngle < 0.0))
    c1 = -c1;

  return Quaternion(c1*a[0] + c2*b[0], c1*a[1] + c2*b[1], c1*a[2] + c2*b[2], c1*a[3] + c2*b[3]);
}

/*! Returns the slerp interpolation of the two Quaternions \p a and \p b, at time \p t, using
  tangents \p tgA and \p tgB.

  The resulting Quaternion is "between" \p a and \p b (result is \p a when \p t=0 and \p b for \p
  t=1).

  Use squadTangent() to define the Quaternion tangents \p tgA and \p tgB. */
Quaternion Quaternion::squad(const Quaternion& a, const Quaternion& tgA, const Quaternion& tgB, const Quaternion& b, float t)
{
  Quaternion ab = Quaternion::slerp(a, b, t);
  Quaternion tg = Quaternion::slerp(tgA, tgB, t, false);
  return Quaternion::slerp(ab, tg, 2.0*t*(1.0-t), false);
}

/*! Returns the logarithm of the Quaternion. See also exp(). */
Quaternion Quaternion::log()
{
  float len = sqrt(q[0]*q[0] + q[1]*q[1] + q[2]*q[2]);

  if (len < 1E-6)
    return Quaternion(q[0], q[1], q[2], 0.0);
  else
    {
      float coef = acos(q[3]) / len;
      return Quaternion(q[0]*coef, q[1]*coef, q[2]*coef, 0.0);
    }
}

/*! Returns the exponential of the Quaternion. See also log(). */
Quaternion Quaternion::exp()
{
  float theta = sqrt(q[0]*q[0] + q[1]*q[1] + q[2]*q[2]);

  if (theta < 1E-6)
    return Quaternion(q[0], q[1], q[2], cos(theta));
  else
    {
      float coef = sin(theta) / theta;
      return Quaternion(q[0]*coef, q[1]*coef, q[2]*coef, cos(theta));
    }
}

/*! Returns log(a. inverse() * b). Useful for squadTangent(). */
Quaternion Quaternion::lnDif(const Quaternion& a, const Quaternion& b)
{
  Quaternion dif = a.inverse()*b;
  dif.normalize();
  return dif.log();
}

/*! Returns a tangent Quaternion for \p center, defined by \p before and \p after Quaternions.

 Useful for smooth spline interpolation of Quaternion with squad() and slerp(). */
Quaternion Quaternion::squadTangent(const Quaternion& before, const Quaternion& center, const Quaternion& after)
{
  Quaternion l1 = Quaternion::lnDif(center,before);
  Quaternion l2 = Quaternion::lnDif(center,after);
  Quaternion e;
  for (int i=0; i<4; ++i)
    e.q[i] = -0.25 * (l1.q[i] + l2.q[i]);
  e = center*(e.exp());

  // if (Quaternion::dot(e,b) < 0.0)
    // e.negate();

  return e;
}

ostream& operator<<(ostream& o, const Quaternion& Q)
{
  return o << Q[0] << '\t' << Q[1] << '\t' << Q[2] << '\t' << Q[3];
}

/*! Returns a random unit Quaternion.

You can create a randomly directed unit vector using:
\code
Vec randomDir = Quaternion::randomQuaternion() * Vec(1.0, 0.0, 0.0); // or any other Vec
\endcode

\note This function uses rand() to create pseudo-random numbers and the random number generator can
be initialized using srand().*/
Quaternion Quaternion::randomQuaternion()
{
  // The rand() function is not very portable and may not be available on your system.
  // Add the appropriate include or replace by an other random function in case of problem.
  double seed = rand()/(float)RAND_MAX;
  double r1 = sqrt(1.0 - seed);
  double r2 = sqrt(seed);
  double t1 = 2.0 * M_PI * (rand()/(float)RAND_MAX);
  double t2 = 2.0 * M_PI * (rand()/(float)RAND_MAX);
  return Quaternion(sin(t1)*r1, cos(t1)*r1, sin(t2)*r2, cos(t2)*r2);
}