/Users/jab/Documents/Teaching/02585/GEL2_and_demos/GEL/src/CGLA/ArithQuat.h

#ifndef __CGLA_ARITHQUAT_H__
#define __CGLA_ARITHQUAT_H__

#include "CGLA.h"
#include "ArithVecFloat.h"
#include "ArithSqMatFloat.h"
#include <cmath>

namespace CGLA {

        template<class T, class V, class Q>
  class ArithQuat
  {
  public:

    V qv;

    T qw;

#ifndef NDEBUG
    ArithQuat() : qw(CGLA_INIT_VALUE) {}
#else
    ArithQuat() {}
#endif

    ArithQuat(const V& imaginary, T real = 1.0f) : qv(imaginary) , qw(real) {}

    ArithQuat(T x, T y, T z, T _qw) : qv(x,y,z), qw(_qw) {}

   
    void set(const V& imaginary, T real=1.0f)
    {
      qv = imaginary;
      qw = real;
    }

    void set(T x, T y, T z, T _qw) 
    {
      qv.set(x,y,z);
      qw = _qw;
    }

    /*void set(const Vec4f& v)
    {
      qv.set(v[0], v[1], v[2]);
      qw = v[3];                  
    }*/

    void get(T& x, T& y, T& z, T& _qw) const
    {
      x  = qv[0];
      y  = qv[1];
      z  = qv[2];
      _qw = qw;
    }

    V get_imaginary_part() const { return qv; }

    T get_real_part() const { return qw; }



    void get_rot(T& angle, V& v)
    {
      angle = 2*std::acos(qw);

      if(angle < TINY) 
                                v = V(static_cast<T>(1.0), static_cast<T>(0.0), static_cast<T>(0.0));
      else 
                                v = qv*(static_cast<T>(1.0)/std::sin(angle));

      if(angle > M_PI)
                                v = -v;
      
      v.normalize();      
    }

    void make_rot(T angle, const V& v)
    {
      angle /= static_cast<T>(2.0);
      qv = CGLA::normalize(v)*std::sin(angle);
      qw = std::cos(angle);
    }

    void make_rot(const V& s,const V& t)
    {
      T tmp = std::sqrt(2*(1 + dot(s, t)));
      qv = cross(s, t)*(1.0/tmp);
      qw = tmp/2.0;    
    }

    template <class VT, class MT, unsigned int ROWS>
    void make_rot(ArithSqMatFloat<VT,MT,ROWS>& m)
    {
      assert(ROWS==3 || ROWS==4);
      T trace = m[0][0] + m[1][1] + m[2][2]  + static_cast<T>(1.0);

      //If the trace of the matrix is greater than zero, then
      //perform an "instant" calculation.
      if ( trace > TINY ) 
      {
        T S = sqrt(trace) * static_cast<T>(2.0);
        qv = V(m[2][1] - m[1][2], m[0][2] - m[2][0], m[1][0] - m[0][1] );
        qv /= S;
        qw = static_cast<T>(0.25) * S;
      }
      else
      {
        //If the trace of the matrix is equal to zero (or negative...) then identify
        //which major diagonal element has the greatest value.
        //Depending on this, calculate the following:

        if ( m[0][0] > m[1][1] && m[0][0] > m[2][2] )  {        // Column 0: 
          T S  = sqrt( static_cast<T>(1.0) + m[0][0] - m[1][1] - m[2][2] ) * static_cast<T>(2.0);
          qv[0] = 0.25f * S;
          qv[1] = (m[1][0] + m[0][1] ) / S;
          qv[2] = (m[0][2] + m[2][0] ) / S;
          qw = (m[2][1] - m[1][3] ) / S;
        } else if ( m[1][1] > m[2][2] ) {                       // Column 1: 
          T S  = sqrt( 1.0 + m[1][1] - m[0][0] - m[2][2] ) * 2.0;
          qv[0] = (m[1][0] + m[0][1] ) / S;
          qv[1] = 0.25 * S;
          qv[2] = (m[2][1] + m[1][2] ) / S;
          qw = (m[0][2] - m[2][0] ) / S;
        } else {                                                // Column 2:
          T S  = sqrt( 1.0 + m[2][2] - m[0][0] - m[1][1] ) * 2.0;
          qv[0] = (m[0][2] + m[2][0] ) / S;
          qv[1] = (m[2][1] + m[1][2] ) / S;
          qv[2] = 0.25 * S;
          qw = (m[1][0] - m[0][1] ) / S;
        }
      }
      //The quaternion is then defined as:
      //  Q = | X Y Z W |
    }

    //----------------------------------------------------------------------
    // Binary operators
    //----------------------------------------------------------------------
    
    bool operator==(const ArithQuat<T,V,Q>& q) const
    {
      return qw == q.qw && qv == q.qv;
    }

    bool operator!=(const ArithQuat<T,V,Q>& q) const
    {
      return qw != q.qw || qv != q.qv;
    }

    Q operator*(const ArithQuat<T,V,Q>& q) const
    {
      return Q(cross(qv, q.qv) + qv*q.qw + q.qv*qw, 
                         qw*q.qw - dot(qv, q.qv));      
    }

    Q operator*(T scalar) const
    {
      return Q(qv*scalar, qw*scalar);
    }

    Q operator+(const ArithQuat<T,V,Q>& q) const
    {
      return Q(qv + q.qv, qw + q.qw);
    }

    //----------------------------------------------------------------------
    // Unary operators
    //----------------------------------------------------------------------

    Q operator-() const { return Q(-qv, -qw); }

    T norm() const { return dot(qv, qv) + qw*qw; }

    Q conjugate() const { return Q(-qv, qw); }

    Q inverse() const { return Q(conjugate()*(1/norm())); }
    
    Q normalize() { return Q((*this)*(1/norm())); }

    //----------------------------------------------------------------------
    // Application
    //----------------------------------------------------------------------

    V apply(const V& vec) const 
    {
      return ((*this)*Q(vec)*inverse()).qv;
    }

    V apply_unit(const V& vec) const
    {
          assert(fabs(norm() - 1.0) < SMALL);
      return ((*this)*Q(vec)*conjugate()).qv;
    }
  };

  template<class T, class V, class Q>
  inline Q operator*(T scalar, const ArithQuat<T,V,Q>& q)
  {
    return q*scalar;
  }

        template<class T, class V, class Q>
  inline Q slerp(const ArithQuat<T,V,Q>& q0, const ArithQuat<T,V,Q>& q1, T t)
  {
    T angle = std::acos(q0.qv[0]*q1.qv[0] + q0.qv[1]*q1.qv[1] 
                            + q0.qv[2]*q1.qv[2] + q0.qw*q1.qw);
    return (q0*std::sin((1 - t)*angle) + q1*std::sin(t*angle))*(1/std::sin(angle));
  }

  template<class T, class V, class Q>
  inline std::ostream& operator<<(std::ostream&os, const ArithQuat<T,V,Q>& v)
  {
    os << "[ ";
    for(unsigned int i=0;i<3;i++) os << v.qv[i] << " ";
    os << "~ " << v.qw << " ";
    os << "]";

    return os;
  }
}

















#endif // __CGLA_ARITHQUAT_H__