/*
    Inertial Measurement Unit Maths Library
    Copyright (C) 2013-2014  Samuel Cowen
	www.camelsoftware.com

    Bug fixes and cleanups by Gé Vissers (gvissers@gmail.com)

    This program 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 3 of the License, or
    (at your option) any later version.

    This program 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 this program.  If not, see <http://www.gnu.org/licenses/>.
*/


#ifndef IMUMATH_QUATERNION_HPP
#define IMUMATH_QUATERNION_HPP

#include <stdlib.h>
#include <string.h>
#include <stdint.h>
#include <math.h>

#include "matrix.h"


namespace imu
{

class Quaternion
{
public:
    Quaternion(): _w(1.0), _x(0.0), _y(0.0), _z(0.0) {}

    Quaternion(double w, double x, double y, double z):
        _w(w), _x(x), _y(y), _z(z) {}

    Quaternion(double w, Vector<3> vec):
        _w(w), _x(vec.x()), _y(vec.y()), _z(vec.z()) {}

    double& w()
    {
        return _w;
    }
    double& x()
    {
        return _x;
    }
    double& y()
    {
        return _y;
    }
    double& z()
    {
        return _z;
    }

    double w() const
    {
        return _w;
    }
    double x() const
    {
        return _x;
    }
    double y() const
    {
        return _y;
    }
    double z() const
    {
        return _z;
    }

    double magnitude() const
    {
        return sqrt(_w*_w + _x*_x + _y*_y + _z*_z);
    }

    void normalize()
    {
        double mag = magnitude();
        *this = this->scale(1/mag);
    }

    Quaternion conjugate() const
    {
        return Quaternion(_w, -_x, -_y, -_z);
    }

    void fromAxisAngle(const Vector<3>& axis, double theta)
    {
        _w = cos(theta/2);
        //only need to calculate sine of half theta once
        double sht = sin(theta/2);
        _x = axis.x() * sht;
        _y = axis.y() * sht;
        _z = axis.z() * sht;
    }

    void fromMatrix(const Matrix<3>& m)
    {
        double tr = m.trace();

        double S;
        if (tr > 0)
        {
            S = sqrt(tr+1.0) * 2;
            _w = 0.25 * S;
            _x = (m(2, 1) - m(1, 2)) / S;
            _y = (m(0, 2) - m(2, 0)) / S;
            _z = (m(1, 0) - m(0, 1)) / S;
        }
        else if (m(0, 0) > m(1, 1) && m(0, 0) > m(2, 2))
        {
            S = sqrt(1.0 + m(0, 0) - m(1, 1) - m(2, 2)) * 2;
            _w = (m(2, 1) - m(1, 2)) / S;
            _x = 0.25 * S;
            _y = (m(0, 1) + m(1, 0)) / S;
            _z = (m(0, 2) + m(2, 0)) / S;
        }
        else if (m(1, 1) > m(2, 2))
        {
            S = sqrt(1.0 + m(1, 1) - m(0, 0) - m(2, 2)) * 2;
            _w = (m(0, 2) - m(2, 0)) / S;
            _x = (m(0, 1) + m(1, 0)) / S;
            _y = 0.25 * S;
            _z = (m(1, 2) + m(2, 1)) / S;
        }
        else
        {
            S = sqrt(1.0 + m(2, 2) - m(0, 0) - m(1, 1)) * 2;
            _w = (m(1, 0) - m(0, 1)) / S;
            _x = (m(0, 2) + m(2, 0)) / S;
            _y = (m(1, 2) + m(2, 1)) / S;
            _z = 0.25 * S;
        }
    }

    void toAxisAngle(Vector<3>& axis, double& angle) const
    {
        double sqw = sqrt(1-_w*_w);
        if (sqw == 0) //it's a singularity and divide by zero, avoid
            return;

        angle = 2 * acos(_w);
        axis.x() = _x / sqw;
        axis.y() = _y / sqw;
        axis.z() = _z / sqw;
    }

    Matrix<3> toMatrix() const
    {
        Matrix<3> ret;
        ret.cell(0, 0) = 1 - 2*_y*_y - 2*_z*_z;
        ret.cell(0, 1) = 2*_x*_y - 2*_w*_z;
        ret.cell(0, 2) = 2*_x*_z + 2*_w*_y;

        ret.cell(1, 0) = 2*_x*_y + 2*_w*_z;
        ret.cell(1, 1) = 1 - 2*_x*_x - 2*_z*_z;
        ret.cell(1, 2) = 2*_y*_z - 2*_w*_x;

        ret.cell(2, 0) = 2*_x*_z - 2*_w*_y;
        ret.cell(2, 1) = 2*_y*_z + 2*_w*_x;
        ret.cell(2, 2) = 1 - 2*_x*_x - 2*_y*_y;
        return ret;
    }


    // Returns euler angles that represent the quaternion.  Angles are
    // returned in rotation order and right-handed about the specified
    // axes:
    //
    //   v[0] is applied 1st about z (ie, roll)
    //   v[1] is applied 2nd about y (ie, pitch)
    //   v[2] is applied 3rd about x (ie, yaw)
    //
    // Note that this means result.x() is not a rotation about x;
    // similarly for result.z().
    //
    Vector<3> toEuler() const
    {
        Vector<3> ret;
        double sqw = _w*_w;
        double sqx = _x*_x;
        double sqy = _y*_y;
        double sqz = _z*_z;

        ret.x() = atan2(2.0*(_x*_y+_z*_w),(sqx-sqy-sqz+sqw));
        ret.y() = asin(-2.0*(_x*_z-_y*_w)/(sqx+sqy+sqz+sqw));
        ret.z() = atan2(2.0*(_y*_z+_x*_w),(-sqx-sqy+sqz+sqw));

        return ret;
    }

    Vector<3> toAngularVelocity(double dt) const
    {
        Vector<3> ret;
        Quaternion one(1.0, 0.0, 0.0, 0.0);
        Quaternion delta = one - *this;
        Quaternion r = (delta/dt);
        r = r * 2;
        r = r * one;

        ret.x() = r.x();
        ret.y() = r.y();
        ret.z() = r.z();
        return ret;
    }

    Vector<3> rotateVector(const Vector<2>& v) const
    {
        return rotateVector(Vector<3>(v.x(), v.y()));
    }

    Vector<3> rotateVector(const Vector<3>& v) const
    {
        Vector<3> qv(_x, _y, _z);
        Vector<3> t = qv.cross(v) * 2.0;
        return v + t*_w + qv.cross(t);
    }


    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) const
    {
        return Quaternion(_w + q._w, _x + q._x, _y + q._y, _z + q._z);
    }

    Quaternion operator-(const Quaternion& q) const
    {
        return Quaternion(_w - q._w, _x - q._x, _y - q._y, _z - q._z);
    }

    Quaternion operator/(double scalar) const
    {
        return Quaternion(_w / scalar, _x / scalar, _y / scalar, _z / scalar);
    }

    Quaternion operator*(double scalar) const
    {
        return scale(scalar);
    }

    Quaternion scale(double scalar) const
    {
        return Quaternion(_w * scalar, _x * scalar, _y * scalar, _z * scalar);
    }

private:
    double _w, _x, _y, _z;
};

} // namespace

#endif