#include "euler.hpp"
#include <cmath>

namespace euler {

euler_t OTR_COMPAT_EXPORT rmat_to_euler(const rmat& R)
{
    using std::atan2;
    using std::sqrt;

    const double cy = sqrt(R(2,2)*R(2, 2) + R(2, 1)*R(2, 1));
    const bool large_enough = cy > 1e-10;
    if (large_enough)
        return euler_t(atan2(-R(1, 0), R(0, 0)),
                       atan2(R(2, 0), cy),
                       atan2(-R(2, 1), R(2, 2)));
    else
        return euler_t(atan2(R(0, 1), R(1, 1)),
                       atan2(R(2, 0), cy),
                       0);
}

// tait-bryan angles, not euler
rmat OTR_COMPAT_EXPORT euler_to_rmat(const euler_t& input)
{
    const double H = -input(0);
    const double P = -input(1);
    const double B = -input(2);

    using std::cos;
    using std::sin;

    const auto c1 = cos(H);
    const auto s1 = sin(H);
    const auto c2 = cos(P);
    const auto s2 = sin(P);
    const auto c3 = cos(B);
    const auto s3 = sin(B);

    return rmat(
                // z
                c1 * c2,
                c1 * s2 * s3 - c3 * s1,
                s1 * s3 + c1 * c3 * s2,
                // y
                c2 * s1,
                c1 * c3 + s1 * s2 * s3,
                c3 * s1 * s2 - c1 * s3,
                // x
                -s2,
                c2 * s3,
                c2 * c3
                );
}

// https://en.wikipedia.org/wiki/Davenport_chained_rotations#Tait.E2.80.93Bryan_chained_rotations
void OTR_COMPAT_EXPORT tait_bryan_to_matrices(const euler_t& input,
                                                    rmat& r_roll,
                                                    rmat& r_pitch,
                                                    rmat& r_yaw)
{
    using std::cos;
    using std::sin;

    {
        const double phi = -input(2);
        const double sin_phi = sin(phi);
        const double cos_phi = cos(phi);

        r_roll = rmat(1, 0, 0,
                      0, cos_phi, -sin_phi,
                      0, sin_phi, cos_phi);
    }

    {
        const double theta = input(1);
        const double sin_theta = sin(theta);
        const double cos_theta = cos(theta);

        r_pitch = rmat(cos_theta, 0, -sin_theta,
                       0, 1, 0,
                       sin_theta, 0, cos_theta);
    }

    {
        const double psi = -input(0);
        const double sin_psi = sin(psi);
        const double cos_psi = cos(psi);

        r_yaw = rmat(cos_psi, -sin_psi, 0,
                     sin_psi, cos_psi, 0,
                     0, 0, 1);
    }
}

// from http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion/
Quat matrix_to_quat(const rmat& M)
{
    Quat q(1, 0, 0, 0);

    using std::sqrt;

    double trace = M(0, 0) + M(1, 1) + M(2, 2); // I removed + 1.0; see discussion with Ethan
    if( trace > 0 ) {// I changed M_EPSILON to 0
        double s = .5 / std::sqrt(trace + 1);
        q.w() = .25 / s;
        q.x() = ( M(2, 1) - M(1, 2) ) * s;
        q.y() = ( M(0, 2) - M(2, 0) ) * s;
        q.z() = ( M(1, 0) - M(0, 1) ) * s;
    } else {
        if ( M(0, 0) > M(1, 1) && M(0, 0) > M(2, 2) ) {
            double s = 2.0 * sqrt( 1.0 + M(0, 0) - M(1, 1) - M(2, 2));
            q.w() = (M(2, 1) - M(1, 2) ) / s;
            q.x() = .25 * s;
            q.y() = (M(0, 1) + M(1, 0) ) / s;
            q.z() = (M(0, 2) + M(2, 0) ) / s;
        } else if (M(1, 1) > M(2, 2)) {
            double s = 2.0 * sqrt( 1.0 + M(1, 1) - M(0, 0) - M(2, 2));
            q.w() = (M(0, 2) - M(2, 0) ) / s;
            q.x() = (M(0, 1) + M(1, 0) ) / s;
            q.y() = .25 * s;
            q.z() = (M(1, 2) + M(2, 1) ) / s;
        } else {
            double s = 2.0 * sqrt( 1.0 + M(2, 2) - M(0, 0) - M(1, 1) );
            q.w() = (M(1, 0) - M(0, 1) ) / s;
            q.x() = (M(0, 2) + M(2, 0) ) / s;
            q.y() = (M(1, 2) + M(2, 1) ) / s;
            q.z() = .25 * s;
        }
    }

    return q;
}

} // end ns euler