paz_math/quat.cpp at main · pazvirtual/paz_math · GitHub

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#include "PAZ_Math"

paz::Mat paz::to_mat(const MatRef& q)
{
    if(q.rows() != 4 || q.cols() != 1)
    {
        throw std::runtime_error("Not a quaternion.");
    }
    const auto xx = q(0)*q(0);
    const auto yy = q(1)*q(1);
    const auto zz = q(2)*q(2);
    const auto xy = q(0)*q(1);
    const auto zw = q(2)*q(3);
    const auto xz = q(0)*q(2);
    const auto yw = q(1)*q(3);
    const auto yz = q(1)*q(2);
    const auto xw = q(0)*q(3);
    return {{1. - 2.*(yy + zz),      2.*(xy + zw),      2.*(xz - yw)},
            {     2.*(xy - zw), 1. - 2.*(xx + zz),      2.*(yz + xw)},
            {     2.*(xz + yw),      2.*(yz - xw), 1. - 2.*(xx + yy)}};
}

paz::Vec paz::to_quat(const MatRef& m)
{
    if(m.rows() != 3 || m.cols() != 3)
    {
        throw std::runtime_error("Not a rotation matrix.");
    }
    const auto fourXSqMinus1 = m(0, 0) - m(1, 1) - m(2, 2);
    const auto fourYSqMinus1 = m(1, 1) - m(0, 0) - m(2, 2);
    const auto fourZSqMinus1 = m(2, 2) - m(0, 0) - m(1, 1);
    const auto fourWSqMinus1 = m(0, 0) + m(1, 1) + m(2, 2);
    auto maxVal = fourWSqMinus1;
    int maxIdx = 0;
    if(fourXSqMinus1 > maxVal)
    {
        maxVal = fourXSqMinus1;
        maxIdx = 1;
    }
    if(fourYSqMinus1 > maxVal)
    {
        maxVal = fourYSqMinus1;
        maxIdx = 2;
    }
    if(fourZSqMinus1 > maxVal)
    {
        maxVal = fourZSqMinus1;
        maxIdx = 3;
    }
    maxVal = 0.5*std::sqrt(maxVal + 1.);
    const auto mult = 0.25/maxVal;
    switch(maxIdx)
    {
        case 0:
            return {{(m(1, 2) - m(2, 1))*mult,
                     (m(2, 0) - m(0, 2))*mult,
                     (m(0, 1) - m(1, 0))*mult,
                                       maxVal}};
        case 1:
            return {{                  maxVal,
                     (m(0, 1) + m(1, 0))*mult,
                     (m(2, 0) + m(0, 2))*mult,
                     (m(1, 2) - m(2, 1))*mult}};
        case 2:
            return {{(m(0, 1) + m(1, 0))*mult,
                                       maxVal,
                     (m(1, 2) + m(2, 1))*mult,
                     (m(2, 0) - m(0, 2))*mult}};
        default:
            return {{(m(2, 0) + m(0, 2))*mult,
                     (m(1, 2) + m(2, 1))*mult,
                                       maxVal,
                     (m(0, 1) - m(1, 0))*mult}};
    }
}

paz::Vec paz::qinv(const MatRef& q)
{
    if(q.rows() != 4 || q.cols() != 1)
    {
        throw std::runtime_error("Not a quaternion.");
    }
    return {{-q(0), -q(1), -q(2), q(3)}};
}

paz::Mat paz::xi(const MatRef& q)
{
    if(q.rows() != 4 || q.cols() != 1)
    {
        throw std::runtime_error("Not a quaternion.");
    }
    return {{ q(3), -q(2),  q(1)},
            { q(2),  q(3), -q(0)},
            {-q(1),  q(0),  q(3)},
            {-q(0), -q(1), -q(2)}};
}

paz::Vec paz::qmult(const MatRef& p, const MatRef& q)
{
    if(p.rows() != 4 || p.cols() != 1 || q.rows() != 4 || q.cols() != 1)
    {
        throw std::runtime_error("Not a quaternion.");
    }
    const Vec pVec = p.block(0, 0, 3, 1);
    const Vec qVec = q.block(0, 0, 3, 1);
    const Vec rVec = q(3)*pVec + p(3)*qVec - pVec.cross(qVec);
    return {{rVec(0), rVec(1), rVec(2), p(3)*q(3) - pVec.dot(qVec)}};
}

paz::Vec paz::axis_angle(const MatRef& axis, double angle)
{
    if(axis.rows() != 3 || axis.cols() != 1)
    {
        throw std::runtime_error("Not a 3-vector.");
    }
    const double s = std::sin(0.5*angle);
    return Vec{{s*axis(0), s*axis(1), s*axis(2), std::cos(0.5*angle)}};
}

paz::Vec paz::nlerp(const MatRef& p, const MatRef& q, double k)
{
    if(p.rows() != 4 || p.cols() != 1 || q.rows() != 4 || q.cols() != 1)
    {
        throw std::runtime_error("Not a quaternion.");
    }
    if(p.dot(q) < 0.)
    {
        return mix(p, -q, k).normalized();
    }
    return mix(p, q, k).normalized();
}