quaternion_exponential.inl

#include "scalar_constants.hpp"
 
namespace glm
{
    template<typename T, qualifier Q>
    GLM_FUNC_QUALIFIER qua<T, Q> exp(qua<T, Q> const& q)
    {
        vec<3, T, Q> u(q.x, q.y, q.z);
        T const Angle = glm::length(u);
        if (Angle < epsilon<T>())
            return qua<T, Q>();
 
        vec<3, T, Q> const v(u / Angle);
        return qua<T, Q>(cos(Angle), sin(Angle) * v);
    }
 
    template<typename T, qualifier Q>
    GLM_FUNC_QUALIFIER qua<T, Q> log(qua<T, Q> const& q)
    {
        vec<3, T, Q> u(q.x, q.y, q.z);
        T Vec3Len = length(u);
 
        if (Vec3Len < epsilon<T>())
        {
            if(q.w > static_cast<T>(0))
                return qua<T, Q>(log(q.w), static_cast<T>(0), static_cast<T>(0), static_cast<T>(0));
            else if(q.w < static_cast<T>(0))
                return qua<T, Q>(log(-q.w), pi<T>(), static_cast<T>(0), static_cast<T>(0));
            else
                return qua<T, Q>(std::numeric_limits<T>::infinity(), std::numeric_limits<T>::infinity(), std::numeric_limits<T>::infinity(), std::numeric_limits<T>::infinity());
        }
        else
        {
            T t = atan(Vec3Len, T(q.w)) / Vec3Len;
            T QuatLen2 = Vec3Len * Vec3Len + q.w * q.w;
            return qua<T, Q>(static_cast<T>(0.5) * log(QuatLen2), t * q.x, t * q.y, t * q.z);
        }
    }
 
    template<typename T, qualifier Q>
    GLM_FUNC_QUALIFIER qua<T, Q> pow(qua<T, Q> const& x, T y)
    {
        //Raising to the power of 0 should yield 1
        //Needed to prevent a division by 0 error later on
        if(y > -epsilon<T>() && y < epsilon<T>())
            return qua<T, Q>(1,0,0,0);
 
        //To deal with non-unit quaternions
        T magnitude = sqrt(x.x * x.x + x.y * x.y + x.z * x.z + x.w *x.w);
 
        T Angle;
        if(abs(x.w / magnitude) > cos_one_over_two<T>())
        {
            //Scalar component is close to 1; using it to recover angle would lose precision
            //Instead, we use the non-scalar components since sin() is accurate around 0
 
            //Prevent a division by 0 error later on
            T VectorMagnitude = x.x * x.x + x.y * x.y + x.z * x.z;
            if (glm::abs(VectorMagnitude - static_cast<T>(0)) < glm::epsilon<T>()) {
                //Equivalent to raising a real number to a power
                return qua<T, Q>(pow(x.w, y), 0, 0, 0);
            }
 
            Angle = asin(sqrt(VectorMagnitude) / magnitude);
        }
        else
        {
            //Scalar component is small, shouldn't cause loss of precision
            Angle = acos(x.w / magnitude);
        }
 
        T NewAngle = Angle * y;
        T Div = sin(NewAngle) / sin(Angle);
        T Mag = pow(magnitude, y - static_cast<T>(1));
        return qua<T, Q>(cos(NewAngle) * magnitude * Mag, x.x * Div * Mag, x.y * Div * Mag, x.z * Div * Mag);
    }
 
    template<typename T, qualifier Q>
    GLM_FUNC_QUALIFIER qua<T, Q> sqrt(qua<T, Q> const& x)
    {
        return pow(x, static_cast<T>(0.5));
    }
}//namespace glm