quaternion.inl

 
 
#include <limits>
#include "../gtc/constants.hpp"
 
namespace glm
{
    template<typename T, qualifier Q>
    GLM_FUNC_QUALIFIER GLM_CONSTEXPR qua<T, Q> quat_identity()
    {
        return qua<T, Q>(static_cast<T>(1), static_cast<T>(0), static_cast<T>(0), static_cast<T>(0));
    }
 
    template<typename T, qualifier Q>
    GLM_FUNC_QUALIFIER vec<3, T, Q> cross(vec<3, T, Q> const& v, qua<T, Q> const& q)
    {
        return inverse(q) * v;
    }
 
    template<typename T, qualifier Q>
    GLM_FUNC_QUALIFIER vec<3, T, Q> cross(qua<T, Q> const& q, vec<3, T, Q> const& v)
    {
        return q * v;
    }
 
    template<typename T, qualifier Q>
    GLM_FUNC_QUALIFIER qua<T, Q> squad
    (
        qua<T, Q> const& q1,
        qua<T, Q> const& q2,
        qua<T, Q> const& s1,
        qua<T, Q> const& s2,
        T const& h)
    {
        return mix(mix(q1, q2, h), mix(s1, s2, h), static_cast<T>(2) * (static_cast<T>(1) - h) * h);
    }
 
    template<typename T, qualifier Q>
    GLM_FUNC_QUALIFIER qua<T, Q> intermediate
    (
        qua<T, Q> const& prev,
        qua<T, Q> const& curr,
        qua<T, Q> const& next
    )
    {
        qua<T, Q> invQuat = inverse(curr);
        return exp((log(next * invQuat) + log(prev * invQuat)) / static_cast<T>(-4)) * curr;
    }
 
    template<typename T, qualifier Q>
    GLM_FUNC_QUALIFIER vec<3, T, Q> rotate(qua<T, Q> const& q, vec<3, T, Q> const& v)
    {
        return q * v;
    }
 
    template<typename T, qualifier Q>
    GLM_FUNC_QUALIFIER vec<4, T, Q> rotate(qua<T, Q> const& q, vec<4, T, Q> const& v)
    {
        return q * v;
    }
 
    template<typename T, qualifier Q>
    GLM_FUNC_QUALIFIER T extractRealComponent(qua<T, Q> const& q)
    {
        T w = static_cast<T>(1) - q.x * q.x - q.y * q.y - q.z * q.z;
        if(w < T(0))
            return T(0);
        else
            return -sqrt(w);
    }
 
    template<typename T, qualifier Q>
    GLM_FUNC_QUALIFIER GLM_CONSTEXPR T length2(qua<T, Q> const& q)
    {
        return q.x * q.x + q.y * q.y + q.z * q.z + q.w * q.w;
    }
 
    template<typename T, qualifier Q>
    GLM_FUNC_QUALIFIER qua<T, Q> shortMix(qua<T, Q> const& x, qua<T, Q> const& y, T const& a)
    {
        if(a <= static_cast<T>(0)) return x;
        if(a >= static_cast<T>(1)) return y;
 
        T fCos = dot(x, y);
        qua<T, Q> y2(y); //BUG!!! qua<T> y2;
        if(fCos < static_cast<T>(0))
        {
            y2 = -y;
            fCos = -fCos;
        }
 
        //if(fCos > 1.0f) // problem
        T k0, k1;
        if(fCos > (static_cast<T>(1) - epsilon<T>()))
        {
            k0 = static_cast<T>(1) - a;
            k1 = static_cast<T>(0) + a; //BUG!!! 1.0f + a;
        }
        else
        {
            T fSin = sqrt(T(1) - fCos * fCos);
            T fAngle = atan(fSin, fCos);
            T fOneOverSin = static_cast<T>(1) / fSin;
            k0 = sin((static_cast<T>(1) - a) * fAngle) * fOneOverSin;
            k1 = sin((static_cast<T>(0) + a) * fAngle) * fOneOverSin;
        }
 
        return qua<T, Q>(
            k0 * x.w + k1 * y2.w,
            k0 * x.x + k1 * y2.x,
            k0 * x.y + k1 * y2.y,
            k0 * x.z + k1 * y2.z);
    }
 
    template<typename T, qualifier Q>
    GLM_FUNC_QUALIFIER qua<T, Q> fastMix(qua<T, Q> const& x, qua<T, Q> const& y, T const& a)
    {
        return glm::normalize(x * (static_cast<T>(1) - a) + (y * a));
    }
 
    template<typename T, qualifier Q>
    GLM_FUNC_QUALIFIER qua<T, Q> rotation(vec<3, T, Q> const& orig, vec<3, T, Q> const& dest)
    {
        T cosTheta = dot(orig, dest);
        vec<3, T, Q> rotationAxis;
 
        if(cosTheta >= static_cast<T>(1) - epsilon<T>()) {
            // orig and dest point in the same direction
            return quat_identity<T,Q>();
        }
 
        if(cosTheta < static_cast<T>(-1) + epsilon<T>())
        {
            // special case when vectors in opposite directions :
            // there is no "ideal" rotation axis
            // So guess one; any will do as long as it's perpendicular to start
            // This implementation favors a rotation around the Up axis (Y),
            // since it's often what you want to do.
            rotationAxis = cross(vec<3, T, Q>(0, 0, 1), orig);
            if(length2(rotationAxis) < epsilon<T>()) // bad luck, they were parallel, try again!
                rotationAxis = cross(vec<3, T, Q>(1, 0, 0), orig);
 
            rotationAxis = normalize(rotationAxis);
            return angleAxis(pi<T>(), rotationAxis);
        }
 
        // Implementation from Stan Melax's Game Programming Gems 1 article
        rotationAxis = cross(orig, dest);
 
        T s = sqrt((T(1) + cosTheta) * static_cast<T>(2));
        T invs = static_cast<T>(1) / s;
 
        return qua<T, Q>(
            s * static_cast<T>(0.5f),
            rotationAxis.x * invs,
            rotationAxis.y * invs,
            rotationAxis.z * invs);
    }
}//namespace glm