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/// @ref gtx_quaternion
#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
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