///////////////////////////////////////////////////////////////////////////////////////////////////
// OpenGL Mathematics Copyright (c) 2005 - 2014 G-Truc Creation (www.g-truc.net)
///////////////////////////////////////////////////////////////////////////////////////////////////
// Created : 2005-12-21
// Updated : 2008-11-27
// Licence : This source is under MIT License
// File : glm/gtx/quaternion.inl
///////////////////////////////////////////////////////////////////////////////////////////////////
#include <limits>
namespace glm
{
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tvec3<T, P> cross
(
detail::tvec3<T, P> const & v,
detail::tquat<T, P> const & q
)
{
return inverse(q) * v;
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tvec3<T, P> cross
(
detail::tquat<T, P> const & q,
detail::tvec3<T, P> const & v
)
{
return q * v;
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tquat<T, P> squad
(
detail::tquat<T, P> const & q1,
detail::tquat<T, P> const & q2,
detail::tquat<T, P> const & s1,
detail::tquat<T, P> const & s2,
T const & h)
{
return mix(mix(q1, q2, h), mix(s1, s2, h), T(2) * (T(1) - h) * h);
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tquat<T, P> intermediate
(
detail::tquat<T, P> const & prev,
detail::tquat<T, P> const & curr,
detail::tquat<T, P> const & next
)
{
detail::tquat<T, P> invQuat = inverse(curr);
return exp((log(next + invQuat) + log(prev + invQuat)) / T(-4)) * curr;
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tquat<T, P> exp
(
detail::tquat<T, P> const & q
)
{
detail::tvec3<T, P> u(q.x, q.y, q.z);
float Angle = glm::length(u);
detail::tvec3<T, P> v(u / Angle);
return detail::tquat<T, P>(cos(Angle), sin(Angle) * v);
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tquat<T, P> log
(
detail::tquat<T, P> const & q
)
{
if((q.x == static_cast<T>(0)) && (q.y == static_cast<T>(0)) && (q.z == static_cast<T>(0)))
{
if(q.w > T(0))
return detail::tquat<T, P>(log(q.w), T(0), T(0), T(0));
else if(q.w < T(0))
return detail::tquat<T, P>(log(-q.w), T(3.1415926535897932384626433832795), T(0),T(0));
else
return detail::tquat<T, P>(std::numeric_limits<T>::infinity(), std::numeric_limits<T>::infinity(), std::numeric_limits<T>::infinity(), std::numeric_limits<T>::infinity());
}
else
{
T Vec3Len = sqrt(q.x * q.x + q.y * q.y + q.z * q.z);
T QuatLen = sqrt(Vec3Len * Vec3Len + q.w * q.w);
T t = atan(Vec3Len, T(q.w)) / Vec3Len;
return detail::tquat<T, P>(t * q.x, t * q.y, t * q.z, log(QuatLen));
}
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tquat<T, P> pow
(
detail::tquat<T, P> const & x,
T const & y
)
{
if(abs(x.w) > T(0.9999))
return x;
float Angle = acos(y);
float NewAngle = Angle * y;
float Div = sin(NewAngle) / sin(Angle);
return detail::tquat<T, P>(
cos(NewAngle),
x.x * Div,
x.y * Div,
x.z * Div);
}
//template <typename T, precision P>
//GLM_FUNC_QUALIFIER detail::tquat<T, P> sqrt
//(
// detail::tquat<T, P> const & q
//)
//{
// T q0 = static_cast<T>(1) - dot(q, q);
// return T(2) * (T(1) + q0) * q;
//}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tvec3<T, P> rotate
(
detail::tquat<T, P> const & q,
detail::tvec3<T, P> const & v
)
{
return q * v;
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tvec4<T, P> rotate
(
detail::tquat<T, P> const & q,
detail::tvec4<T, P> const & v
)
{
return q * v;
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER T extractRealComponent
(
detail::tquat<T, P> const & q
)
{
T w = static_cast<T>(1.0) - 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, precision P>
GLM_FUNC_QUALIFIER T length2
(
detail::tquat<T, P> const & q
)
{
return q.x * q.x + q.y * q.y + q.z * q.z + q.w * q.w;
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tquat<T, P> shortMix
(
detail::tquat<T, P> const & x,
detail::tquat<T, P> const & y,
T const & a
)
{
if(a <= T(0)) return x;
if(a >= T(1)) return y;
T fCos = dot(x, y);
detail::tquat<T, P> y2(y); //BUG!!! tquat<T> y2;
if(fCos < T(0))
{
y2 = -y;
fCos = -fCos;
}
//if(fCos > 1.0f) // problem
T k0, k1;
if(fCos > T(0.9999))
{
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((T(1) - a) * fAngle) * fOneOverSin;
k1 = sin((T(0) + a) * fAngle) * fOneOverSin;
}
return detail::tquat<T, P>(
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, precision P>
GLM_FUNC_QUALIFIER detail::tquat<T, P> fastMix
(
detail::tquat<T, P> const & x,
detail::tquat<T, P> const & y,
T const & a
)
{
return glm::normalize(x * (T(1) - a) + (y * a));
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tquat<T, P> rotation
(
detail::tvec3<T, P> const & orig,
detail::tvec3<T, P> const & dest
)
{
T cosTheta = dot(orig, dest);
detail::tvec3<T, P> rotationAxis;
if(cosTheta < 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(detail::tvec3<T, P>(0, 0, 1), orig);
if(length2(rotationAxis) < epsilon<T>()) // bad luck, they were parallel, try again!
rotationAxis = cross(detail::tvec3<T, P>(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) * T(2));
T invs = static_cast<T>(1) / s;
return detail::tquat<T, P>(
s * T(0.5f),
rotationAxis.x * invs,
rotationAxis.y * invs,
rotationAxis.z * invs);
}
}//namespace glm