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///////////////////////////////////////////////////////////////////////////////////////////////////
// OpenGL Mathematics Copyright (c) 2005 - 2011 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{
namespace gtx{
namespace quaternion
{
template <typename valType>
GLM_FUNC_QUALIFIER detail::tvec3<valType> cross
(
detail::tvec3<valType> const & v,
detail::tquat<valType> const & q
)
{
return gtc::quaternion::inverse(q) * v;
}
template <typename valType>
GLM_FUNC_QUALIFIER detail::tvec3<valType> cross
(
detail::tquat<valType> const & q,
detail::tvec3<valType> const & v
)
{
return q * v;
}
template <typename T>
GLM_FUNC_QUALIFIER detail::tquat<T> squad
(
detail::tquat<T> const & q1,
detail::tquat<T> const & q2,
detail::tquat<T> const & s1,
detail::tquat<T> const & s2,
T const & h)
{
return mix(mix(q1, q2, h), mix(s1, s2, h), T(2) * h (T(1) - h));
}
template <typename T>
GLM_FUNC_QUALIFIER detail::tquat<T> intermediate
(
detail::tquat<T> const & prev,
detail::tquat<T> const & curr,
detail::tquat<T> const & next
)
{
detail::tquat<T> invQuat = gtc::quaternion::inverse(curr);
return ext((log(next + invQuat) + log(prev + invQuat)) / T(-4)) * curr;
}
template <typename T>
GLM_FUNC_QUALIFIER detail::tquat<T> exp
(
detail::tquat<T> const & q,
T const & exponent
)
{
detail::tvec3<T> u(q.x, q.y, q.z);
float a = glm::length(u);
detail::tvec3<T> v(u / a);
return detail::tquat<T>(cos(a), sin(a) * v);
}
template <typename T>
GLM_FUNC_QUALIFIER detail::tquat<T> log
(
detail::tquat<T> const & q
)
{
if((q.x == T(0)) && (q.y == T(0)) && (q.z == T(0)))
{
if(q.w > T(0))
return detail::tquat<T>(log(q.w), T(0), T(0), T(0));
else if(q.w < T(0))
return detail::tquat<T>(log(-q.w), T(3.1415926535897932384626433832795), T(0),T(0));
else
return detail::tquat<T>(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>(t * q.x, t * q.y, t * q.z, log(QuatLen));
}
}
template <typename T>
GLM_FUNC_QUALIFIER detail::tquat<T> pow
(
detail::tquat<T> 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>(
cos(NewAngle),
x.x * Div,
x.y * Div,
x.z * Div);
}
//template <typename T>
//GLM_FUNC_QUALIFIER detail::tquat<T> sqrt
//(
// detail::tquat<T> const & q
//)
//{
// T q0 = T(1) - dot(q, q);
// return T(2) * (T(1) + q0) * q;
//}
template <typename T>
GLM_FUNC_QUALIFIER detail::tvec3<T> rotate
(
detail::tquat<T> const & q,
detail::tvec3<T> const & v
)
{
return q * v;
}
template <typename T>
GLM_FUNC_QUALIFIER detail::tvec4<T> rotate
(
detail::tquat<T> const & q,
detail::tvec4<T> const & v
)
{
return q * v;
}
template <typename T>
GLM_FUNC_QUALIFIER T angle
(
detail::tquat<T> const & x
)
{
return glm::degrees(acos(x.w) * T(2));
}
template <typename T>
GLM_FUNC_QUALIFIER detail::tvec3<T> axis
(
detail::tquat<T> const & x
)
{
T tmp1 = T(1) - x.w * x.w;
if(tmp1 <= T(0))
return detail::tvec3<T>(0, 0, 1);
T tmp2 = T(1) / sqrt(tmp1);
return detail::tvec3<T>(x.x * tmp2, x.y * tmp2, x.z * tmp2);
}
template <typename valType>
GLM_FUNC_QUALIFIER detail::tquat<valType> angleAxis
(
valType const & angle,
valType const & x,
valType const & y,
valType const & z
)
{
return angleAxis(angle, detail::tvec3<valType>(x, y, z));
}
template <typename valType>
GLM_FUNC_QUALIFIER detail::tquat<valType> angleAxis
(
valType const & angle,
detail::tvec3<valType> const & v
)
{
detail::tquat<valType> result;
valType a = glm::radians(angle);
valType s = glm::sin(a * valType(0.5));
result.w = glm::cos(a * valType(0.5));
result.x = v.x * s;
result.y = v.y * s;
result.z = v.z * s;
return result;
}
template <typename T>
GLM_FUNC_QUALIFIER T extractRealComponent
(
detail::tquat<T> const & q
)
{
T w = 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 valType>
GLM_FUNC_QUALIFIER valType roll
(
detail::tquat<valType> const & q
)
{
return atan2(valType(2) * (q.x * q.y + q.w * q.z), q.w * q.w + q.x * q.x - q.y * q.y - q.z * q.z);
}
template <typename valType>
GLM_FUNC_QUALIFIER valType pitch
(
detail::tquat<valType> const & q
)
{
return atan2(valType(2) * (q.y * q.z + q.w * q.x), q.w * q.w - q.x * q.x - q.y * q.y + q.z * q.z);
}
template <typename valType>
GLM_FUNC_QUALIFIER valType yaw
(
detail::tquat<valType> const & q
)
{
return asin(valType(-2) * (q.x * q.z - q.w * q.y));
}
template <typename valType>
GLM_FUNC_QUALIFIER detail::tvec3<valType> eularAngles
(
detail::tquat<valType> const & x
)
{
return detail::tvec3<valType>(pitch(x), yaw(x), roll(x));
}
template <typename T>
GLM_FUNC_QUALIFIER detail::tquat<T> shortMix
(
detail::tquat<T> const & x,
detail::tquat<T> const & y,
T const & a
)
{
if(a <= typename detail::tquat<T>::value_type(0)) return x;
if(a >= typename detail::tquat<T>::value_type(1)) return y;
T fCos = dot(x, y);
detail::tquat<T> 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 = T(1) - a;
k1 = T(0) + a; //BUG!!! 1.0f + a;
}
else
{
T fSin = sqrt(T(1) - fCos * fCos);
T fAngle = atan(fSin, fCos);
T fOneOverSin = T(1) / fSin;
k0 = sin((T(1) - a) * fAngle) * fOneOverSin;
k1 = sin((T(0) + a) * fAngle) * fOneOverSin;
}
return detail::tquat<T>(
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>
GLM_FUNC_QUALIFIER detail::tquat<T> fastMix
(
detail::tquat<T> const & x,
detail::tquat<T> const & y,
T const & a
)
{
return glm::normalize(x * (T(1) - a) + (y * a));
}
}//namespace quaternion
}//namespace gtx
}//namespace glm
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