Dengine/extern/glm-0.9.7.5/include/glm/gtx/quaternion.inl

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///////////////////////////////////////////////////////////////////////////////////
/// OpenGL Mathematics (glm.g-truc.net)
///
/// Copyright (c) 2005 - 2015 G-Truc Creation (www.g-truc.net)
/// Permission is hereby granted, free of charge, to any person obtaining a copy
/// of this software and associated documentation files (the "Software"), to deal
/// in the Software without restriction, including without limitation the rights
/// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
/// copies of the Software, and to permit persons to whom the Software is
/// furnished to do so, subject to the following conditions:
///
/// The above copyright notice and this permission notice shall be included in
/// all copies or substantial portions of the Software.
///
/// Restrictions:
/// By making use of the Software for military purposes, you choose to make
/// a Bunny unhappy.
///
/// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
/// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
/// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
/// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
/// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
/// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
/// THE SOFTWARE.
///
/// @ref gtx_quaternion
/// @file glm/gtx/quaternion.inl
/// @date 2005-12-21 / 2011-06-07
/// @author Christophe Riccio
///////////////////////////////////////////////////////////////////////////////////
#include <limits>
#include "../gtc/constants.hpp"
namespace glm
{
template <typename T, precision P>
GLM_FUNC_QUALIFIER tvec3<T, P> cross
(
tvec3<T, P> const & v,
tquat<T, P> const & q
)
{
return inverse(q) * v;
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER tvec3<T, P> cross
(
tquat<T, P> const & q,
tvec3<T, P> const & v
)
{
return q * v;
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER tquat<T, P> squad
(
tquat<T, P> const & q1,
tquat<T, P> const & q2,
tquat<T, P> const & s1,
tquat<T, P> 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, precision P>
GLM_FUNC_QUALIFIER tquat<T, P> intermediate
(
tquat<T, P> const & prev,
tquat<T, P> const & curr,
tquat<T, P> const & next
)
{
tquat<T, P> invQuat = inverse(curr);
return exp((log(next + invQuat) + log(prev + invQuat)) / static_cast<T>(-4)) * curr;
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER tquat<T, P> exp
(
tquat<T, P> const & q
)
{
tvec3<T, P> u(q.x, q.y, q.z);
T Angle = glm::length(u);
if (Angle < epsilon<T>())
return tquat<T, P>();
tvec3<T, P> v(u / Angle);
return tquat<T, P>(cos(Angle), sin(Angle) * v);
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER tquat<T, P> log
(
tquat<T, P> const & q
)
{
tvec3<T, P> u(q.x, q.y, q.z);
T Vec3Len = length(u);
if (Vec3Len < epsilon<T>())
{
if(q.w > static_cast<T>(0))
return tquat<T, P>(log(q.w), static_cast<T>(0), static_cast<T>(0), static_cast<T>(0));
else if(q.w < static_cast<T>(0))
return tquat<T, P>(log(-q.w), pi<T>(), static_cast<T>(0), static_cast<T>(0));
else
return 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 QuatLen = sqrt(Vec3Len * Vec3Len + q.w * q.w);
T t = atan(Vec3Len, T(q.w)) / Vec3Len;
return tquat<T, P>(log(QuatLen), t * q.x, t * q.y, t * q.z);
}
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER tquat<T, P> pow(tquat<T, P> const & x, T const & 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 tquat<T, P>(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);
//Equivalent to raising a real number to a power
//Needed to prevent a division by 0 error later on
if(abs(x.w / magnitude) > static_cast<T>(1) - epsilon<T>() && abs(x.w / magnitude) < static_cast<T>(1) + epsilon<T>())
return tquat<T, P>(pow(x.w, y),0,0,0);
T Angle = acos(x.w / magnitude);
T NewAngle = Angle * y;
T Div = sin(NewAngle) / sin(Angle);
T Mag = pow(magnitude, y-1);
return tquat<T, P>(cos(NewAngle) * magnitude * Mag, x.x * Div * Mag, x.y * Div * Mag, x.z * Div * Mag);
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER tvec3<T, P> rotate
(
tquat<T, P> const & q,
tvec3<T, P> const & v
)
{
return q * v;
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER tvec4<T, P> rotate
(
tquat<T, P> const & q,
tvec4<T, P> const & v
)
{
return q * v;
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER T extractRealComponent
(
tquat<T, P> 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, precision P>
GLM_FUNC_QUALIFIER T length2
(
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 tquat<T, P> shortMix
(
tquat<T, P> const & x,
tquat<T, P> 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);
tquat<T, P> y2(y); //BUG!!! tquat<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 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 tquat<T, P> fastMix
(
tquat<T, P> const & x,
tquat<T, P> const & y,
T const & a
)
{
return glm::normalize(x * (static_cast<T>(1) - a) + (y * a));
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER tquat<T, P> rotation
(
tvec3<T, P> const & orig,
tvec3<T, P> const & dest
)
{
T cosTheta = dot(orig, dest);
tvec3<T, P> rotationAxis;
if(cosTheta >= static_cast<T>(1) - epsilon<T>())
return quat();
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(tvec3<T, P>(0, 0, 1), orig);
if(length2(rotationAxis) < epsilon<T>()) // bad luck, they were parallel, try again!
rotationAxis = cross(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) * static_cast<T>(2));
T invs = static_cast<T>(1) / s;
return tquat<T, P>(
s * static_cast<T>(0.5f),
rotationAxis.x * invs,
rotationAxis.y * invs,
rotationAxis.z * invs);
}
}//namespace glm