///////////////////////////////////////////////////////////////////////////////////
/// OpenGL Mathematics (glm.g-truc.net)
///
/// Copyright (c) 2005 - 2014 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.
///
/// 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 gtc_quaternion
/// @file glm/gtc/quaternion.inl
/// @date 2009-05-21 / 2011-06-15
/// @author Christophe Riccio
///////////////////////////////////////////////////////////////////////////////////
#include "../trigonometric.hpp"
#include "../geometric.hpp"
#include "../exponential.hpp"
#include <limits>
namespace glm{
namespace detail
{
template <typename T, precision P>
GLM_FUNC_QUALIFIER GLM_CONSTEXPR length_t tquat<T, P>::length() const
{
return 4;
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER tquat<T, P>::tquat() :
x(0),
y(0),
z(0),
w(1)
{}
template <typename T, precision P>
template <typename U, precision Q>
GLM_FUNC_QUALIFIER tquat<T, P>::tquat
(
tquat<U, Q> const & q
) :
x(q.x),
y(q.y),
z(q.z),
w(q.w)
{}
template <typename T, precision P>
GLM_FUNC_QUALIFIER tquat<T, P>::tquat
(
T const & s,
tvec3<T, P> const & v
) :
x(v.x),
y(v.y),
z(v.z),
w(s)
{}
template <typename T, precision P>
GLM_FUNC_QUALIFIER tquat<T, P>::tquat
(
T const & w,
T const & x,
T const & y,
T const & z
) :
x(x),
y(y),
z(z),
w(w)
{}
//////////////////////////////////////////////////////////////
// tquat conversions
//template <typename valType>
//GLM_FUNC_QUALIFIER tquat<valType>::tquat
//(
// valType const & pitch,
// valType const & yaw,
// valType const & roll
//)
//{
// tvec3<valType> eulerAngle(pitch * valType(0.5), yaw * valType(0.5), roll * valType(0.5));
// tvec3<valType> c = glm::cos(eulerAngle * valType(0.5));
// tvec3<valType> s = glm::sin(eulerAngle * valType(0.5));
//
// this->w = c.x * c.y * c.z + s.x * s.y * s.z;
// this->x = s.x * c.y * c.z - c.x * s.y * s.z;
// this->y = c.x * s.y * c.z + s.x * c.y * s.z;
// this->z = c.x * c.y * s.z - s.x * s.y * c.z;
//}
template <typename T, precision P>
GLM_FUNC_QUALIFIER tquat<T, P>::tquat
(
detail::tvec3<T, P> const & u,
detail::tvec3<T, P> const & v
)
{
detail::tvec3<T, P> w = cross(u, v);
T Dot = detail::compute_dot<detail::tvec3, T, P>::call(u, v);
detail::tquat<T, P> q(T(1) + Dot, w.x, w.y, w.z);
*this = normalize(q);
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER tquat<T, P>::tquat
(
tvec3<T, P> const & eulerAngle
)
{
tvec3<T, P> c = glm::cos(eulerAngle * T(0.5));
tvec3<T, P> s = glm::sin(eulerAngle * T(0.5));
this->w = c.x * c.y * c.z + s.x * s.y * s.z;
this->x = s.x * c.y * c.z - c.x * s.y * s.z;
this->y = c.x * s.y * c.z + s.x * c.y * s.z;
this->z = c.x * c.y * s.z - s.x * s.y * c.z;
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER tquat<T, P>::tquat
(
tmat3x3<T, P> const & m
)
{
*this = quat_cast(m);
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER tquat<T, P>::tquat
(
tmat4x4<T, P> const & m
)
{
*this = quat_cast(m);
}
//////////////////////////////////////////////////////////////
// tquat<T, P> accesses
template <typename T, precision P>
GLM_FUNC_QUALIFIER T & tquat<T, P>::operator[] (length_t i)
{
assert(i >= 0 && i < this->length());
return (&x)[i];
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER T const & tquat<T, P>::operator[] (length_t i) const
{
assert(i >= 0 && i < this->length());
return (&x)[i];
}
}//namespace detail
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tquat<T, P> conjugate
(
detail::tquat<T, P> const & q
)
{
return detail::tquat<T, P>(q.w, -q.x, -q.y, -q.z);
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tquat<T, P> inverse
(
detail::tquat<T, P> const & q
)
{
return conjugate(q) / dot(q, q);
}
namespace detail
{
//////////////////////////////////////////////////////////////
// tquat<valType> operators
template <typename T, precision P>
GLM_FUNC_QUALIFIER tquat<T, P> & tquat<T, P>::operator +=
(
tquat<T, P> const & q
)
{
this->w += q.w;
this->x += q.x;
this->y += q.y;
this->z += q.z;
return *this;
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER tquat<T, P> & tquat<T, P>::operator *=
(
tquat<T, P> const & q
)
{
tquat<T, P> const p(*this);
this->w = p.w * q.w - p.x * q.x - p.y * q.y - p.z * q.z;
this->x = p.w * q.x + p.x * q.w + p.y * q.z - p.z * q.y;
this->y = p.w * q.y + p.y * q.w + p.z * q.x - p.x * q.z;
this->z = p.w * q.z + p.z * q.w + p.x * q.y - p.y * q.x;
return *this;
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER tquat<T, P> & tquat<T, P>::operator *=
(
T const & s
)
{
this->w *= s;
this->x *= s;
this->y *= s;
this->z *= s;
return *this;
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER tquat<T, P> & tquat<T, P>::operator /=
(
T const & s
)
{
this->w /= s;
this->x /= s;
this->y /= s;
this->z /= s;
return *this;
}
//////////////////////////////////////////////////////////////
// tquat<T, P> external functions
template <typename T, precision P>
struct compute_dot<tquat, T, P>
{
static T call(tquat<T, P> const & x, tquat<T, P> const & y)
{
tvec4<T, P> tmp(x.x * y.x, x.y * y.y, x.z * y.z, x.w * y.w);
return (tmp.x + tmp.y) + (tmp.z + tmp.w);
}
};
//////////////////////////////////////////////////////////////
// tquat<T, P> external operators
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tquat<T, P> operator-
(
detail::tquat<T, P> const & q
)
{
return detail::tquat<T, P>(-q.w, -q.x, -q.y, -q.z);
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tquat<T, P> operator+
(
detail::tquat<T, P> const & q,
detail::tquat<T, P> const & p
)
{
return detail::tquat<T, P>(q) += p;
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tquat<T, P> operator*
(
detail::tquat<T, P> const & q,
detail::tquat<T, P> const & p
)
{
return detail::tquat<T, P>(q) *= p;
}
// Transformation
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tvec3<T, P> operator*
(
detail::tquat<T, P> const & q,
detail::tvec3<T, P> const & v
)
{
T Two(2);
detail::tvec3<T, P> uv, uuv;
detail::tvec3<T, P> QuatVector(q.x, q.y, q.z);
uv = glm::cross(QuatVector, v);
uuv = glm::cross(QuatVector, uv);
uv *= (Two * q.w);
uuv *= Two;
return v + uv + uuv;
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tvec3<T, P> operator*
(
detail::tvec3<T, P> const & v,
detail::tquat<T, P> const & q
)
{
return glm::inverse(q) * v;
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tvec4<T, P> operator*
(
detail::tquat<T, P> const & q,
detail::tvec4<T, P> const & v
)
{
return detail::tvec4<T, P>(q * detail::tvec3<T, P>(v), v.w);
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tvec4<T, P> operator*
(
detail::tvec4<T, P> const & v,
detail::tquat<T, P> const & q
)
{
return glm::inverse(q) * v;
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tquat<T, P> operator*
(
detail::tquat<T, P> const & q,
T const & s
)
{
return detail::tquat<T, P>(
q.w * s, q.x * s, q.y * s, q.z * s);
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tquat<T, P> operator*
(
T const & s,
detail::tquat<T, P> const & q
)
{
return q * s;
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tquat<T, P> operator/
(
detail::tquat<T, P> const & q,
T const & s
)
{
return detail::tquat<T, P>(
q.w / s, q.x / s, q.y / s, q.z / s);
}
//////////////////////////////////////
// Boolean operators
template <typename T, precision P>
GLM_FUNC_QUALIFIER bool operator==
(
detail::tquat<T, P> const & q1,
detail::tquat<T, P> const & q2
)
{
return (q1.x == q2.x) && (q1.y == q2.y) && (q1.z == q2.z) && (q1.w == q2.w);
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER bool operator!=
(
detail::tquat<T, P> const & q1,
detail::tquat<T, P> const & q2
)
{
return (q1.x != q2.x) || (q1.y != q2.y) || (q1.z != q2.z) || (q1.w != q2.w);
}
}//namespace detail
////////////////////////////////////////////////////////
template <typename T, precision P>
GLM_FUNC_QUALIFIER T length
(
detail::tquat<T, P> const & q
)
{
return glm::sqrt(dot(q, q));
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tquat<T, P> normalize
(
detail::tquat<T, P> const & q
)
{
T len = length(q);
if(len <= T(0)) // Problem
return detail::tquat<T, P>(1, 0, 0, 0);
T oneOverLen = T(1) / len;
return detail::tquat<T, P>(q.w * oneOverLen, q.x * oneOverLen, q.y * oneOverLen, q.z * oneOverLen);
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tquat<T, P> cross
(
detail::tquat<T, P> const & q1,
detail::tquat<T, P> const & q2
)
{
return detail::tquat<T, P>(
q1.w * q2.w - q1.x * q2.x - q1.y * q2.y - q1.z * q2.z,
q1.w * q2.x + q1.x * q2.w + q1.y * q2.z - q1.z * q2.y,
q1.w * q2.y + q1.y * q2.w + q1.z * q2.x - q1.x * q2.z,
q1.w * q2.z + q1.z * q2.w + q1.x * q2.y - q1.y * q2.x);
}
/*
// (x * sin(1 - a) * angle / sin(angle)) + (y * sin(a) * angle / sin(angle))
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tquat<T, P> mix
(
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;
float fCos = dot(x, y);
detail::tquat<T, P> y2(y); //BUG!!! tquat<T, P> y2;
if(fCos < T(0))
{
y2 = -y;
fCos = -fCos;
}
//if(fCos > 1.0f) // problem
float 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 = 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> mix2
(
detail::tquat<T, P> const & x,
detail::tquat<T, P> const & y,
T const & a
)
{
bool flip = false;
if(a <= static_cast<T>(0)) return x;
if(a >= static_cast<T>(1)) return y;
T cos_t = dot(x, y);
if(cos_t < T(0))
{
cos_t = -cos_t;
flip = true;
}
T alpha(0), beta(0);
if(T(1) - cos_t < 1e-7)
beta = static_cast<T>(1) - alpha;
else
{
T theta = acos(cos_t);
T sin_t = sin(theta);
beta = sin(theta * (T(1) - alpha)) / sin_t;
alpha = sin(alpha * theta) / sin_t;
}
if(flip)
alpha = -alpha;
return normalize(beta * x + alpha * y);
}
*/
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tquat<T, P> mix
(
detail::tquat<T, P> const & x,
detail::tquat<T, P> const & y,
T const & a
)
{
T cosTheta = dot(x, y);
// Perform a linear interpolation when cosTheta is close to 1 to avoid side effect of sin(angle) becoming a zero denominator
if(cosTheta > T(1) - epsilon<T>())
{
// Linear interpolation
return detail::tquat<T, P>(
mix(x.w, y.w, a),
mix(x.x, y.x, a),
mix(x.y, y.y, a),
mix(x.z, y.z, a));
}
else
{
// Essential Mathematics, page 467
T angle = acos(cosTheta);
return (sin((T(1) - a) * angle) * x + sin(a * angle) * y) / sin(angle);
}
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tquat<T, P> lerp
(
detail::tquat<T, P> const & x,
detail::tquat<T, P> const & y,
T const & a
)
{
// Lerp is only defined in [0, 1]
assert(a >= static_cast<T>(0));
assert(a <= static_cast<T>(1));
return x * (T(1) - a) + (y * a);
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tquat<T, P> slerp
(
detail::tquat<T, P> const & x,
detail::tquat<T, P> const & y,
T const & a
)
{
detail::tquat<T, P> z = y;
T cosTheta = dot(x, y);
// If cosTheta < 0, the interpolation will take the long way around the sphere.
// To fix this, one quat must be negated.
if (cosTheta < T(0))
{
z = -y;
cosTheta = -cosTheta;
}
// Perform a linear interpolation when cosTheta is close to 1 to avoid side effect of sin(angle) becoming a zero denominator
if(cosTheta > T(1) - epsilon<T>())
{
// Linear interpolation
return detail::tquat<T, P>(
mix(x.w, y.w, a),
mix(x.x, y.x, a),
mix(x.y, y.y, a),
mix(x.z, y.z, a));
}
else
{
// Essential Mathematics, page 467
T angle = acos(cosTheta);
return (sin((T(1) - a) * angle) * x + sin(a * angle) * z) / sin(angle);
}
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tquat<T, P> rotate
(
detail::tquat<T, P> const & q,
T const & angle,
detail::tvec3<T, P> const & v
)
{
detail::tvec3<T, P> Tmp = v;
// Axis of rotation must be normalised
T len = glm::length(Tmp);
if(abs(len - T(1)) > T(0.001))
{
T oneOverLen = static_cast<T>(1) / len;
Tmp.x *= oneOverLen;
Tmp.y *= oneOverLen;
Tmp.z *= oneOverLen;
}
#ifdef GLM_FORCE_RADIANS
T const AngleRad(angle);
#else
# pragma message("GLM: rotate function taking degrees as a parameter is deprecated. #define GLM_FORCE_RADIANS before including GLM headers to remove this message.")
T const AngleRad = radians(angle);
#endif
T const Sin = sin(AngleRad * T(0.5));
return q * detail::tquat<T, P>(cos(AngleRad * T(0.5)), Tmp.x * Sin, Tmp.y * Sin, Tmp.z * Sin);
//return gtc::quaternion::cross(q, detail::tquat<T, P>(cos(AngleRad * T(0.5)), Tmp.x * fSin, Tmp.y * fSin, Tmp.z * fSin));
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tvec3<T, P> eulerAngles
(
detail::tquat<T, P> const & x
)
{
return detail::tvec3<T, P>(pitch(x), yaw(x), roll(x));
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER T roll
(
detail::tquat<T, P> const & q
)
{
#ifdef GLM_FORCE_RADIANS
return T(atan(T(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));
#else
# pragma message("GLM: roll function returning degrees is deprecated. #define GLM_FORCE_RADIANS before including GLM headers to remove this message.")
return glm::degrees(atan(T(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));
#endif
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER T pitch
(
detail::tquat<T, P> const & q
)
{
#ifdef GLM_FORCE_RADIANS
return T(atan(T(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));
#else
# pragma message("GLM: pitch function returning degrees is deprecated. #define GLM_FORCE_RADIANS before including GLM headers to remove this message.")
return glm::degrees(atan(T(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));
#endif
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER T yaw
(
detail::tquat<T, P> const & q
)
{
#ifdef GLM_FORCE_RADIANS
return asin(T(-2) * (q.x * q.z - q.w * q.y));
#else
# pragma message("GLM: yaw function returning degrees is deprecated. #define GLM_FORCE_RADIANS before including GLM headers to remove this message.")
return glm::degrees(asin(T(-2) * (q.x * q.z - q.w * q.y)));
#endif
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tmat3x3<T, P> mat3_cast
(
detail::tquat<T, P> const & q
)
{
detail::tmat3x3<T, P> Result(T(1));
T qxx(q.x * q.x);
T qyy(q.y * q.y);
T qzz(q.z * q.z);
T qxz(q.x * q.z);
T qxy(q.x * q.y);
T qyz(q.y * q.z);
T qwx(q.w * q.x);
T qwy(q.w * q.y);
T qwz(q.w * q.z);
Result[0][0] = 1 - 2 * (qyy + qzz);
Result[0][1] = 2 * (qxy + qwz);
Result[0][2] = 2 * (qxz - qwy);
Result[1][0] = 2 * (qxy - qwz);
Result[1][1] = 1 - 2 * (qxx + qzz);
Result[1][2] = 2 * (qyz + qwx);
Result[2][0] = 2 * (qxz + qwy);
Result[2][1] = 2 * (qyz - qwx);
Result[2][2] = 1 - 2 * (qxx + qyy);
return Result;
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tmat4x4<T, P> mat4_cast
(
detail::tquat<T, P> const & q
)
{
return detail::tmat4x4<T, P>(mat3_cast(q));
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tquat<T, P> quat_cast
(
detail::tmat3x3<T, P> const & m
)
{
T fourXSquaredMinus1 = m[0][0] - m[1][1] - m[2][2];
T fourYSquaredMinus1 = m[1][1] - m[0][0] - m[2][2];
T fourZSquaredMinus1 = m[2][2] - m[0][0] - m[1][1];
T fourWSquaredMinus1 = m[0][0] + m[1][1] + m[2][2];
int biggestIndex = 0;
T fourBiggestSquaredMinus1 = fourWSquaredMinus1;
if(fourXSquaredMinus1 > fourBiggestSquaredMinus1)
{
fourBiggestSquaredMinus1 = fourXSquaredMinus1;
biggestIndex = 1;
}
if(fourYSquaredMinus1 > fourBiggestSquaredMinus1)
{
fourBiggestSquaredMinus1 = fourYSquaredMinus1;
biggestIndex = 2;
}
if(fourZSquaredMinus1 > fourBiggestSquaredMinus1)
{
fourBiggestSquaredMinus1 = fourZSquaredMinus1;
biggestIndex = 3;
}
T biggestVal = sqrt(fourBiggestSquaredMinus1 + T(1)) * T(0.5);
T mult = static_cast<T>(0.25) / biggestVal;
detail::tquat<T, P> Result;
switch(biggestIndex)
{
case 0:
Result.w = biggestVal;
Result.x = (m[1][2] - m[2][1]) * mult;
Result.y = (m[2][0] - m[0][2]) * mult;
Result.z = (m[0][1] - m[1][0]) * mult;
break;
case 1:
Result.w = (m[1][2] - m[2][1]) * mult;
Result.x = biggestVal;
Result.y = (m[0][1] + m[1][0]) * mult;
Result.z = (m[2][0] + m[0][2]) * mult;
break;
case 2:
Result.w = (m[2][0] - m[0][2]) * mult;
Result.x = (m[0][1] + m[1][0]) * mult;
Result.y = biggestVal;
Result.z = (m[1][2] + m[2][1]) * mult;
break;
case 3:
Result.w = (m[0][1] - m[1][0]) * mult;
Result.x = (m[2][0] + m[0][2]) * mult;
Result.y = (m[1][2] + m[2][1]) * mult;
Result.z = biggestVal;
break;
default: // Silence a -Wswitch-default warning in GCC. Should never actually get here. Assert is just for sanity.
assert(false);
break;
}
return Result;
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tquat<T, P> quat_cast
(
detail::tmat4x4<T, P> const & m4
)
{
return quat_cast(detail::tmat3x3<T, P>(m4));
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER T angle
(
detail::tquat<T, P> const & x
)
{
#ifdef GLM_FORCE_RADIANS
return acos(x.w) * T(2);
#else
# pragma message("GLM: angle function returning degrees is deprecated. #define GLM_FORCE_RADIANS before including GLM headers to remove this message.")
return glm::degrees(acos(x.w) * T(2));
#endif
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tvec3<T, P> axis
(
detail::tquat<T, P> const & x
)
{
T tmp1 = static_cast<T>(1) - x.w * x.w;
if(tmp1 <= static_cast<T>(0))
return detail::tvec3<T, P>(0, 0, 1);
T tmp2 = static_cast<T>(1) / sqrt(tmp1);
return detail::tvec3<T, P>(x.x * tmp2, x.y * tmp2, x.z * tmp2);
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tquat<T, P> angleAxis
(
T const & angle,
detail::tvec3<T, P> const & v
)
{
detail::tquat<T, P> result;
#ifdef GLM_FORCE_RADIANS
T const a(angle);
#else
# pragma message("GLM: angleAxis function taking degrees as a parameter is deprecated. #define GLM_FORCE_RADIANS before including GLM headers to remove this message.")
T const a(glm::radians(angle));
#endif
T s = glm::sin(a * T(0.5));
result.w = glm::cos(a * T(0.5));
result.x = v.x * s;
result.y = v.y * s;
result.z = v.z * s;
return result;
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tvec4<bool, P> lessThan
(
detail::tquat<T, P> const & x,
detail::tquat<T, P> const & y
)
{
detail::tvec4<bool, P> Result;
for(length_t i = 0; i < x.length(); ++i)
Result[i] = x[i] < y[i];
return Result;
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tvec4<bool, P> lessThanEqual
(
detail::tquat<T, P> const & x,
detail::tquat<T, P> const & y
)
{
detail::tvec4<bool, P> Result;
for(length_t i = 0; i < x.length(); ++i)
Result[i] = x[i] <= y[i];
return Result;
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tvec4<bool, P> greaterThan
(
detail::tquat<T, P> const & x,
detail::tquat<T, P> const & y
)
{
detail::tvec4<bool, P> Result;
for(length_t i = 0; i < x.length(); ++i)
Result[i] = x[i] > y[i];
return Result;
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tvec4<bool, P> greaterThanEqual
(
detail::tquat<T, P> const & x,
detail::tquat<T, P> const & y
)
{
detail::tvec4<bool, P> Result;
for(length_t i = 0; i < x.length(); ++i)
Result[i] = x[i] >= y[i];
return Result;
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tvec4<bool, P> equal
(
detail::tquat<T, P> const & x,
detail::tquat<T, P> const & y
)
{
detail::tvec4<bool, P> Result;
for(length_t i = 0; i < x.length(); ++i)
Result[i] = x[i] == y[i];
return Result;
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tvec4<bool, P> notEqual
(
detail::tquat<T, P> const & x,
detail::tquat<T, P> const & y
)
{
detail::tvec4<bool, P> Result;
for(length_t i = 0; i < x.length(); ++i)
Result[i] = x[i] != y[i];
return Result;
}
}//namespace glm