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///////////////////////////////////////////////////////////////////////////////////
/// OpenGL Mathematics (glm.g-truc.net)
///
/// Copyright (c) 2005 - 2013 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 <limits>
namespace glm{
namespace detail
{
template <typename T>
GLM_FUNC_QUALIFIER typename tquat<T>::size_type tquat<T>::length() const
{
return 4;
}
template <typename T>
GLM_FUNC_QUALIFIER tquat<T>::tquat() :
x(0),
y(0),
z(0),
w(1)
{}
template <typename T>
GLM_FUNC_QUALIFIER tquat<T>::tquat
(
value_type const & s,
tvec3<T> const & v
) :
x(v.x),
y(v.y),
z(v.z),
w(s)
{}
template <typename T>
GLM_FUNC_QUALIFIER tquat<T>::tquat
(
value_type const & w,
value_type const & x,
value_type const & y,
value_type 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>
GLM_FUNC_QUALIFIER tquat<T>::tquat
(
tvec3<T> const & eulerAngle
)
{
tvec3<T> c = glm::cos(eulerAngle * value_type(0.5));
tvec3<T> s = glm::sin(eulerAngle * value_type(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>
GLM_FUNC_QUALIFIER tquat<T>::tquat
(
tmat3x3<T> const & m
)
{
*this = quat_cast(m);
}
template <typename T>
GLM_FUNC_QUALIFIER tquat<T>::tquat
(
tmat4x4<T> const & m
)
{
*this = quat_cast(m);
}
//////////////////////////////////////////////////////////////
// tquat<T> accesses
template <typename T>
GLM_FUNC_QUALIFIER typename tquat<T>::value_type & tquat<T>::operator [] (int i)
{
return (&x)[i];
}
template <typename T>
GLM_FUNC_QUALIFIER typename tquat<T>::value_type const & tquat<T>::operator [] (int i) const
{
return (&x)[i];
}
//////////////////////////////////////////////////////////////
// tquat<valType> operators
template <typename T>
GLM_FUNC_QUALIFIER tquat<T> & tquat<T>::operator *=
(
value_type const & s
)
{
this->w *= s;
this->x *= s;
this->y *= s;
this->z *= s;
return *this;
}
template <typename T>
GLM_FUNC_QUALIFIER tquat<T> & tquat<T>::operator /=
(
value_type const & s
)
{
this->w /= s;
this->x /= s;
this->y /= s;
this->z /= s;
return *this;
}
//////////////////////////////////////////////////////////////
// tquat<valType> external operators
template <typename T>
GLM_FUNC_QUALIFIER detail::tquat<T> operator-
(
detail::tquat<T> const & q
)
{
return detail::tquat<T>(-q.w, -q.x, -q.y, -q.z);
}
template <typename T>
GLM_FUNC_QUALIFIER detail::tquat<T> operator+
(
detail::tquat<T> const & q,
detail::tquat<T> const & p
)
{
return detail::tquat<T>(
q.w + p.w,
q.x + p.x,
q.y + p.y,
q.z + p.z);
}
template <typename T>
GLM_FUNC_QUALIFIER detail::tquat<T> operator*
(
detail::tquat<T> const & q,
detail::tquat<T> const & p
)
{
return detail::tquat<T>(
q.w * p.w - q.x * p.x - q.y * p.y - q.z * p.z,
q.w * p.x + q.x * p.w + q.y * p.z - q.z * p.y,
q.w * p.y + q.y * p.w + q.z * p.x - q.x * p.z,
q.w * p.z + q.z * p.w + q.x * p.y - q.y * p.x);
}
// Transformation
template <typename T>
GLM_FUNC_QUALIFIER detail::tvec3<T> operator*
(
detail::tquat<T> const & q,
detail::tvec3<T> const & v
)
{
typename detail::tquat<T>::value_type Two(2);
detail::tvec3<T> uv, uuv;
detail::tvec3<T> 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>
GLM_FUNC_QUALIFIER detail::tvec3<T> operator*
(
detail::tvec3<T> const & v,
detail::tquat<T> const & q
)
{
return inverse(q) * v;
}
template <typename T>
GLM_FUNC_QUALIFIER detail::tvec4<T> operator*
(
detail::tquat<T> const & q,
detail::tvec4<T> const & v
)
{
return detail::tvec4<T>(q * detail::tvec3<T>(v), v.w);
}
template <typename T>
GLM_FUNC_QUALIFIER detail::tvec4<T> operator*
(
detail::tvec4<T> const & v,
detail::tquat<T> const & q
)
{
return inverse(q) * v;
}
template <typename T>
GLM_FUNC_QUALIFIER detail::tquat<T> operator*
(
detail::tquat<T> const & q,
typename detail::tquat<T>::value_type const & s
)
{
return detail::tquat<T>(
q.w * s, q.x * s, q.y * s, q.z * s);
}
template <typename T>
GLM_FUNC_QUALIFIER detail::tquat<T> operator*
(
typename detail::tquat<T>::value_type const & s,
detail::tquat<T> const & q
)
{
return q * s;
}
template <typename T>
GLM_FUNC_QUALIFIER detail::tquat<T> operator/
(
detail::tquat<T> const & q,
typename detail::tquat<T>::value_type const & s
)
{
return detail::tquat<T>(
q.w / s, q.x / s, q.y / s, q.z / s);
}
//////////////////////////////////////
// Boolean operators
template <typename T>
GLM_FUNC_QUALIFIER bool operator==
(
detail::tquat<T> const & q1,
detail::tquat<T> const & q2
)
{
return (q1.x == q2.x) && (q1.y == q2.y) && (q1.z == q2.z) && (q1.w == q2.w);
}
template <typename T>
GLM_FUNC_QUALIFIER bool operator!=
(
detail::tquat<T> const & q1,
detail::tquat<T> const & q2
)
{
return (q1.x != q2.x) || (q1.y != q2.y) || (q1.z != q2.z) || (q1.w != q2.w);
}
}//namespace detail
////////////////////////////////////////////////////////
template <typename T>
GLM_FUNC_QUALIFIER T length
(
detail::tquat<T> const & q
)
{
return glm::sqrt(dot(q, q));
}
template <typename T>
GLM_FUNC_QUALIFIER detail::tquat<T> normalize
(
detail::tquat<T> const & q
)
{
typename detail::tquat<T>::value_type len = length(q);
if(len <= typename detail::tquat<T>::value_type(0)) // Problem
return detail::tquat<T>(1, 0, 0, 0);
typename detail::tquat<T>::value_type oneOverLen = typename detail::tquat<T>::value_type(1) / len;
return detail::tquat<T>(q.w * oneOverLen, q.x * oneOverLen, q.y * oneOverLen, q.z * oneOverLen);
}
template <typename T>
GLM_FUNC_QUALIFIER T dot
(
detail::tquat<T> const & q1,
detail::tquat<T> const & q2
)
{
return q1.x * q2.x + q1.y * q2.y + q1.z * q2.z + q1.w * q2.w;
}
template <typename T>
GLM_FUNC_QUALIFIER detail::tquat<T> cross
(
detail::tquat<T> const & q1,
detail::tquat<T> const & q2
)
{
return detail::tquat<T>(
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>
GLM_FUNC_QUALIFIER detail::tquat<T> mix
(
detail::tquat<T> const & x,
detail::tquat<T> const & y,
typename detail::tquat<T>::value_type const & a
)
{
if(a <= typename detail::tquat<T>::value_type(0)) return x;
if(a >= typename detail::tquat<T>::value_type(1)) return y;
float fCos = dot(x, y);
detail::tquat<T> y2(y); //BUG!!! tquat<T> y2;
if(fCos < typename detail::tquat<T>::value_type(0))
{
y2 = -y;
fCos = -fCos;
}
//if(fCos > 1.0f) // problem
float k0, k1;
if(fCos > typename detail::tquat<T>::value_type(0.9999))
{
k0 = typename detail::tquat<T>::value_type(1) - a;
k1 = typename detail::tquat<T>::value_type(0) + a; //BUG!!! 1.0f + a;
}
else
{
typename detail::tquat<T>::value_type fSin = sqrt(T(1) - fCos * fCos);
typename detail::tquat<T>::value_type fAngle = atan(fSin, fCos);
typename detail::tquat<T>::value_type fOneOverSin = T(1) / fSin;
k0 = sin((typename detail::tquat<T>::value_type(1) - a) * fAngle) * fOneOverSin;
k1 = sin((typename detail::tquat<T>::value_type(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> mix2
(
detail::tquat<T> const & x,
detail::tquat<T> const & y,
T const & a
)
{
bool flip = false;
if(a <= T(0)) return x;
if(a >= 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 = 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>
GLM_FUNC_QUALIFIER detail::tquat<T> mix
(
detail::tquat<T> const & x,
detail::tquat<T> 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>(
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>
GLM_FUNC_QUALIFIER detail::tquat<T> lerp
(
detail::tquat<T> const & x,
detail::tquat<T> const & y,
T const & a
)
{
// Lerp is only defined in [0, 1]
assert(a >= T(0));
assert(a <= T(1));
return x * (T(1) - a) + (y * a);
}
template <typename T>
GLM_FUNC_QUALIFIER detail::tquat<T> slerp
(
detail::tquat<T> const & x,
detail::tquat<T> const & y,
T const & a
)
{
detail::tquat<T> 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>(
mix(x.w, z.w, a),
mix(x.x, z.x, a),
mix(x.y, z.y, a),
mix(x.z, z.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>
GLM_FUNC_QUALIFIER detail::tquat<T> conjugate
(
detail::tquat<T> const & q
)
{
return detail::tquat<T>(q.w, -q.x, -q.y, -q.z);
}
template <typename T>
GLM_FUNC_QUALIFIER detail::tquat<T> inverse
(
detail::tquat<T> const & q
)
{
return conjugate(q) / dot(q, q);
}
template <typename T>
GLM_FUNC_QUALIFIER detail::tquat<T> rotate
(
detail::tquat<T> const & q,
typename detail::tquat<T>::value_type const & angle,
detail::tvec3<T> const & v
)
{
detail::tvec3<T> Tmp = v;
// Axis of rotation must be normalised
typename detail::tquat<T>::value_type len = glm::length(Tmp);
if(abs(len - T(1)) > T(0.001))
{
T oneOverLen = T(1) / len;
Tmp.x *= oneOverLen;
Tmp.y *= oneOverLen;
Tmp.z *= oneOverLen;
}
#ifdef GLM_FORCE_RADIANS
typename detail::tquat<T>::value_type const AngleRad(angle);
#else
typename detail::tquat<T>::value_type const AngleRad = radians(angle);
#endif
typename detail::tquat<T>::value_type const Sin = sin(AngleRad * T(0.5));
return q * detail::tquat<T>(cos(AngleRad * T(0.5)), Tmp.x * Sin, Tmp.y * Sin, Tmp.z * Sin);
//return gtc::quaternion::cross(q, detail::tquat<T>(cos(AngleRad * T(0.5)), Tmp.x * fSin, Tmp.y * fSin, Tmp.z * fSin));
}
template <typename T>
GLM_FUNC_QUALIFIER detail::tvec3<T> eulerAngles
(
detail::tquat<T> const & x
)
{
return detail::tvec3<T>(pitch(x), yaw(x), roll(x));
}
template <typename valType>
GLM_FUNC_QUALIFIER valType roll
(
detail::tquat<valType> const & q
)
{
#ifdef GLM_FORCE_RADIANS
return valType(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));
#else
return glm::degrees(atan(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));
#endif
}
template <typename valType>
GLM_FUNC_QUALIFIER valType pitch
(
detail::tquat<valType> const & q
)
{
#ifdef GLM_FORCE_RADIANS
return valType(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));
#else
return glm::degrees(atan(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));
#endif
}
template <typename valType>
GLM_FUNC_QUALIFIER valType yaw
(
detail::tquat<valType> const & q
)
{
#ifdef GLM_FORCE_RADIANS
return asin(valType(-2) * (q.x * q.z - q.w * q.y));
#else
return glm::degrees(asin(valType(-2) * (q.x * q.z - q.w * q.y)));
#endif
}
template <typename T>
GLM_FUNC_QUALIFIER detail::tmat3x3<T> mat3_cast
(
detail::tquat<T> const & q
)
{
detail::tmat3x3<T> Result(T(1));
Result[0][0] = 1 - 2 * q.y * q.y - 2 * q.z * q.z;
Result[0][1] = 2 * q.x * q.y + 2 * q.w * q.z;
Result[0][2] = 2 * q.x * q.z - 2 * q.w * q.y;
Result[1][0] = 2 * q.x * q.y - 2 * q.w * q.z;
Result[1][1] = 1 - 2 * q.x * q.x - 2 * q.z * q.z;
Result[1][2] = 2 * q.y * q.z + 2 * q.w * q.x;
Result[2][0] = 2 * q.x * q.z + 2 * q.w * q.y;
Result[2][1] = 2 * q.y * q.z - 2 * q.w * q.x;
Result[2][2] = 1 - 2 * q.x * q.x - 2 * q.y * q.y;
return Result;
}
template <typename T>
GLM_FUNC_QUALIFIER detail::tmat4x4<T> mat4_cast
(
detail::tquat<T> const & q
)
{
return detail::tmat4x4<T>(mat3_cast(q));
}
template <typename T>
GLM_FUNC_QUALIFIER detail::tquat<T> quat_cast
(
detail::tmat3x3<T> const & m
)
{
typename detail::tquat<T>::value_type fourXSquaredMinus1 = m[0][0] - m[1][1] - m[2][2];
typename detail::tquat<T>::value_type fourYSquaredMinus1 = m[1][1] - m[0][0] - m[2][2];
typename detail::tquat<T>::value_type fourZSquaredMinus1 = m[2][2] - m[0][0] - m[1][1];
typename detail::tquat<T>::value_type fourWSquaredMinus1 = m[0][0] + m[1][1] + m[2][2];
int biggestIndex = 0;
typename detail::tquat<T>::value_type fourBiggestSquaredMinus1 = fourWSquaredMinus1;
if(fourXSquaredMinus1 > fourBiggestSquaredMinus1)
{
fourBiggestSquaredMinus1 = fourXSquaredMinus1;
biggestIndex = 1;
}
if(fourYSquaredMinus1 > fourBiggestSquaredMinus1)
{
fourBiggestSquaredMinus1 = fourYSquaredMinus1;
biggestIndex = 2;
}
if(fourZSquaredMinus1 > fourBiggestSquaredMinus1)
{
fourBiggestSquaredMinus1 = fourZSquaredMinus1;
biggestIndex = 3;
}
typename detail::tquat<T>::value_type biggestVal = sqrt(fourBiggestSquaredMinus1 + T(1)) * T(0.5);
typename detail::tquat<T>::value_type mult = T(0.25) / biggestVal;
detail::tquat<T> 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>
GLM_FUNC_QUALIFIER detail::tquat<T> quat_cast
(
detail::tmat4x4<T> const & m4
)
{
return quat_cast(detail::tmat3x3<T>(m4));
}
template <typename T>
GLM_FUNC_QUALIFIER T angle
(
detail::tquat<T> const & x
)
{
#ifdef GLM_FORCE_RADIANS
return acos(x.w) * T(2);
#else
return glm::degrees(acos(x.w) * T(2));
#endif
}
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;
#ifdef GLM_FORCE_RADIANS
valType a(angle);
#else
valType a(glm::radians(angle));
#endif
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;
}
}//namespace glm