/// @ref gtc_quaternion
/// @file glm/gtc/quaternion.inl
#include "../trigonometric.hpp"
#include "../geometric.hpp"
#include "../exponential.hpp"
#include "../detail/compute_vector_relational.hpp"
#include "epsilon.hpp"
#include <limits>
namespace glm{
namespace detail
{
template<typename T, qualifier Q, bool Aligned>
struct compute_dot<tquat<T, Q>, T, Aligned>
{
static GLM_FUNC_QUALIFIER T call(tquat<T, Q> const& a, tquat<T, Q> const& b)
{
vec<4, T, Q> tmp(a.x * b.x, a.y * b.y, a.z * b.z, a.w * b.w);
return (tmp.x + tmp.y) + (tmp.z + tmp.w);
}
};
template<typename T, qualifier Q, bool Aligned>
struct compute_quat_add
{
static tquat<T, Q> call(tquat<T, Q> const& q, tquat<T, Q> const& p)
{
return tquat<T, Q>(q.w + p.w, q.x + p.x, q.y + p.y, q.z + p.z);
}
};
template<typename T, qualifier Q, bool Aligned>
struct compute_quat_sub
{
static tquat<T, Q> call(tquat<T, Q> const& q, tquat<T, Q> const& p)
{
return tquat<T, Q>(q.w - p.w, q.x - p.x, q.y - p.y, q.z - p.z);
}
};
template<typename T, qualifier Q, bool Aligned>
struct compute_quat_mul_scalar
{
static tquat<T, Q> call(tquat<T, Q> const& q, T s)
{
return tquat<T, Q>(q.w * s, q.x * s, q.y * s, q.z * s);
}
};
template<typename T, qualifier Q, bool Aligned>
struct compute_quat_div_scalar
{
static tquat<T, Q> call(tquat<T, Q> const& q, T s)
{
return tquat<T, Q>(q.w / s, q.x / s, q.y / s, q.z / s);
}
};
template<typename T, qualifier Q, bool Aligned>
struct compute_quat_mul_vec4
{
static vec<4, T, Q> call(tquat<T, Q> const& q, vec<4, T, Q> const& v)
{
return vec<4, T, Q>(q * vec<3, T, Q>(v), v.w);
}
};
}//namespace detail
// -- Component accesses --
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER T & tquat<T, Q>::operator[](typename tquat<T, Q>::length_type i)
{
assert(i >= 0 && i < this->length());
return (&x)[i];
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER T const& tquat<T, Q>::operator[](typename tquat<T, Q>::length_type i) const
{
assert(i >= 0 && i < this->length());
return (&x)[i];
}
// -- Implicit basic constructors --
# if !GLM_HAS_DEFAULTED_FUNCTIONS || defined(GLM_FORCE_CTOR_INIT)
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER GLM_CONSTEXPR tquat<T, Q>::tquat()
# ifdef GLM_FORCE_CTOR_INIT
: x(0), y(0), z(0), w(1)
# endif
{}
# endif
# if !GLM_HAS_DEFAULTED_FUNCTIONS
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER GLM_CONSTEXPR tquat<T, Q>::tquat(tquat<T, Q> const& q)
: x(q.x), y(q.y), z(q.z), w(q.w)
{}
# endif//!GLM_HAS_DEFAULTED_FUNCTIONS
template<typename T, qualifier Q>
template<qualifier P>
GLM_FUNC_QUALIFIER GLM_CONSTEXPR tquat<T, Q>::tquat(tquat<T, P> const& q)
: x(q.x), y(q.y), z(q.z), w(q.w)
{}
// -- Explicit basic constructors --
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER GLM_CONSTEXPR tquat<T, Q>::tquat(T s, vec<3, T, Q> const& v)
: x(v.x), y(v.y), z(v.z), w(s)
{}
template <typename T, qualifier Q>
GLM_FUNC_QUALIFIER GLM_CONSTEXPR tquat<T, Q>::tquat(T _w, T _x, T _y, T _z)
: x(_x), y(_y), z(_z), w(_w)
{}
// -- Conversion constructors --
template<typename T, qualifier Q>
template<typename U, qualifier P>
GLM_FUNC_QUALIFIER GLM_CONSTEXPR tquat<T, Q>::tquat(tquat<U, P> const& q)
: x(static_cast<T>(q.x))
, y(static_cast<T>(q.y))
, z(static_cast<T>(q.z))
, w(static_cast<T>(q.w))
{}
//template<typename valType>
//GLM_FUNC_QUALIFIER tquat<valType>::tquat
//(
// valType const& pitch,
// valType const& yaw,
// valType const& roll
//)
//{
// vec<3, valType> eulerAngle(pitch * valType(0.5), yaw * valType(0.5), roll * valType(0.5));
// vec<3, valType> c = glm::cos(eulerAngle * valType(0.5));
// vec<3, 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, qualifier Q>
GLM_FUNC_QUALIFIER tquat<T, Q>::tquat(vec<3, T, Q> const& u, vec<3, T, Q> const& v)
{
T norm_u_norm_v = sqrt(dot(u, u) * dot(v, v));
T real_part = norm_u_norm_v + dot(u, v);
vec<3, T, Q> t;
if(real_part < static_cast<T>(1.e-6f) * norm_u_norm_v)
{
// If u and v are exactly opposite, rotate 180 degrees
// around an arbitrary orthogonal axis. Axis normalisation
// can happen later, when we normalise the quaternion.
real_part = static_cast<T>(0);
t = abs(u.x) > abs(u.z) ? vec<3, T, Q>(-u.y, u.x, static_cast<T>(0)) : vec<3, T, Q>(static_cast<T>(0), -u.z, u.y);
}
else
{
// Otherwise, build quaternion the standard way.
t = cross(u, v);
}
*this = normalize(tquat<T, Q>(real_part, t.x, t.y, t.z));
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER tquat<T, Q>::tquat(vec<3, T, Q> const& eulerAngle)
{
vec<3, T, Q> c = glm::cos(eulerAngle * T(0.5));
vec<3, T, Q> 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, qualifier Q>
GLM_FUNC_QUALIFIER tquat<T, Q>::tquat(mat<3, 3, T, Q> const& m)
{
*this = quat_cast(m);
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER tquat<T, Q>::tquat(mat<4, 4, T, Q> const& m)
{
*this = quat_cast(m);
}
# if GLM_HAS_EXPLICIT_CONVERSION_OPERATORS
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER tquat<T, Q>::operator mat<3, 3, T, Q>()
{
return mat3_cast(*this);
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER tquat<T, Q>::operator mat<4, 4, T, Q>()
{
return mat4_cast(*this);
}
# endif//GLM_HAS_EXPLICIT_CONVERSION_OPERATORS
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER tquat<T, Q> conjugate(tquat<T, Q> const& q)
{
return tquat<T, Q>(q.w, -q.x, -q.y, -q.z);
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER tquat<T, Q> inverse(tquat<T, Q> const& q)
{
return conjugate(q) / dot(q, q);
}
// -- Unary arithmetic operators --
# if !GLM_HAS_DEFAULTED_FUNCTIONS
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER tquat<T, Q> & tquat<T, Q>::operator=(tquat<T, Q> const& q)
{
this->w = q.w;
this->x = q.x;
this->y = q.y;
this->z = q.z;
return *this;
}
# endif//!GLM_HAS_DEFAULTED_FUNCTIONS
template<typename T, qualifier Q>
template<typename U>
GLM_FUNC_QUALIFIER tquat<T, Q> & tquat<T, Q>::operator=(tquat<U, Q> const& q)
{
this->w = static_cast<T>(q.w);
this->x = static_cast<T>(q.x);
this->y = static_cast<T>(q.y);
this->z = static_cast<T>(q.z);
return *this;
}
template<typename T, qualifier Q>
template<typename U>
GLM_FUNC_QUALIFIER tquat<T, Q> & tquat<T, Q>::operator+=(tquat<U, Q> const& q)
{
return (*this = detail::compute_quat_add<T, Q, detail::is_aligned<Q>::value>::call(*this, tquat<T, Q>(q)));
}
template<typename T, qualifier Q>
template<typename U>
GLM_FUNC_QUALIFIER tquat<T, Q> & tquat<T, Q>::operator-=(tquat<U, Q> const& q)
{
return (*this = detail::compute_quat_sub<T, Q, detail::is_aligned<Q>::value>::call(*this, tquat<T, Q>(q)));
}
template<typename T, qualifier Q>
template<typename U>
GLM_FUNC_QUALIFIER tquat<T, Q> & tquat<T, Q>::operator*=(tquat<U, Q> const& r)
{
tquat<T, Q> const p(*this);
tquat<T, Q> const q(r);
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, qualifier Q>
template<typename U>
GLM_FUNC_QUALIFIER tquat<T, Q> & tquat<T, Q>::operator*=(U s)
{
return (*this = detail::compute_quat_mul_scalar<T, Q, detail::is_aligned<Q>::value>::call(*this, static_cast<U>(s)));
}
template<typename T, qualifier Q>
template<typename U>
GLM_FUNC_QUALIFIER tquat<T, Q> & tquat<T, Q>::operator/=(U s)
{
return (*this = detail::compute_quat_div_scalar<T, Q, detail::is_aligned<Q>::value>::call(*this, static_cast<U>(s)));
}
// -- Unary bit operators --
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER tquat<T, Q> operator+(tquat<T, Q> const& q)
{
return q;
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER tquat<T, Q> operator-(tquat<T, Q> const& q)
{
return tquat<T, Q>(-q.w, -q.x, -q.y, -q.z);
}
// -- Binary operators --
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER tquat<T, Q> operator+(tquat<T, Q> const& q, tquat<T, Q> const& p)
{
return tquat<T, Q>(q) += p;
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER tquat<T, Q> operator-(tquat<T, Q> const& q, tquat<T, Q> const& p)
{
return tquat<T, Q>(q) -= p;
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER tquat<T, Q> operator*(tquat<T, Q> const& q, tquat<T, Q> const& p)
{
return tquat<T, Q>(q) *= p;
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER vec<3, T, Q> operator*(tquat<T, Q> const& q, vec<3, T, Q> const& v)
{
vec<3, T, Q> const QuatVector(q.x, q.y, q.z);
vec<3, T, Q> const uv(glm::cross(QuatVector, v));
vec<3, T, Q> const uuv(glm::cross(QuatVector, uv));
return v + ((uv * q.w) + uuv) * static_cast<T>(2);
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER vec<3, T, Q> operator*(vec<3, T, Q> const& v, tquat<T, Q> const& q)
{
return glm::inverse(q) * v;
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER vec<4, T, Q> operator*(tquat<T, Q> const& q, vec<4, T, Q> const& v)
{
return detail::compute_quat_mul_vec4<T, Q, detail::is_aligned<Q>::value>::call(q, v);
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER vec<4, T, Q> operator*(vec<4, T, Q> const& v, tquat<T, Q> const& q)
{
return glm::inverse(q) * v;
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER tquat<T, Q> operator*(tquat<T, Q> const& q, T const& s)
{
return tquat<T, Q>(
q.w * s, q.x * s, q.y * s, q.z * s);
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER tquat<T, Q> operator*(T const& s, tquat<T, Q> const& q)
{
return q * s;
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER tquat<T, Q> operator/(tquat<T, Q> const& q, T const& s)
{
return tquat<T, Q>(
q.w / s, q.x / s, q.y / s, q.z / s);
}
// -- Boolean operators --
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER bool operator==(tquat<T, Q> const& q1, tquat<T, Q> const& q2)
{
return all(epsilonEqual(q1, q2, epsilon<T>()));
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER bool operator!=(tquat<T, Q> const& q1, tquat<T, Q> const& q2)
{
return any(epsilonNotEqual(q1, q2, epsilon<T>()));
}
// -- Operations --
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER T dot(tquat<T, Q> const& x, tquat<T, Q> const& y)
{
GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'dot' accepts only floating-point inputs");
return detail::compute_dot<tquat<T, Q>, T, detail::is_aligned<Q>::value>::call(x, y);
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER T length(tquat<T, Q> const& q)
{
return glm::sqrt(dot(q, q));
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER tquat<T, Q> normalize(tquat<T, Q> const& q)
{
T len = length(q);
if(len <= T(0)) // Problem
return tquat<T, Q>(static_cast<T>(1), static_cast<T>(0), static_cast<T>(0), static_cast<T>(0));
T oneOverLen = T(1) / len;
return tquat<T, Q>(q.w * oneOverLen, q.x * oneOverLen, q.y * oneOverLen, q.z * oneOverLen);
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER tquat<T, Q> cross(tquat<T, Q> const& q1, tquat<T, Q> const& q2)
{
return tquat<T, Q>(
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, qualifier Q>
GLM_FUNC_QUALIFIER tquat<T, Q> mix(tquat<T, Q> const& x, tquat<T, Q> const& y, T const& a)
{
if(a <= T(0)) return x;
if(a >= T(1)) return y;
float fCos = dot(x, y);
tquat<T, Q> y2(y); //BUG!!! tquat<T, Q> 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 tquat<T, Q>(
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, qualifier Q>
GLM_FUNC_QUALIFIER tquat<T, Q> mix2
(
tquat<T, Q> const& x,
tquat<T, Q> 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, qualifier Q>
GLM_FUNC_QUALIFIER tquat<T, Q> mix(tquat<T, Q> const& x, tquat<T, Q> const& y, T 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 tquat<T, Q>(
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, qualifier Q>
GLM_FUNC_QUALIFIER tquat<T, Q> lerp(tquat<T, Q> const& x, tquat<T, Q> const& y, T 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, qualifier Q>
GLM_FUNC_QUALIFIER tquat<T, Q> slerp(tquat<T, Q> const& x, tquat<T, Q> const& y, T a)
{
tquat<T, Q> 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 tquat<T, Q>(
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, qualifier Q>
GLM_FUNC_QUALIFIER tquat<T, Q> rotate(tquat<T, Q> const& q, T const& angle, vec<3, T, Q> const& v)
{
vec<3, T, Q> 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;
}
T const AngleRad(angle);
T const Sin = sin(AngleRad * T(0.5));
return q * tquat<T, Q>(cos(AngleRad * T(0.5)), Tmp.x * Sin, Tmp.y * Sin, Tmp.z * Sin);
//return gtc::quaternion::cross(q, tquat<T, Q>(cos(AngleRad * T(0.5)), Tmp.x * fSin, Tmp.y * fSin, Tmp.z * fSin));
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER vec<3, T, Q> eulerAngles(tquat<T, Q> const& x)
{
return vec<3, T, Q>(pitch(x), yaw(x), roll(x));
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER T roll(tquat<T, Q> const& q)
{
return static_cast<T>(atan(static_cast<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));
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER T pitch(tquat<T, Q> const& q)
{
//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));
const T y = static_cast<T>(2) * (q.y * q.z + q.w * q.x);
const T x = q.w * q.w - q.x * q.x - q.y * q.y + q.z * q.z;
if(detail::compute_equal<T>::call(y, static_cast<T>(0)) && detail::compute_equal<T>::call(x, static_cast<T>(0))) //avoid atan2(0,0) - handle singularity - Matiis
return static_cast<T>(static_cast<T>(2) * atan(q.x,q.w));
return static_cast<T>(atan(y,x));
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER T yaw(tquat<T, Q> const& q)
{
return asin(clamp(static_cast<T>(-2) * (q.x * q.z - q.w * q.y), static_cast<T>(-1), static_cast<T>(1)));
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER mat<3, 3, T, Q> mat3_cast(tquat<T, Q> const& q)
{
mat<3, 3, T, Q> 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] = T(1) - T(2) * (qyy + qzz);
Result[0][1] = T(2) * (qxy + qwz);
Result[0][2] = T(2) * (qxz - qwy);
Result[1][0] = T(2) * (qxy - qwz);
Result[1][1] = T(1) - T(2) * (qxx + qzz);
Result[1][2] = T(2) * (qyz + qwx);
Result[2][0] = T(2) * (qxz + qwy);
Result[2][1] = T(2) * (qyz - qwx);
Result[2][2] = T(1) - T(2) * (qxx + qyy);
return Result;
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER mat<4, 4, T, Q> mat4_cast(tquat<T, Q> const& q)
{
return mat<4, 4, T, Q>(mat3_cast(q));
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER tquat<T, Q> quat_cast(mat<3, 3, T, Q> 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 + static_cast<T>(1)) * static_cast<T>(0.5);
T mult = static_cast<T>(0.25) / biggestVal;
switch(biggestIndex)
{
case 0:
return tquat<T, Q>(biggestVal, (m[1][2] - m[2][1]) * mult, (m[2][0] - m[0][2]) * mult, (m[0][1] - m[1][0]) * mult);
case 1:
return tquat<T, Q>((m[1][2] - m[2][1]) * mult, biggestVal, (m[0][1] + m[1][0]) * mult, (m[2][0] + m[0][2]) * mult);
case 2:
return tquat<T, Q>((m[2][0] - m[0][2]) * mult, (m[0][1] + m[1][0]) * mult, biggestVal, (m[1][2] + m[2][1]) * mult);
case 3:
return tquat<T, Q>((m[0][1] - m[1][0]) * mult, (m[2][0] + m[0][2]) * mult, (m[1][2] + m[2][1]) * mult, biggestVal);
default: // Silence a -Wswitch-default warning in GCC. Should never actually get here. Assert is just for sanity.
assert(false);
return tquat<T, Q>(1, 0, 0, 0);
}
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER tquat<T, Q> quat_cast(mat<4, 4, T, Q> const& m4)
{
return quat_cast(mat<3, 3, T, Q>(m4));
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER T angle(tquat<T, Q> const& x)
{
return acos(x.w) * static_cast<T>(2);
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER vec<3, T, Q> axis(tquat<T, Q> const& x)
{
T tmp1 = static_cast<T>(1) - x.w * x.w;
if(tmp1 <= static_cast<T>(0))
return vec<3, T, Q>(0, 0, 1);
T tmp2 = static_cast<T>(1) / sqrt(tmp1);
return vec<3, T, Q>(x.x * tmp2, x.y * tmp2, x.z * tmp2);
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER tquat<T, Q> angleAxis(T const& angle, vec<3, T, Q> const& v)
{
tquat<T, Q> Result;
T const a(angle);
T const s = glm::sin(a * static_cast<T>(0.5));
Result.w = glm::cos(a * static_cast<T>(0.5));
Result.x = v.x * s;
Result.y = v.y * s;
Result.z = v.z * s;
return Result;
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER vec<4, bool, Q> lessThan(tquat<T, Q> const& x, tquat<T, Q> const& y)
{
vec<4, bool, Q> Result;
for(length_t i = 0; i < x.length(); ++i)
Result[i] = x[i] < y[i];
return Result;
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER vec<4, bool, Q> lessThanEqual(tquat<T, Q> const& x, tquat<T, Q> const& y)
{
vec<4, bool, Q> Result;
for(length_t i = 0; i < x.length(); ++i)
Result[i] = x[i] <= y[i];
return Result;
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER vec<4, bool, Q> greaterThan(tquat<T, Q> const& x, tquat<T, Q> const& y)
{
vec<4, bool, Q> Result;
for(length_t i = 0; i < x.length(); ++i)
Result[i] = x[i] > y[i];
return Result;
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER vec<4, bool, Q> greaterThanEqual(tquat<T, Q> const& x, tquat<T, Q> const& y)
{
vec<4, bool, Q> Result;
for(length_t i = 0; i < x.length(); ++i)
Result[i] = x[i] >= y[i];
return Result;
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER vec<4, bool, Q> equal(tquat<T, Q> const& x, tquat<T, Q> const& y)
{
vec<4, bool, Q> Result;
for(length_t i = 0; i < x.length(); ++i)
Result[i] = detail::compute_equal<T>::call(x[i], y[i]);
return Result;
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER vec<4, bool, Q> notEqual(tquat<T, Q> const& x, tquat<T, Q> const& y)
{
vec<4, bool, Q> Result;
for(length_t i = 0; i < x.length(); ++i)
Result[i] = !detail::compute_equal<T>::call(x[i], y[i]);
return Result;
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER vec<4, bool, Q> isnan(tquat<T, Q> const& q)
{
GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'isnan' only accept floating-point inputs");
return vec<4, bool, Q>(isnan(q.x), isnan(q.y), isnan(q.z), isnan(q.w));
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER vec<4, bool, Q> isinf(tquat<T, Q> const& q)
{
GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'isinf' only accept floating-point inputs");
return vec<4, bool, Q>(isinf(q.x), isinf(q.y), isinf(q.z), isinf(q.w));
}
}//namespace glm
#if GLM_ARCH != GLM_ARCH_PURE && GLM_HAS_ALIGNED_TYPE
# include "quaternion_simd.inl"
#endif
