|  |  |  | @ -20,8 +20,8 @@ | 
			
		
	
		
			
				
					|  |  |  |  | /// 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 | 
			
		
	
		
			
				
					|  |  |  |  | /// @ref gtx_dual_quaternion | 
			
		
	
		
			
				
					|  |  |  |  | /// @file glm/gtx/dual_quaternion.inl | 
			
		
	
		
			
				
					|  |  |  |  | /// @date 2013-02-10 / 2013-02-13 | 
			
		
	
		
			
				
					|  |  |  |  | /// @author Maksim Vorobiev (msomeone@gmail.com) | 
			
		
	
		
			
				
					|  |  |  |  | /////////////////////////////////////////////////////////////////////////////////// | 
			
		
	
	
		
			
				
					|  |  |  | @ -40,7 +40,7 @@ namespace detail | 
			
		
	
		
			
				
					|  |  |  |  | 	template <typename T> | 
			
		
	
		
			
				
					|  |  |  |  | 	GLM_FUNC_QUALIFIER tdualquat<T>::tdualquat() : | 
			
		
	
		
			
				
					|  |  |  |  | 		real(tquat<T>()), | 
			
		
	
		
			
				
					|  |  |  |  |           dual(tquat<T>(tdualquat<T>::value_type(0),tdualquat<T>::value_type(0),tdualquat<T>::value_type(0),tdualquat<T>::value_type(0))) | 
			
		
	
		
			
				
					|  |  |  |  | 		dual(tquat<T>(T(0), T(0), T(0), T(0))) | 
			
		
	
		
			
				
					|  |  |  |  | 	{} | 
			
		
	
		
			
				
					|  |  |  |  | 
 | 
			
		
	
		
			
				
					|  |  |  |  | 	template <typename T> | 
			
		
	
	
		
			
				
					|  |  |  | @ -49,7 +49,7 @@ namespace detail | 
			
		
	
		
			
				
					|  |  |  |  | 		tquat<T> const & r | 
			
		
	
		
			
				
					|  |  |  |  | 	) : | 
			
		
	
		
			
				
					|  |  |  |  | 		real(r), | 
			
		
	
		
			
				
					|  |  |  |  |         dual(tquat<T>(tdualquat<T>::value_type(0),tdualquat<T>::value_type(0),tdualquat<T>::value_type(0),tdualquat<T>::value_type(0))) | 
			
		
	
		
			
				
					|  |  |  |  | 		dual(tquat<T>(T(0), T(0), T(0), T(0))) | 
			
		
	
		
			
				
					|  |  |  |  | 	{} | 
			
		
	
		
			
				
					|  |  |  |  | 
 | 
			
		
	
		
			
				
					|  |  |  |  | 	template <typename T> | 
			
		
	
	
		
			
				
					|  |  |  | @ -69,7 +69,8 @@ namespace detail | 
			
		
	
		
			
				
					|  |  |  |  | 		tvec3<T> const& p | 
			
		
	
		
			
				
					|  |  |  |  | 	) : | 
			
		
	
		
			
				
					|  |  |  |  | 		real(q), | 
			
		
	
		
			
				
					|  |  |  |  |         dual(-0.5f*( p.x*q.x + p.y*q.y + p.z*q.z), | 
			
		
	
		
			
				
					|  |  |  |  | 		dual( | 
			
		
	
		
			
				
					|  |  |  |  | 			-0.5f*( p.x*q.x + p.y*q.y + p.z*q.z), | 
			
		
	
		
			
				
					|  |  |  |  | 			 0.5f*( p.x*q.w + p.y*q.z - p.z*q.y), | 
			
		
	
		
			
				
					|  |  |  |  | 			 0.5f*(-p.x*q.z + p.y*q.w + p.z*q.x), | 
			
		
	
		
			
				
					|  |  |  |  | 			 0.5f*( p.x*q.y - p.y*q.x + p.z*q.w)) | 
			
		
	
	
		
			
				
					|  |  |  | @ -80,10 +81,10 @@ namespace detail | 
			
		
	
		
			
				
					|  |  |  |  | 	template <typename T> | 
			
		
	
		
			
				
					|  |  |  |  | 	GLM_FUNC_QUALIFIER tdualquat<T>::tdualquat | 
			
		
	
		
			
				
					|  |  |  |  | 	( | 
			
		
	
		
			
				
					|  |  |  |  |         tmat2x4<T> const & holder_mat | 
			
		
	
		
			
				
					|  |  |  |  | 		tmat2x4<T> const & m | 
			
		
	
		
			
				
					|  |  |  |  | 	) | 
			
		
	
		
			
				
					|  |  |  |  | 	{ | 
			
		
	
		
			
				
					|  |  |  |  |         *this = dualquat_cast<> | 
			
		
	
		
			
				
					|  |  |  |  | 		*this = dualquat_cast(m); | 
			
		
	
		
			
				
					|  |  |  |  | 	} | 
			
		
	
		
			
				
					|  |  |  |  | 
 | 
			
		
	
		
			
				
					|  |  |  |  | 	template <typename T> | 
			
		
	
	
		
			
				
					|  |  |  | @ -144,7 +145,7 @@ namespace detail | 
			
		
	
		
			
				
					|  |  |  |  | 		detail::tdualquat<T> const & q | 
			
		
	
		
			
				
					|  |  |  |  | 	) | 
			
		
	
		
			
				
					|  |  |  |  | 	{ | 
			
		
	
		
			
				
					|  |  |  |  |         return detail::tdualquat<T>(-this->real,-this->dual); | 
			
		
	
		
			
				
					|  |  |  |  | 		return detail::tdualquat<T>(-q.real,-q.dual); | 
			
		
	
		
			
				
					|  |  |  |  | 	} | 
			
		
	
		
			
				
					|  |  |  |  | 
 | 
			
		
	
		
			
				
					|  |  |  |  | 	template <typename T> | 
			
		
	
	
		
			
				
					|  |  |  | @ -175,9 +176,9 @@ namespace detail | 
			
		
	
		
			
				
					|  |  |  |  | 		detail::tvec3<T> const & v | 
			
		
	
		
			
				
					|  |  |  |  | 	) | 
			
		
	
		
			
				
					|  |  |  |  | 	{ | 
			
		
	
		
			
				
					|  |  |  |  |         const detail::tvec3<T> real_v3(q.real.x,q.real.y,q.real.z); | 
			
		
	
		
			
				
					|  |  |  |  |         const detail::tvec3<T> dual_v3(q.dual.x,q.dual.y,q.dual.z); | 
			
		
	
		
			
				
					|  |  |  |  |         return (cross(real_v3, cross(real_v3,v) + v * q.real.w + dual_v3) + dual_v3 * q.real.w - real_v3 * q.dual.w) * detail::tdualquat<T>::value_type(2) + v;     | 
			
		
	
		
			
				
					|  |  |  |  | 		detail::tvec3<T> const real_v3(q.real.x,q.real.y,q.real.z); | 
			
		
	
		
			
				
					|  |  |  |  | 		detail::tvec3<T> const dual_v3(q.dual.x,q.dual.y,q.dual.z); | 
			
		
	
		
			
				
					|  |  |  |  | 		return (cross(real_v3, cross(real_v3,v) + v * q.real.w + dual_v3) + dual_v3 * q.real.w - real_v3 * q.dual.w) * T(2) + v; | 
			
		
	
		
			
				
					|  |  |  |  | 	} | 
			
		
	
		
			
				
					|  |  |  |  | 
 | 
			
		
	
		
			
				
					|  |  |  |  | 	template <typename T> | 
			
		
	
	
		
			
				
					|  |  |  | @ -201,9 +202,11 @@ namespace detail | 
			
		
	
		
			
				
					|  |  |  |  | 	} | 
			
		
	
		
			
				
					|  |  |  |  | 
 | 
			
		
	
		
			
				
					|  |  |  |  | 	template <typename T> | 
			
		
	
		
			
				
					|  |  |  |  |     GLM_FUNC_QUALIFIER detail::tvec4<T> operator* ( | 
			
		
	
		
			
				
					|  |  |  |  | 	GLM_FUNC_QUALIFIER detail::tvec4<T> operator* | 
			
		
	
		
			
				
					|  |  |  |  | 	( | 
			
		
	
		
			
				
					|  |  |  |  | 		detail::tvec4<T> const & v, | 
			
		
	
		
			
				
					|  |  |  |  |         detail::tdualquat<T> const & q) | 
			
		
	
		
			
				
					|  |  |  |  | 		detail::tdualquat<T> const & q | 
			
		
	
		
			
				
					|  |  |  |  | 	) | 
			
		
	
		
			
				
					|  |  |  |  | 	{ | 
			
		
	
		
			
				
					|  |  |  |  | 		return inverse(q) * v; | 
			
		
	
		
			
				
					|  |  |  |  | 	} | 
			
		
	
	
		
			
				
					|  |  |  | @ -278,12 +281,13 @@ namespace detail | 
			
		
	
		
			
				
					|  |  |  |  | 		detail::tdualquat<T> const & y, | 
			
		
	
		
			
				
					|  |  |  |  | 		typename detail::tdualquat<T>::value_type const & a | 
			
		
	
		
			
				
					|  |  |  |  | 	) | 
			
		
	
		
			
				
					|  |  |  |  |     { // Dual Quaternion Linear blend aka DLB: | 
			
		
	
		
			
				
					|  |  |  |  | 	{ | 
			
		
	
		
			
				
					|  |  |  |  | 		// Dual Quaternion Linear blend aka DLB: | 
			
		
	
		
			
				
					|  |  |  |  | 		// Lerp is only defined in [0, 1] | 
			
		
	
		
			
				
					|  |  |  |  | 		assert(a >= T(0)); | 
			
		
	
		
			
				
					|  |  |  |  | 		assert(a <= T(1)); | 
			
		
	
		
			
				
					|  |  |  |  |         const detail::tdualquat<T>::value_type k = dot(x.real,y.real) < detail::tdualquat<T>::value_type(0) ? -a : a; | 
			
		
	
		
			
				
					|  |  |  |  |         const detail::tdualquat<T>::value_type one(1); | 
			
		
	
		
			
				
					|  |  |  |  | 		T const k = dot(x.real,y.real) < detail::tdualquat<T>::value_type(0) ? -a : a; | 
			
		
	
		
			
				
					|  |  |  |  | 		T const one(1); | 
			
		
	
		
			
				
					|  |  |  |  | 		return detail::tdualquat<T>(x * (one - a) + y * k); | 
			
		
	
		
			
				
					|  |  |  |  | 	} | 
			
		
	
		
			
				
					|  |  |  |  | 
 | 
			
		
	
	
		
			
				
					|  |  |  | @ -297,7 +301,7 @@ namespace detail | 
			
		
	
		
			
				
					|  |  |  |  | 		const glm::detail::tquat<T> dual = conjugate(q.dual); | 
			
		
	
		
			
				
					|  |  |  |  | 		return detail::tdualquat<T>(real, dual + (real * (-2.0f * dot(real,dual)))); | 
			
		
	
		
			
				
					|  |  |  |  | 	} | 
			
		
	
		
			
				
					|  |  |  |  |      | 
			
		
	
		
			
				
					|  |  |  |  | 	/* | 
			
		
	
		
			
				
					|  |  |  |  | 	 template <typename T> | 
			
		
	
		
			
				
					|  |  |  |  | 	 GLM_FUNC_QUALIFIER detail::tmat3x3<T> mat3_cast | 
			
		
	
		
			
				
					|  |  |  |  | 	 ( | 
			
		
	
	
		
			
				
					|  |  |  | @ -305,7 +309,7 @@ namespace detail | 
			
		
	
		
			
				
					|  |  |  |  | 	 ) | 
			
		
	
		
			
				
					|  |  |  |  | 	 { | 
			
		
	
		
			
				
					|  |  |  |  | 	 } | 
			
		
	
		
			
				
					|  |  |  |  | 
 | 
			
		
	
		
			
				
					|  |  |  |  | 	 */ | 
			
		
	
		
			
				
					|  |  |  |  | 	template <typename T> | 
			
		
	
		
			
				
					|  |  |  |  | 	GLM_FUNC_QUALIFIER detail::tmat2x4<T> mat2x4_cast | 
			
		
	
		
			
				
					|  |  |  |  | 	( | 
			
		
	
	
		
			
				
					|  |  |  | @ -323,36 +327,33 @@ namespace detail | 
			
		
	
		
			
				
					|  |  |  |  | 	{ | 
			
		
	
		
			
				
					|  |  |  |  | 		detail::tquat<T> r = x.real / length2(x.real); | 
			
		
	
		
			
				
					|  |  |  |  | 		 | 
			
		
	
		
			
				
					|  |  |  |  |         const detail::tquat<T> rr(r.w * x.real.w, r.x * x.real.x, r.y * x.real.y, r.z * x.real.z); | 
			
		
	
		
			
				
					|  |  |  |  |         r *= detail::tdualquat<T>::value_type(2); | 
			
		
	
		
			
				
					|  |  |  |  | 		detail::tquat<T> const rr(r.w * x.real.w, r.x * x.real.x, r.y * x.real.y, r.z * x.real.z); | 
			
		
	
		
			
				
					|  |  |  |  | 		r *= T(2); | 
			
		
	
		
			
				
					|  |  |  |  | 		 | 
			
		
	
		
			
				
					|  |  |  |  |         const detail::tdualquat<T>::value_type xy = r.x*d.real.y; | 
			
		
	
		
			
				
					|  |  |  |  |         const detail::tdualquat<T>::value_type xz = r.x*d.real.z; | 
			
		
	
		
			
				
					|  |  |  |  |         const detail::tdualquat<T>::value_type yz = r.y*d.real.z; | 
			
		
	
		
			
				
					|  |  |  |  |         const detail::tdualquat<T>::value_type wx = r.w*d.real.x; | 
			
		
	
		
			
				
					|  |  |  |  |         const detail::tdualquat<T>::value_type wy = r.w*d.real.y; | 
			
		
	
		
			
				
					|  |  |  |  |         const detail::tdualquat<T>::value_type wz = r.w*d.real.z; | 
			
		
	
		
			
				
					|  |  |  |  | 		T const xy = r.x * x.real.y; | 
			
		
	
		
			
				
					|  |  |  |  | 		T const xz = r.x * x.real.z; | 
			
		
	
		
			
				
					|  |  |  |  | 		T const yz = r.y * x.real.z; | 
			
		
	
		
			
				
					|  |  |  |  | 		T const wx = r.w * x.real.x; | 
			
		
	
		
			
				
					|  |  |  |  | 		T const wy = r.w * x.real.y; | 
			
		
	
		
			
				
					|  |  |  |  | 		T const wz = r.w * x.real.z; | 
			
		
	
		
			
				
					|  |  |  |  | 		 | 
			
		
	
		
			
				
					|  |  |  |  |         const detail::tvec4<T> a(   | 
			
		
	
		
			
				
					|  |  |  |  | 		detail::tvec4<T> const a( | 
			
		
	
		
			
				
					|  |  |  |  | 			rr.w + rr.x - rr.y - rr.z, | 
			
		
	
		
			
				
					|  |  |  |  | 			xy - wz, | 
			
		
	
		
			
				
					|  |  |  |  | 			xz + wy, | 
			
		
	
		
			
				
					|  |  |  |  |                                   -(x.dual.w * r.x - x.dual.x * r.w + x.dual.y * r.z - x.dual.z * r.y)  | 
			
		
	
		
			
				
					|  |  |  |  |         ); | 
			
		
	
		
			
				
					|  |  |  |  | 			-(x.dual.w * r.x - x.dual.x * r.w + x.dual.y * r.z - x.dual.z * r.y)); | 
			
		
	
		
			
				
					|  |  |  |  | 		 | 
			
		
	
		
			
				
					|  |  |  |  |         const detail::tvec4<T> b( | 
			
		
	
		
			
				
					|  |  |  |  | 		detail::tvec4<T> const b( | 
			
		
	
		
			
				
					|  |  |  |  | 			xy + wz, | 
			
		
	
		
			
				
					|  |  |  |  | 			rr.w + rr.y - rr.x - rr.z, | 
			
		
	
		
			
				
					|  |  |  |  | 			yz - wx, | 
			
		
	
		
			
				
					|  |  |  |  |                                   -(x.dual.w * r.y - x.dual.x * r.z - x.dual.y * r.w + x.dual.z * r.x) | 
			
		
	
		
			
				
					|  |  |  |  |         ); | 
			
		
	
		
			
				
					|  |  |  |  | 			-(x.dual.w * r.y - x.dual.x * r.z - x.dual.y * r.w + x.dual.z * r.x)); | 
			
		
	
		
			
				
					|  |  |  |  | 		 | 
			
		
	
		
			
				
					|  |  |  |  |         const detail::tvec4<T> c( | 
			
		
	
		
			
				
					|  |  |  |  | 		detail::tvec4<T> const c( | 
			
		
	
		
			
				
					|  |  |  |  | 			xz - wy, | 
			
		
	
		
			
				
					|  |  |  |  | 			yz + wx, | 
			
		
	
		
			
				
					|  |  |  |  | 			rr.w + rr.z - rr.x - rr.y, | 
			
		
	
		
			
				
					|  |  |  |  |                                   -(x.dual.w * r.z + x.dual.x * r.y - x.dual.y * r.x - x.dual.z * r.w) | 
			
		
	
		
			
				
					|  |  |  |  |         ); | 
			
		
	
		
			
				
					|  |  |  |  | 			-(x.dual.w * r.z + x.dual.x * r.y - x.dual.y * r.x - x.dual.z * r.w)); | 
			
		
	
		
			
				
					|  |  |  |  | 		 | 
			
		
	
		
			
				
					|  |  |  |  | 		return detail::tmat3x4<T>(a, b, c); | 
			
		
	
		
			
				
					|  |  |  |  | 	} | 
			
		
	
	
		
			
				
					|  |  |  | @ -363,10 +364,9 @@ namespace detail | 
			
		
	
		
			
				
					|  |  |  |  | 		detail::tmat2x4<T> const & x | 
			
		
	
		
			
				
					|  |  |  |  | 	) | 
			
		
	
		
			
				
					|  |  |  |  | 	{ | 
			
		
	
		
			
				
					|  |  |  |  |         return detail::tdualquat ( | 
			
		
	
		
			
				
					|  |  |  |  | 		return detail::tdualquat<T>( | 
			
		
	
		
			
				
					|  |  |  |  | 			detail::tquat<T>( x[0].w, x[0].x, x[0].y, x[0].z ), | 
			
		
	
		
			
				
					|  |  |  |  |             detail::tquat<T> ( x[1].w, x[1].x, x[1].y, x[1].z ) | 
			
		
	
		
			
				
					|  |  |  |  |         ); | 
			
		
	
		
			
				
					|  |  |  |  | 			detail::tquat<T>( x[1].w, x[1].x, x[1].y, x[1].z )); | 
			
		
	
		
			
				
					|  |  |  |  | 	} | 
			
		
	
		
			
				
					|  |  |  |  | 
 | 
			
		
	
		
			
				
					|  |  |  |  | 	template <typename T> | 
			
		
	
	
		
			
				
					|  |  |  | @ -377,11 +377,11 @@ namespace detail | 
			
		
	
		
			
				
					|  |  |  |  | 	{ | 
			
		
	
		
			
				
					|  |  |  |  | 		detail::tquat<T> real; | 
			
		
	
		
			
				
					|  |  |  |  | 		 | 
			
		
	
		
			
				
					|  |  |  |  |         const detail::tdualquat<T>::value_type trace = x[0].x + x[1].y + x[2].z; | 
			
		
	
		
			
				
					|  |  |  |  | 		T const trace = x[0].x + x[1].y + x[2].z; | 
			
		
	
		
			
				
					|  |  |  |  | 		if(trace > detail::tdualquat<T>::value_type(0)) | 
			
		
	
		
			
				
					|  |  |  |  | 		{ | 
			
		
	
		
			
				
					|  |  |  |  |             const detail::tdualquat<T>::value_type r = sqrt(detail::tdualquat<T>::value_type(1) + trace); | 
			
		
	
		
			
				
					|  |  |  |  |             const detail::tdualquat<T>::value_type invr = detail::tdualquat<T>::value_type(0.5) / r; | 
			
		
	
		
			
				
					|  |  |  |  | 			T const r = sqrt(detail::tdualquat<T>::value_type(1) + trace); | 
			
		
	
		
			
				
					|  |  |  |  | 			T const invr = detail::tdualquat<T>::value_type(0.5) / r; | 
			
		
	
		
			
				
					|  |  |  |  | 			real.w = detail::tdualquat<T>::value_type(0.5) * r; | 
			
		
	
		
			
				
					|  |  |  |  | 			real.x = (x[2].y - x[1].z) * invr; | 
			
		
	
		
			
				
					|  |  |  |  | 			real.y = (x[0].z - x[2].x) * invr; | 
			
		
	
	
		
			
				
					|  |  |  | @ -389,8 +389,8 @@ namespace detail | 
			
		
	
		
			
				
					|  |  |  |  | 		} | 
			
		
	
		
			
				
					|  |  |  |  | 		else if(x[0].x > x[1].y && x[0].x > x[2].z) | 
			
		
	
		
			
				
					|  |  |  |  | 		{ | 
			
		
	
		
			
				
					|  |  |  |  |             const detail::tdualquat<T>::value_type r = sqrt(detail::tdualquat<T>::value_type(1) + x[0].x - x[1].y - x[2].z); | 
			
		
	
		
			
				
					|  |  |  |  |             const detail::tdualquat<T>::value_type invr = detail::tdualquat<T>::value_type(0.5) / r; | 
			
		
	
		
			
				
					|  |  |  |  | 			T const r = sqrt(detail::tdualquat<T>::value_type(1) + x[0].x - x[1].y - x[2].z); | 
			
		
	
		
			
				
					|  |  |  |  | 			T const invr = detail::tdualquat<T>::value_type(0.5) / r; | 
			
		
	
		
			
				
					|  |  |  |  | 			real.x = detail::tdualquat<T>::value_type(0.5)*r; | 
			
		
	
		
			
				
					|  |  |  |  | 			real.y = (x[1].x + x[0].y) * invr; | 
			
		
	
		
			
				
					|  |  |  |  | 			real.z = (x[0].z + x[2].x) * invr; | 
			
		
	
	
		
			
				
					|  |  |  | @ -398,28 +398,28 @@ namespace detail | 
			
		
	
		
			
				
					|  |  |  |  | 		} | 
			
		
	
		
			
				
					|  |  |  |  | 		else if(x[1].y > x[2].z) | 
			
		
	
		
			
				
					|  |  |  |  | 		{ | 
			
		
	
		
			
				
					|  |  |  |  |             const detail::tdualquat<T>::value_type r = sqrt(detail::tdualquat<T>::value_type(1) + x[1].y - x[0].x - x[2].z); | 
			
		
	
		
			
				
					|  |  |  |  |             const detail::tdualquat<T>::value_type invr = detail::tdualquat<T>::value_type(0.5) / r; | 
			
		
	
		
			
				
					|  |  |  |  |             x = (x[1].x + x[0].y) * invr; | 
			
		
	
		
			
				
					|  |  |  |  |             y = detail::tdualquat<T>::value_type(0.5) * r; | 
			
		
	
		
			
				
					|  |  |  |  |             z = (x[2].y + x[1].z) * invr; | 
			
		
	
		
			
				
					|  |  |  |  |             w = (x[0].z - x[2].x) * invr; | 
			
		
	
		
			
				
					|  |  |  |  | 			T const r = sqrt(T(1) + x[1].y - x[0].x - x[2].z); | 
			
		
	
		
			
				
					|  |  |  |  | 			T const invr = T(0.5) / r; | 
			
		
	
		
			
				
					|  |  |  |  | 			real.x = (x[1].x + x[0].y) * invr; | 
			
		
	
		
			
				
					|  |  |  |  | 			real.y = T(0.5) * r; | 
			
		
	
		
			
				
					|  |  |  |  | 			real.z = (x[2].y + x[1].z) * invr; | 
			
		
	
		
			
				
					|  |  |  |  | 			real.w = (x[0].z - x[2].x) * invr; | 
			
		
	
		
			
				
					|  |  |  |  | 		} | 
			
		
	
		
			
				
					|  |  |  |  | 		else | 
			
		
	
		
			
				
					|  |  |  |  | 		{ | 
			
		
	
		
			
				
					|  |  |  |  |             const detail::tdualquat<T>::value_type r = sqrt(detail::tdualquat<T>::value_type(1) + x[2].z - x[0].x - x[1].y); | 
			
		
	
		
			
				
					|  |  |  |  |             const detail::tdualquat<T>::value_type invr = detail::tdualquat<T>::value_type(0.5) / r; | 
			
		
	
		
			
				
					|  |  |  |  |             x = (x[0].z + x[2].x) * invr; | 
			
		
	
		
			
				
					|  |  |  |  |             y = (x[2].y + x[1].z) * invr; | 
			
		
	
		
			
				
					|  |  |  |  |             z = detail::tdualquat<T>::value_type(0.5) * r; | 
			
		
	
		
			
				
					|  |  |  |  |             w = (x[1].x - x[0].y) * invr; | 
			
		
	
		
			
				
					|  |  |  |  | 			T const r = sqrt(T(1) + x[2].z - x[0].x - x[1].y); | 
			
		
	
		
			
				
					|  |  |  |  | 			T const invr = T(0.5) / r; | 
			
		
	
		
			
				
					|  |  |  |  | 			real.x = (x[0].z + x[2].x) * invr; | 
			
		
	
		
			
				
					|  |  |  |  | 			real.y = (x[2].y + x[1].z) * invr; | 
			
		
	
		
			
				
					|  |  |  |  | 			real.z = T(0.5) * r; | 
			
		
	
		
			
				
					|  |  |  |  | 			real.w = (x[1].x - x[0].y) * invr; | 
			
		
	
		
			
				
					|  |  |  |  | 		} | 
			
		
	
		
			
				
					|  |  |  |  | 		 | 
			
		
	
		
			
				
					|  |  |  |  |         const detail::tquat<T> dual; | 
			
		
	
		
			
				
					|  |  |  |  |         dual.x =  0.5f*( x[0].w*real.w + x[1].w*real.z - x[2].w*real.y); | 
			
		
	
		
			
				
					|  |  |  |  |         dual.y =  0.5f*(-x[0].w*real.z + x[1].w*real.w + x[2].w*real.x); | 
			
		
	
		
			
				
					|  |  |  |  |         dual.z =  0.5f*( x[0].w*real.y - x[1].w*real.x + x[2].w*real.w); | 
			
		
	
		
			
				
					|  |  |  |  |         dual.w = -0.5f*( x[0].w*real.x + x[1].w*real.y + x[2].w*real.z); | 
			
		
	
		
			
				
					|  |  |  |  | 		detail::tquat<T> dual; | 
			
		
	
		
			
				
					|  |  |  |  | 		dual.x =  T(0.5) * ( x[0].w * real.w + x[1].w * real.z - x[2].w * real.y); | 
			
		
	
		
			
				
					|  |  |  |  | 		dual.y =  T(0.5) * (-x[0].w * real.z + x[1].w * real.w + x[2].w * real.x); | 
			
		
	
		
			
				
					|  |  |  |  | 		dual.z =  T(0.5) * ( x[0].w * real.y - x[1].w * real.x + x[2].w * real.w); | 
			
		
	
		
			
				
					|  |  |  |  | 		dual.w = -T(0.5) * ( x[0].w * real.x + x[1].w * real.y + x[2].w * real.z); | 
			
		
	
		
			
				
					|  |  |  |  | 		return detail::tdualquat<T>(real, dual); | 
			
		
	
		
			
				
					|  |  |  |  | 	} | 
			
		
	
		
			
				
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