rootHEADmaster

1 files changed, 784 insertions, 0 deletions

diff --git a/3rdparty/include/glm/gtc/quaternion.inl b/3rdparty/include/glm/gtc/quaternion.inl
new file mode 100644
index 0000000..33ca82c
--- /dev/null
+++ b/3rdparty/include/glm/gtc/quaternion.inl
@@ -0,0 +1,784 @@
+///////////////////////////////////////////////////////////////////////////////////
+/// 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 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>
+	struct compute_dot<tquat, T, P>
+	{
+		static GLM_FUNC_QUALIFIER 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);
+		}
+	};
+}//namespace detail
+
+	//////////////////////////////////////
+	// Component accesses
+
+#	ifdef GLM_FORCE_SIZE_FUNC
+		template <typename T, precision P>
+		GLM_FUNC_QUALIFIER GLM_CONSTEXPR typename tquat<T, P>::size_type tquat<T, P>::size() const
+		{
+			return 4;
+		}
+
+		template <typename T, precision P>
+		GLM_FUNC_QUALIFIER T & tquat<T, P>::operator[](typename tquat<T, P>::size_type i)
+		{
+			assert(i >= 0 && static_cast<detail::component_count_t>(i) < detail::component_count(*this));
+			return (&x)[i];
+		}
+
+		template <typename T, precision P>
+		GLM_FUNC_QUALIFIER T const & tquat<T, P>::operator[](typename tquat<T, P>::size_type i) const
+		{
+			assert(i >= 0 && static_cast<detail::component_count_t>(i) < detail::component_count(*this));
+			return (&x)[i];
+		}
+#	else
+		template <typename T, precision P>
+		GLM_FUNC_QUALIFIER GLM_CONSTEXPR typename tquat<T, P>::length_type tquat<T, P>::length() const
+		{
+			return 4;
+		}
+
+		template <typename T, precision P>
+		GLM_FUNC_QUALIFIER T & tquat<T, P>::operator[](typename tquat<T, P>::length_type i)
+		{
+			assert(i >= 0 && static_cast<detail::component_count_t>(i) < detail::component_count(*this));
+			return (&x)[i];
+		}
+
+		template <typename T, precision P>
+		GLM_FUNC_QUALIFIER T const & tquat<T, P>::operator[](typename tquat<T, P>::length_type i) const
+		{
+			assert(i >= 0 && static_cast<detail::component_count_t>(i) < detail::component_count(*this));
+			return (&x)[i];
+		}
+#	endif//GLM_FORCE_SIZE_FUNC
+
+	//////////////////////////////////////
+	// Implicit basic constructors
+
+	template <typename T, precision P>
+	GLM_FUNC_QUALIFIER tquat<T, P>::tquat()
+#		ifndef GLM_FORCE_NO_CTOR_INIT
+			: x(0), y(0), z(0), w(1)
+#		endif
+	{}
+
+	template <typename T, precision P>
+	GLM_FUNC_QUALIFIER tquat<T, P>::tquat(tquat<T, P> const & q)
+		: x(q.x), y(q.y), z(q.z), w(q.w)
+	{}
+
+	template <typename T, precision P>
+	template <precision Q>
+	GLM_FUNC_QUALIFIER tquat<T, P>::tquat(tquat<T, Q> const & q)
+		: x(q.x), y(q.y), z(q.z), w(q.w)
+	{}
+
+	//////////////////////////////////////
+	// Explicit basic constructors
+
+	template <typename T, precision P>
+	GLM_FUNC_QUALIFIER tquat<T, P>::tquat(ctor)
+	{}
+
+	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)
+	{}
+
+	//////////////////////////////////////////////////////////////
+	// Conversions
+
+	template <typename T, precision P>
+	template <typename U, precision Q>
+	GLM_FUNC_QUALIFIER tquat<T, P>::tquat(tquat<U, Q> 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
+	//)
+	//{
+	//	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(tvec3<T, P> const & u, tvec3<T, P> const & v)
+	{
+		tvec3<T, P> const LocalW(cross(u, v));
+		T Dot = detail::compute_dot<tvec3, T, P>::call(u, v);
+		tquat<T, P> q(T(1) + Dot, LocalW.x, LocalW.y, LocalW.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);
+	}
+
+#	if GLM_HAS_EXPLICIT_CONVERSION_OPERATORS
+	template <typename T, precision P>
+	GLM_FUNC_QUALIFIER tquat<T, P>::operator tmat3x3<T, P>()
+	{
+		return mat3_cast(*this);
+	}
+	
+	template <typename T, precision P>	
+	GLM_FUNC_QUALIFIER tquat<T, P>::operator tmat4x4<T, P>()
+	{
+		return mat4_cast(*this);
+	}
+#	endif//GLM_HAS_EXPLICIT_CONVERSION_OPERATORS
+
+	template <typename T, precision P>
+	GLM_FUNC_QUALIFIER tquat<T, P> conjugate(tquat<T, P> const & q)
+	{
+		return tquat<T, P>(q.w, -q.x, -q.y, -q.z);
+	}
+
+	template <typename T, precision P>
+	GLM_FUNC_QUALIFIER tquat<T, P> inverse(tquat<T, P> const & q)
+	{
+		return conjugate(q) / dot(q, q);
+	}
+
+	//////////////////////////////////////////////////////////////
+	// 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>
+	template <typename U>
+	GLM_FUNC_QUALIFIER tquat<T, P> & tquat<T, P>::operator=(tquat<U, P> 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, precision P>
+	template <typename U>
+	GLM_FUNC_QUALIFIER tquat<T, P> & tquat<T, P>::operator+=(tquat<U, P> 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, precision P>
+	template <typename U>
+	GLM_FUNC_QUALIFIER tquat<T, P> & tquat<T, P>::operator*=(tquat<U, P> const & r)
+	{
+		tquat<T, P> const p(*this);
+		tquat<T, P> 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, precision P>
+	template <typename U>
+	GLM_FUNC_QUALIFIER tquat<T, P> & tquat<T, P>::operator*=(U s)
+	{
+		this->w *= static_cast<U>(s);
+		this->x *= static_cast<U>(s);
+		this->y *= static_cast<U>(s);
+		this->z *= static_cast<U>(s);
+		return *this;
+	}
+
+	template <typename T, precision P>
+	template <typename U>
+	GLM_FUNC_QUALIFIER tquat<T, P> & tquat<T, P>::operator/=(U s)
+	{
+		this->w /= static_cast<U>(s);
+		this->x /= static_cast<U>(s);
+		this->y /= static_cast<U>(s);
+		this->z /= static_cast<U>(s);
+		return *this;
+	}
+
+	//////////////////////////////////////////////////////////////
+	// tquat<T, P> external operators
+
+	template <typename T, precision P>
+	GLM_FUNC_QUALIFIER tquat<T, P> operator-(tquat<T, P> const & q)
+	{
+		return tquat<T, P>(-q.w, -q.x, -q.y, -q.z);
+	}
+
+	template <typename T, precision P>
+	GLM_FUNC_QUALIFIER tquat<T, P> operator+(tquat<T, P> const & q,	tquat<T, P> const & p)
+	{
+		return tquat<T, P>(q) += p;
+	}
+
+	template <typename T, precision P>
+	GLM_FUNC_QUALIFIER tquat<T, P> operator*(tquat<T, P> const & q,	tquat<T, P> const & p)
+	{
+		return tquat<T, P>(q) *= p;
+	}
+
+	// Transformation
+	template <typename T, precision P>
+	GLM_FUNC_QUALIFIER tvec3<T, P> operator*(tquat<T, P> const & q,	tvec3<T, P> const & v)
+	{
+		tvec3<T, P> const QuatVector(q.x, q.y, q.z);
+		tvec3<T, P> const uv(glm::cross(QuatVector, v));
+		tvec3<T, P> const uuv(glm::cross(QuatVector, uv));
+
+		return v + ((uv * q.w) + uuv) * static_cast<T>(2);
+	}
+
+	template <typename T, precision P>
+	GLM_FUNC_QUALIFIER tvec3<T, P> operator*(tvec3<T, P> const & v, tquat<T, P> const & q)
+	{
+		return glm::inverse(q) * v;
+	}
+
+	template <typename T, precision P>
+	GLM_FUNC_QUALIFIER tvec4<T, P> operator*(tquat<T, P> const & q,	tvec4<T, P> const & v)
+	{
+		return tvec4<T, P>(q * tvec3<T, P>(v), v.w);
+	}
+
+	template <typename T, precision P>
+	GLM_FUNC_QUALIFIER tvec4<T, P> operator*(tvec4<T, P> const & v, tquat<T, P> const & q)
+	{
+		return glm::inverse(q) * v;
+	}
+
+	template <typename T, precision P>
+	GLM_FUNC_QUALIFIER tquat<T, P> operator*(tquat<T, P> const & q, T const & s)
+	{
+		return tquat<T, P>(
+			q.w * s, q.x * s, q.y * s, q.z * s);
+	}
+
+	template <typename T, precision P>
+	GLM_FUNC_QUALIFIER tquat<T, P> operator*(T const & s, tquat<T, P> const & q)
+	{
+		return q * s;
+	}
+
+	template <typename T, precision P>
+	GLM_FUNC_QUALIFIER tquat<T, P> operator/(tquat<T, P> const & q, T const & s)
+	{
+		return 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==(tquat<T, P> const & q1, 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!=(tquat<T, P> const & q1, 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 T length(tquat<T, P> const & q)
+	{
+		return glm::sqrt(dot(q, q));
+	}
+
+	template <typename T, precision P>
+	GLM_FUNC_QUALIFIER tquat<T, P> normalize(tquat<T, P> const & q)
+	{
+		T len = length(q);
+		if(len <= T(0)) // Problem
+			return tquat<T, P>(1, 0, 0, 0);
+		T oneOverLen = T(1) / len;
+		return tquat<T, P>(q.w * oneOverLen, q.x * oneOverLen, q.y * oneOverLen, q.z * oneOverLen);
+	}
+
+	template <typename T, precision P>
+	GLM_FUNC_QUALIFIER tquat<T, P> cross(tquat<T, P> const & q1, tquat<T, P> const & q2)
+	{
+		return 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 tquat<T, P> mix(tquat<T, P> const & x, 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);
+		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 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> mix2
+	(
+		tquat<T, P> const & x, 
+		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 tquat<T, P> mix(tquat<T, P> const & x, tquat<T, P> 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, 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 tquat<T, P> lerp(tquat<T, P> const & x, tquat<T, P> 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, precision P>
+	GLM_FUNC_QUALIFIER tquat<T, P> slerp(tquat<T, P> const & x,	tquat<T, P> const & y, T a)
+	{
+		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 tquat<T, P>(
+				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, precision P>
+	GLM_FUNC_QUALIFIER tquat<T, P> rotate(tquat<T, P> const & q, T const & angle, tvec3<T, P> const & v)
+	{
+		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;
+		}
+
+		T const AngleRad(angle);
+		T const Sin = sin(AngleRad * T(0.5));
+
+		return q * tquat<T, P>(cos(AngleRad * T(0.5)), Tmp.x * Sin, Tmp.y * Sin, Tmp.z * Sin);
+		//return gtc::quaternion::cross(q, 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 tvec3<T, P> eulerAngles(tquat<T, P> const & x)
+	{
+		return tvec3<T, P>(pitch(x), yaw(x), roll(x));
+	}
+
+	template <typename T, precision P>
+	GLM_FUNC_QUALIFIER T roll(tquat<T, P> const & q)
+	{
+		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));
+	}
+
+	template <typename T, precision P>
+	GLM_FUNC_QUALIFIER T pitch(tquat<T, P> 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));
+	}
+
+	template <typename T, precision P>
+	GLM_FUNC_QUALIFIER T yaw(tquat<T, P> const & q)
+	{
+		return asin(T(-2) * (q.x * q.z - q.w * q.y));
+	}
+
+	template <typename T, precision P>
+	GLM_FUNC_QUALIFIER tmat3x3<T, P> mat3_cast(tquat<T, P> const & q)
+	{
+		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 tmat4x4<T, P> mat4_cast(tquat<T, P> const & q)
+	{
+		return tmat4x4<T, P>(mat3_cast(q));
+	}
+
+	template <typename T, precision P>
+	GLM_FUNC_QUALIFIER tquat<T, P> quat_cast(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;
+
+		tquat<T, P> Result(uninitialize);
+		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 tquat<T, P> quat_cast(tmat4x4<T, P> const & m4)
+	{
+		return quat_cast(tmat3x3<T, P>(m4));
+	}
+
+	template <typename T, precision P>
+	GLM_FUNC_QUALIFIER T angle(tquat<T, P> const & x)
+	{
+		return acos(x.w) * T(2);
+	}
+
+	template <typename T, precision P>
+	GLM_FUNC_QUALIFIER tvec3<T, P> axis(tquat<T, P> const & x)
+	{
+		T tmp1 = static_cast<T>(1) - x.w * x.w;
+		if(tmp1 <= static_cast<T>(0))
+			return tvec3<T, P>(0, 0, 1);
+		T tmp2 = static_cast<T>(1) / sqrt(tmp1);
+		return tvec3<T, P>(x.x * tmp2, x.y * tmp2, x.z * tmp2);
+	}
+
+	template <typename T, precision P>
+	GLM_FUNC_QUALIFIER tquat<T, P> angleAxis(T const & angle, tvec3<T, P> const & v)
+	{
+		tquat<T, P> Result(uninitialize);
+
+		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, precision P>
+	GLM_FUNC_QUALIFIER tvec4<bool, P> lessThan(tquat<T, P> const & x, tquat<T, P> const & y)
+	{
+		tvec4<bool, P> Result(uninitialize);
+		for(detail::component_count_t i = 0; i < detail::component_count(x); ++i)
+			Result[i] = x[i] < y[i];
+		return Result;
+	}
+
+	template <typename T, precision P>
+	GLM_FUNC_QUALIFIER tvec4<bool, P> lessThanEqual(tquat<T, P> const & x, tquat<T, P> const & y)
+	{
+		tvec4<bool, P> Result(uninitialize);
+		for(detail::component_count_t i = 0; i < detail::component_count(x); ++i)
+			Result[i] = x[i] <= y[i];
+		return Result;
+	}
+
+	template <typename T, precision P>
+	GLM_FUNC_QUALIFIER tvec4<bool, P> greaterThan(tquat<T, P> const & x, tquat<T, P> const & y)
+	{
+		tvec4<bool, P> Result(uninitialize);
+		for(detail::component_count_t i = 0; i < detail::component_count(x); ++i)
+			Result[i] = x[i] > y[i];
+		return Result;
+	}
+
+	template <typename T, precision P>
+	GLM_FUNC_QUALIFIER tvec4<bool, P> greaterThanEqual(tquat<T, P> const & x, tquat<T, P> const & y)
+	{
+		tvec4<bool, P> Result(uninitialize);
+		for(detail::component_count_t i = 0; i < detail::component_count(x); ++i)
+			Result[i] = x[i] >= y[i];
+		return Result;
+	}
+
+	template <typename T, precision P>
+	GLM_FUNC_QUALIFIER tvec4<bool, P> equal(tquat<T, P> const & x, tquat<T, P> const & y)
+	{
+		tvec4<bool, P> Result(uninitialize);
+		for(detail::component_count_t i = 0; i < detail::component_count(x); ++i)
+			Result[i] = x[i] == y[i];
+		return Result;
+	}
+
+	template <typename T, precision P>
+	GLM_FUNC_QUALIFIER tvec4<bool, P> notEqual(tquat<T, P> const & x, tquat<T, P> const & y)
+	{
+		tvec4<bool, P> Result(uninitialize);
+		for(detail::component_count_t i = 0; i < detail::component_count(x); ++i)
+			Result[i] = x[i] != y[i];
+		return Result;
+	}
+}//namespace glm