Merge pull request #3 from saurabhb17/master

secondary files

1 files changed, 792 insertions, 0 deletions

diff --git a/include/gal/opengl/glm/gtc/quaternion.inl b/include/gal/opengl/glm/gtc/quaternion.inl
new file mode 100644
index 0000000..8b83865
--- /dev/null
+++ b/include/gal/opengl/glm/gtc/quaternion.inl
@@ -0,0 +1,792 @@
+///////////////////////////////////////////////////////////////////////////////////
+/// 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