///////////////////////////////////////////////////////////////////////////////////
/// 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 gtx_rotate_vector
/// @file glm/gtx/rotate_vector.inl
/// @date 2006-11-02 / 2011-06-07
/// @author Christophe Riccio
///////////////////////////////////////////////////////////////////////////////////

namespace glm
{
	template <typename T, precision P>
	GLM_FUNC_QUALIFIER tvec3<T, P> slerp
	(
		tvec3<T, P> const & x,
		tvec3<T, P> const & y,
		T const & a
	)
	{
		// get cosine of angle between vectors (-1 -> 1)
		T CosAlpha = dot(x, y);
		// get angle (0 -> pi)
		T Alpha = acos(CosAlpha);
		// get sine of angle between vectors (0 -> 1)
		T SinAlpha = sin(Alpha);
		// this breaks down when SinAlpha = 0, i.e. Alpha = 0 or pi
		T t1 = sin((static_cast<T>(1) - a) * Alpha) / SinAlpha;
		T t2 = sin(a * Alpha) / SinAlpha;

		// interpolate src vectors
		return x * t1 + y * t2;
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER tvec2<T, P> rotate
	(
		tvec2<T, P> const & v,
		T const & angle
	)
	{
		tvec2<T, P> Result;
		T const Cos(cos(angle));
		T const Sin(sin(angle));

		Result.x = v.x * Cos - v.y * Sin;
		Result.y = v.x * Sin + v.y * Cos;
		return Result;
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER tvec3<T, P> rotate
	(
		tvec3<T, P> const & v,
		T const & angle,
		tvec3<T, P> const & normal
	)
	{
		return tmat3x3<T, P>(glm::rotate(angle, normal)) * v;
	}
	/*
	template <typename T, precision P>
	GLM_FUNC_QUALIFIER tvec3<T, P> rotateGTX(
		const tvec3<T, P>& x,
		T angle,
		const tvec3<T, P>& normal)
	{
		const T Cos = cos(radians(angle));
		const T Sin = sin(radians(angle));
		return x * Cos + ((x * normal) * (T(1) - Cos)) * normal + cross(x, normal) * Sin;
	}
	*/
	template <typename T, precision P>
	GLM_FUNC_QUALIFIER tvec4<T, P> rotate
	(
		tvec4<T, P> const & v,
		T const & angle,
		tvec3<T, P> const & normal
	)
	{
		return rotate(angle, normal) * v;
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER tvec3<T, P> rotateX
	(
		tvec3<T, P> const & v,
		T const & angle
	)
	{
		tvec3<T, P> Result(v);
		T const Cos(cos(angle));
		T const Sin(sin(angle));

		Result.y = v.y * Cos - v.z * Sin;
		Result.z = v.y * Sin + v.z * Cos;
		return Result;
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER tvec3<T, P> rotateY
	(
		tvec3<T, P> const & v,
		T const & angle
	)
	{
		tvec3<T, P> Result = v;
		T const Cos(cos(angle));
		T const Sin(sin(angle));

		Result.x =  v.x * Cos + v.z * Sin;
		Result.z = -v.x * Sin + v.z * Cos;
		return Result;
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER tvec3<T, P> rotateZ
	(
		tvec3<T, P> const & v,
		T const & angle
	)
	{
		tvec3<T, P> Result = v;
		T const Cos(cos(angle));
		T const Sin(sin(angle));

		Result.x = v.x * Cos - v.y * Sin;
		Result.y = v.x * Sin + v.y * Cos;
		return Result;
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER tvec4<T, P> rotateX
	(
		tvec4<T, P> const & v,
		T const & angle
	)
	{
		tvec4<T, P> Result = v;
		T const Cos(cos(angle));
		T const Sin(sin(angle));

		Result.y = v.y * Cos - v.z * Sin;
		Result.z = v.y * Sin + v.z * Cos;
		return Result;
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER tvec4<T, P> rotateY
	(
		tvec4<T, P> const & v,
		T const & angle
	)
	{
		tvec4<T, P> Result = v;
		T const Cos(cos(angle));
		T const Sin(sin(angle));

		Result.x =  v.x * Cos + v.z * Sin;
		Result.z = -v.x * Sin + v.z * Cos;
		return Result;
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER tvec4<T, P> rotateZ
	(
		tvec4<T, P> const & v,
		T const & angle
	)
	{
		tvec4<T, P> Result = v;
		T const Cos(cos(angle));
		T const Sin(sin(angle));

		Result.x = v.x * Cos - v.y * Sin;
		Result.y = v.x * Sin + v.y * Cos;
		return Result;
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER tmat4x4<T, P> orientation
	(
		tvec3<T, P> const & Normal,
		tvec3<T, P> const & Up
	)
	{
		if(all(equal(Normal, Up)))
			return tmat4x4<T, P>(T(1));

		tvec3<T, P> RotationAxis = cross(Up, Normal);
		T Angle = acos(dot(Normal, Up));

		return rotate(Angle, RotationAxis);
	}
}//namespace glm