///////////////////////////////////////////////////////////////////////////////////////////////////
// OpenGL Mathematics Copyright (c) 2005 - 2011 G-Truc Creation (www.g-truc.net)
///////////////////////////////////////////////////////////////////////////////////////////////////
// Created : 2007-01-25
// Updated : 2009-02-19
// Licence : This source is under MIT License
// File    : glm/gtx/spline.inl
///////////////////////////////////////////////////////////////////////////////////////////////////

namespace glm{
namespace gtx{
namespace spline
{
	template <typename genType>
	GLM_FUNC_QUALIFIER genType catmullRom
	(
		genType const & v1, 
		genType const & v2, 
		genType const & v3, 
		genType const & v4, 
		typename genType::value_type const & s
	)
	{
		typename genType::value_type s1 = s;
		typename genType::value_type s2 = optimum_pow::pow2(s);
		typename genType::value_type s3 = optimum_pow::pow3(s);

		typename genType::value_type f1 = -s3 + typename genType::value_type(2) * s2 - s;
		typename genType::value_type f2 = typename genType::value_type(3) * s3 - typename genType::value_type(5) * s2 + typename genType::value_type(2);
		typename genType::value_type f3 = typename genType::value_type(-3) * s3 + typename genType::value_type(4) * s2 + s;
		typename genType::value_type f4 = s3 - s2;

		return (f1 * v1 + f2 * v2 + f3 * v3 + f4 * v4) / typename genType::value_type(2);

	}

	template <typename genType>
	GLM_FUNC_QUALIFIER genType hermite
	(
		genType const & v1, 
		genType const & t1, 
		genType const & v2, 
		genType const & t2, 
		typename genType::value_type const & s
	)
	{
		typename genType::value_type s1 = s;
		typename genType::value_type s2 = optimum_pow::pow2(s);
		typename genType::value_type s3 = optimum_pow::pow3(s);

		typename genType::value_type f1 = typename genType::value_type(2) * s3 - typename genType::value_type(3) * s2 + typename genType::value_type(1);
		typename genType::value_type f2 = typename genType::value_type(-2) * s3 + typename genType::value_type(3) * s2;
		typename genType::value_type f3 = s3 - typename genType::value_type(2) * s2 + s;
		typename genType::value_type f4 = s3 - s2;

		return f1 * v1 + f2 * v2 + f3 * t1 + f4 * t2;
	}

	template <typename genType>
	GLM_FUNC_QUALIFIER genType cubic
	(
		genType const & v1, 
		genType const & v2, 
		genType const & v3, 
		genType const & v4, 
		typename genType::value_type const & s
	)
	{
		return ((v1 * s + v2) * s + v3) * s + v4;
	}

}//namespace spline
}//namespace gtx
}//namespace glm