///////////////////////////////////////////////////////////////////////////////////////////////////
// OpenGL Mathematics Copyright (c) 2005 - 2013 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{

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 = pow2(s);
	typename genType::value_type s3 = 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 = pow2(s);
	typename genType::value_type s3 = 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 glm
