quintic_spline.h

/**
* \file cubic_spline.h
* \brief Definition of a cubic spline.
* \author Steve T.
* \version 0.1
* \date 06/17/2013
*
* This file contains definitions for the CubicFunction struct.
* It allows the creation and evaluation of natural
* smooth cubic splines of arbitrary dimension
*/


#ifndef _STRUCT_QUINTIC_SPLINE
#define _STRUCT_QUINTIC_SPLINE

#include "MathDefs.h"

#include "polynom.h"

#include <stdexcept>

namespace spline
{
/// \brief Creates coefficient vector of a quintic spline defined on the interval
/// [tBegin, tEnd]. It follows the equation
/// x(t) = a + b(t - t_min_) + c(t - t_min_)^2 + d(t - t_min_)^3 + e(t - t_min_)^4  + f(t - t_min_)^5
///
template<typename Point, typename T_Point>
T_Point make_quintic_vector(Point const& a, Point const& b, Point const& c,
                   Point const &d, Point const& e, Point const& f)
{
    T_Point res;
    res.push_back(a);res.push_back(b);res.push_back(c);
    res.push_back(d);res.push_back(e);res.push_back(f);
    return res;
}

template<typename Time, typename Numeric, std::size_t Dim, bool Safe, typename Point, typename T_Point>
polynom<Time,Numeric,Dim,Safe,Point,T_Point> create_quintic(Point const& a, Point const& b, Point const& c, Point const &d, Point const &e, Point const &f,
               const Time min, const Time max)
{
    T_Point coeffs = make_quintic_vector<Point, T_Point>(a,b,c,d,e,f);
    return polynom<Time,Numeric,Dim,Safe,Point,T_Point>(coeffs.begin(),coeffs.end(), min, max);
}
}
#endif //_STRUCT_QUINTIC_SPLINE