Cubic.h

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//
// Copyright (c) 2009, Markus Rickert
// All rights reserved.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are met:
//
// * Redistributions of source code must retain the above copyright notice,
//   this list of conditions and the following disclaimer.
// * Redistributions in binary form must reproduce the above copyright notice,
//   this list of conditions and the following disclaimer in the documentation
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#ifndef _RL_MATH_CUBIC_H_
#define _RL_MATH_CUBIC_H_
 
#include <cmath>
#include <limits>
 
#include "Real.h"
 
namespace rl
{
    namespace math
    {
        template< typename T >
        class Cubic
        {
        public:
            Cubic() :
                te(::std::numeric_limits<Real>::max()),
                x0(),
                xe(),
                v0(),
                ve(),
                c0(),
                c1(),
                c2(),
                c3()
            {
            }
            
            virtual ~Cubic()
            {
            }
            
            T a(const Real& t) const
            {
                return 2 * c2 + 6 * c3 * t;
            }
            
            void interpolate()
            {
                c0 = x0;
                c1 = v0;
                c2 = -(2 * te * v0 + 3 * x0 - 3 * xe + te * ve) / ::std::pow(te, 2);
                c3 = (2 * x0 + te * v0 - 2 * xe + te * ve) / ::std::pow(te, 3);
            }
            
            T v(const Real& t) const
            {
                return c1 + 2 * c2 * t + 3 * c3 * ::std::pow(t, 2);
            }
            
            T x(const Real& t) const
            {
                return c0 + c1 * t + c2 * ::std::pow(t, 2) + c3 * ::std::pow(t, 3);
            }
            
            Real te;
            
            T x0;
            
            T xe;
            
            T v0;
            
            T ve;
            
        protected:
            
        private:
            T c0;
            
            T c1;
            
            T c2;
            
            T c3;
        };
    }
}
 
#endif // _RL_MATH_CUBIC_H_