Quintic.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
//   and/or other materials provided with the distribution.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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#ifndef _RL_MATH_QUINTIC_H_
#define _RL_MATH_QUINTIC_H_
 
#include <cmath>
#include <limits>
 
#include "Real.h"
 
namespace rl
{
    namespace math
    {
        template< typename T >
        class Quintic
        {
        public:
            Quintic() :
                a0(),
                ae(),
                te(::std::numeric_limits<Real>::max()),
                x0(),
                xe(),
                v0(),
                ve(),
                c0(),
                c1(),
                c2(),
                c3(),
                c4(),
                c5()
            {
            }
            
            virtual ~Quintic()
            {
            }
            
            T a(const Real& t) const
            {
                return 2 * c2 + 6 * c3 * t + 12 * c4 * ::std::pow(t, 2) + 20 * c5 * ::std::pow(t, 3);
            }
            
            void interpolate()
            {
                c0 = x0;
                c1 = v0;
                c2 = a0 / 2;
                c3 = -(3 * ::std::pow(te, 2) * a0 + 12 * te * v0 - ::std::pow(te, 2) * ae + 20 * x0 + 8 * te * ve - 20 * xe) / (2 * ::std::pow(te, 3));
                c4 = (16 * te * v0 - 2 * ::std::pow(te, 2) * ae + 30 * x0 + 14 * te * ve - 30 * xe + 3 * ::std::pow(te, 2) * a0) / (2 * ::std::pow(te, 4));
                c5 = -(12 * x0 + 6 * te * v0 + 6 * te * ve - 12 * xe + ::std::pow(te, 2) * a0 - ::std::pow(te, 2) * ae) / (2 * ::std::pow(te, 5));
            }
            
            T j(const Real& t) const
            {
                return 6 * c3 + 24 * c4 * t + 60 * c5 * ::std::pow(t, 2);
            }
            
            T v(const Real& t) const
            {
                return c1 + 2 * c2 * t + 3 * c3 * ::std::pow(t, 2) + 4 * c4 * ::std::pow(t, 3) + 5 * c5 * ::std::pow(t, 4);
            }
            
            T x(const Real& t) const
            {
                return c0 + c1 * t + c2 * ::std::pow(t, 2) + c3 * ::std::pow(t, 3) + c4 * ::std::pow(t, 4) + c5 * ::std::pow(t, 5);
            }
            
            T a0;
            
            T ae;
            
            Real te;
            
            T x0;
            
            T xe;
            
            T v0;
            
            T ve;
            
        protected:
            
        private:
            T c0;
            
            T c1;
            
            T c2;
            
            T c3;
            
            T c4;
            
            T c5;
        };
    }
}
 
#endif // _RL_MATH_QUINTIC_H_