/*
Copyright (c) 2006, Michael Kazhdan and Matthew Bolitho
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. 

Neither the name of the Johns Hopkins University nor the names of its contributors
may be used to endorse or promote products derived from this software without specific
prior written permission. 

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 OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
TO, PROCUREMENT OF SUBSTITUTE  GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR
BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH
DAMAGE.
*/

#ifndef P_POLYNOMIAL_INCLUDED
#define P_POLYNOMIAL_INCLUDED
#include <vector>
#include "Polynomial.h"

template<int Degree>
class StartingPolynomial{
public:
	Polynomial<Degree> p;
	double start;

	template<int Degree2>
	StartingPolynomial<Degree+Degree2>  operator * (const StartingPolynomial<Degree2>& p) const;
	StartingPolynomial scale(const double& s) const;
	StartingPolynomial shift(const double& t) const;
	int operator < (const StartingPolynomial& sp) const;
	static int Compare(const void* v1,const void* v2);
};

template<int Degree>
class PPolynomial{
public:
	size_t polyCount;
	StartingPolynomial<Degree>* polys;

	PPolynomial(void);
	PPolynomial(const PPolynomial<Degree>& p);
	~PPolynomial(void);

	PPolynomial& operator = (const PPolynomial& p);

	int size(void) const;

	void set(const size_t& size);
	// Note: this method will sort the elements in sps
	void set(StartingPolynomial<Degree>* sps,const int& count);
	void reset(const size_t& newSize);


	double operator()(const double& t) const;
	double integral(const double& tMin,const double& tMax) const;
	double Integral(void) const;

	template<int Degree2>
	PPolynomial<Degree>& operator = (const PPolynomial<Degree2>& p);

	PPolynomial  operator + (const PPolynomial& p) const;
	PPolynomial  operator - (const PPolynomial& p) const;

	template<int Degree2>
	PPolynomial<Degree+Degree2> operator * (const Polynomial<Degree2>& p) const;

	template<int Degree2>
	PPolynomial<Degree+Degree2> operator * (const PPolynomial<Degree2>& p) const;


	PPolynomial& operator += (const double& s);
	PPolynomial& operator -= (const double& s);
	PPolynomial& operator *= (const double& s);
	PPolynomial& operator /= (const double& s);
	PPolynomial  operator +  (const double& s) const;
	PPolynomial  operator -  (const double& s) const;
	PPolynomial  operator *  (const double& s) const;
	PPolynomial  operator /  (const double& s) const;

	PPolynomial& addScaled(const PPolynomial& poly,const double& scale);

	PPolynomial scale(const double& s) const;
	PPolynomial shift(const double& t) const;

	PPolynomial<Degree-1> derivative(void) const;
	PPolynomial<Degree+1> integral(void) const;

	void getSolutions(const double& c,std::vector<double>& roots,const double& EPS,const double& min=-DBL_MAX,const double& max=DBL_MAX) const;

	void printnl(void) const;

	PPolynomial<Degree+1> MovingAverage(const double& radius);

	static PPolynomial ConstantFunction(const double& width=0.5);
	static PPolynomial GaussianApproximation(const double& width=0.5);
	void write(FILE* fp,const int& samples,const double& min,const double& max) const;
};
#include "PPolynomial.inl"
#endif // P_POLYNOMIAL_INCLUDED
