#include <iostream>
#include <fstream>
#include <cmath>
#include <vector>

using namespace std;

vector < vector <double> > bezm(25, vector <double> (25));

void paragon(int n, int i, int &k)
{
	int ks = max(i,n-i)+1;
	int kp = min(i,n-i);
	k=1;
	for(int iii=ks;iii<=n;iii++)
		k = k*iii;
	for(int iii=1;iii<=kp;iii++)
		k = k/iii;
}

void inibezier(int nco)
{
	int kres1,kres2,kres3;
	for(int mi=0;mi<nco;mi++)
	{
		double b=0.e0;
		double c=0.e0;
		for(int i=0;i<nco;i++)
		{
			paragon(nco-1,i,kres1);
			paragon(i,mi,kres2);
			kres3=pow(-1,(i-mi));
			double coeffi = double(kres1*kres2*kres3);
			if(mi>i)	coeffi=0.e0;
			bezm[mi][i]=coeffi;
		}
	}

}

void usebezier( vector <double> xco, vector <double> yco, int nco,
		vector <double> &x  , vector <double> &y  , int ideg)
{
	double aa1 = 0.5e0;
	double  dd = 0.1e0;
	for(int k=0;k<=ideg+1;k++)
		y[k] = double(k-1)/double(ideg);
	
	for(int kpoi=0;kpoi<=ideg+1;kpoi++)
	{
		int kpoi1=kpoi;//+1;
		double tlocal = y[kpoi1];
		x[kpoi1]=0.e0;
		y[kpoi1]=0.e0;
		for(int mi=0;mi<nco;mi++)
		{
			double b=0.e0;	
			for(int i=0;i<nco;i++)
				b = b + bezm[mi][i]*pow(tlocal,i);
			x[kpoi1] += b*xco[mi];
			y[kpoi1] += b*yco[mi];
		}
		
	}
}

int main(int argc, char** argv)
{
	string line;
	vector <double> val(1000,0);
	vector <double>   x(1000,0);
	vector <double>   y(1000,0);
	vector <double>  xb(  25,0);
	vector <double>  yb(  25,0);
	
	ifstream in("bezier.dat");
	int nb=0;
	for(int i=0;i<26;i++)
	{
		in>>xb[i]>>yb[i];
		getline(in,line);
		if(in.eof())
		{
			nb = i;
			break;
		}
	}
	in.close();
	
	inibezier(nb);
	
	int ideg;
	cout<<"Type the number of points along the final curve"<<endl;
	cin>>ideg;
	
	usebezier(xb,yb,nb,x,y,ideg-1);
	
	ofstream out("curve");
	for(int i=1;i<ideg+1;i++)
		out<<"\t"<<x[i]<<"\t"<<y[i]<<endl;
	out.close();
}