/*This is an extract from the main program (lens_distortion_estimation.c), dealing with the 
* zoom normalization
*/ 

/**
* \fn void ami_lens_distortion_zoom_normalization(double **x,double **y,int Nl,
int *Np,double x0,double y0,double *a,int Na)
* \brief function to apply the zoom strategy
* \Author Luis Alvarez and Luis Gomez
* \return return void
*/
void ami_lens_distortion_zoom_normalization(
    double **x,double **y  /** ORIGINAL COLECCION OF LINES DISTRIBUTION (INPUT)*/,
    int Nl                 /** NUMBER OF LINES */,
    int *Np                /** NUMBER OF POINTS FOR EACH LINE(INPUT)*/,
    double x0,double y0    /** CENTER OF THE IMAGE (INPUT)*/,
    double *a              /** Lens Distortion Polynomial model (INPUT-OUTPUT)*/,
    int Na                 /** Degree of Polynomial model (INPUT)*/
    )
{
  int i,k,m,N=0;
  double Z,d,suma_Ad,A;

  /* WE UPDATE a BY ESTIMATING A ZOOM FACTOR Z */
   suma_Ad=0;
    for(m=0;m<Nl;m++){
      for(i=0;i<Np[m];i++){
        N++;
        d=sqrt( (x[m][i]-x0)*(x[m][i]-x0)+(y[m][i]-y0)*(y[m][i]-y0) );
        A=a[0];
        for(k=1;k<=Na;k++) A+=a[k]*pow(d,(double) k);
        suma_Ad+=A*A;
      }
    }
    Z=sqrt((double) N/suma_Ad);
    for(k=0;k<=Na;k++) a[k]*=Z;
}