double findShape(Point2f &ctr, vector<Point> contour){
unsigned int cnt = contour.size();
vector<double> dist;
double mean = 0.0;
for(unsigned int i = 0; i < cnt; i++){
double d = sqrt(sqre(contour[i].x - ctr.x)+sqre(contour[i].y - ctr.y));
dist.push_back(d);
mean += d;
}
mean = mean/cnt;
float standDev= 0.0;
for(unsigned int i = 0; i < cnt; i++){
standDev += sqre(dist[i]-mean);
}
standDev = sqrt(standDev/cnt);
return standDev;
}
double dist_square(Point &p1, Point &p2){
return (sqre(p1.x - p2.x)+sqre(p1.y -p2.y));
}
int King_model(double w0, double rmin, double dlogr, int Nmax,
double *radius, double *potential, double *mass)
/*
Purpose:
This function will compute a king model of parameter w0 from rmin
up to the tidal radius of the cluster, logarithmically stepping
by dlogr.
Arguments:
double w0 - King parameter, the higher the deeper.
double rmin - starting radius, will be radius[0],
double dlogr - log radius bin
int Nmax - Maximum number of points we want
double *radius - Malloc'd (Nmax) array
double *potential - Malloc'd (Nmax) array
double *mass - Malloc'd (Nmax) array
Returns:
nrg - actual number of data points stored in the arrays
*/
{
/* ERROR CONTROL */
double eps = 1e-6;
/* MISC VARIABLES */
double sigma2=1.0;
double den1=1.0;
int i,j,nok,nbad,nk,nr,nrg;
int nvar = 2, Nrmax = Nmax;
double h1=1e-3, hmin = 1e-8;
double r1, r2, rt, ppot, a,b;
double oldpot1, oldpot2;
double p,tote,totm,h,r0,p0,ss,d0;
double pot[2];
double *den = ALLOC(Nrmax, double);
double *dene = ALLOC(Nrmax, double);
double *denm = ALLOC(Nrmax, double);
double *dene2 = ALLOC(Nrmax, double);
double *denm2 = ALLOC(Nrmax, double);
double *der = ALLOC(Nrmax, double);
double *v2 = ALLOC(Nrmax, double);
pot[0] = w0 * sigma2;
pot[1] = 0;
r2 = rmin;
/*--------------------------------------------------------------------
Integrate outward to tidal boundary. Store potential and
density, and mass at every step.
--------------------------------------------------------------------*/
for( nr=0; nr<Nrmax; nr++ ){
r1 = r2;
r2 = pow(10, log10(r1)+dlogr);
oldpot1 = pot[0];
oldpot2 = pot[1];
odeint( pot, nvar, r1, r2, eps, h1, hmin, &nok, &nbad,
sigma2 , den1, potdir, rkqs);
//printf("nr %d pot %le %le \n", nr, pot[0], pot[1]);
if(pot[0] > 0){
/* Have not reached rt yet; store data and continue.*/
radius[nr] = r2;
potential[nr] = pot[0];
mass[nr] = -pot[1]*r2*r2;
p = pot[0]/sigma2;
den[nr] = den1 * ( exp(p) * erf(sqrt(p)) -
sqrt(4.*p/M_PI)*(1. +2.*p/3) );
}else{
if (pot[0] == 0){
break;
}
/* Have passed rt. Use bisection to find it.*/
for( i=0; i<20; i++ ){
pot[0] = oldpot1;
pot[1] = oldpot2;
rt = 0.5 * (r1+r2);
odeint( pot, nvar, r1, rt, eps, h1, hmin, &nok,
&nbad, sigma2 , den1, potdir, rkqs);
if(pot[0] > 0){
r1 = rt;
oldpot1 = pot[0];
oldpot2 = pot[1];
}else if(pot[0] < 0){
r2 = rt;
}else{
break;
}
}
radius[nr] = rt;
potential[nr] = 0;
mass[nr] = -pot[1]*r2*r2;
den[nr] = 0;
break;
}
if(den[nr] < 0) break;
}
nrg = nr;
/*-------------------------------------------------------------------
Compute total mass and energy.
--------------------------------------------------------------------*/
for( nr=0; nr<nrg; nr++ ){
dene[nr] = radius[nr]*radius[nr] * den[nr] * potential[nr];
denm[nr] = radius[nr]*radius[nr] * den[nr];
}
spline(radius, dene, nrg, 0, 2e30, dene2);
spline(radius, denm, nrg, 0, 2e30, denm2);
tote = 0;
totm = 0;
for( nr=0; nr<nrg-1; nr++ ){
h = radius[nr+1]-radius[nr];
tote = tote + 0.5*h*( dene[nr+1] + dene[nr] ) -
cub(h)/24.*( dene2[nr+1] + dene2[nr] );
totm = totm + 0.5*h*( denm[nr+1] + denm[nr] ) -
cub(h)/24.*( denm2[nr+1] + denm2[nr] );
}
totm = 4.*M_PI*totm;
tote = 2.*M_PI*tote + 0.5*totm*totm/radius[nrg-1];
tote = 0.5*tote;
r0 = 4.*tote/sqre(totm);
p0 = totm/(4.*tote);
d0 = pow(totm,5)/cub(4.*tote);
for( nr=0; nr<nrg; nr++ ){
radius[nr] = r0*radius[nr];
potential[nr] = p0*potential[nr];
mass[nr] = mass[nr]/totm;
den[nr] = d0*den[nr];
}
/*--------------------------------------------------------------------
Get the mean square velocity v2 as a function of radius.
--------------------------------------------------------------------*/
/* for( nr=0; nr<nrg; nr++ ){ */
/* nk = 2; */
/* ppot = potential[nr]; */
/* a = 0; b = sqrt(2*ppot); */
/* ss = qromo(a, b, eps, kgvfnc, midpoint, nk, ppot, sigma2); */
/* v2[nr] = ss; */
/* nk = 0; */
/* ss = qromo(a, b, eps, kgvfnc, midpoint, nk, ppot, sigma2); */
/* v2[nr] = v2[nr]/ss; */
/* } */
free(v2);
free(den); free(dene); free(denm);
free(dene2); free(denm2); free(der);
return nrg;
}