#include <cmath>
#include <ifmwindow>
using namespace std;

const int resol = 400;
IfmWindow win(2*resol+20, 2*resol+20);

inline int rounded(double d) { return (int)floor(d + .5); }

bool drawCircle(double A, double B, double C, double D)
{
       // Convert to inversive coords 
    double a = (-2*A + B + C)    * sqrt(3.)/6.;
    double b = (-B + C) / 2.;
    double c = -D;
    double d = (A + B + C + 3*D) * sqrt(3.)/6.;

       // Convert to Cartesian coords 
    double r = 1./(d-c);  if (r < 1./resol) return false;
    double x = a*r;       
    double y = b*r;       

    win << FilledCircle(rounded(resol * (1+x)) + 10,
                        rounded(resol * (1+y)) + 10, 
			rounded(resol * r    ) +  1);
    return true;
}

void generate(int i, double A, double B, double C, double D)     
{
    switch(i) {
        case 0:  A =  -A + 2*B + 2*C + 2*D;  break;
        case 1:  B = 2*A    -B + 2*C + 2*D;  break;
        case 2:  C = 2*A + 2*B    -C + 2*D;  break;
        case 3:  D = 2*A + 2*B + 2*C    -D;  break;
    }

    if (drawCircle(A, B, C, D)) {
        for (int j = 0; j < 4; j++) if (j != i) generate(j, A, B, C, D);
    }
}

int main()
{
    win << red;
    drawCircle(  -1,  1,  1,  1);
    generate(0,  -1,  1,  1,  1);

    win << green;
    drawCircle(   1, -1,  1,  1);
    generate(1,   1, -1,  1,  1);

    win << blue;
    drawCircle(   1,  1, -1,  1);
    generate(2,   1,  1, -1,  1);

    win << yellow;
    generate(3,   1,  1,  1, -1);

    win.flush().wait_for_mouse_click();
    return 0;
}