// elltst.cpp -- incremental scan conversion of tilted ellipse
// (C) 2002, C. Bond. All rights reserved.
//
#include <iostream.h>
#include <math.h>

//
//  scan conversion of X-Y plot of tilted ellipse.
//
//  The parametric equations are:
//
//      x = a cos(theta)cos(phi) - b sin(theta)sin(phi)
//      y = a cos(theta)sin(phi) + b sin(theta)cos(phi)
//
//  where 'theta' is the parameter, 0 < theta < 2pi, 'phi' is the
//  tilt angle of the ellipse, 'a' is the major axis, and 'b' is
//  the minor axis.
//

int main()
{
    double phi,theta,a,b,x,y,dx,dy,sn,cs,s,c;

// initialize major axis, minor axis, tilt angle 
    a = 40.0;                    // major axis
    b = 30.0;                    // minor axis
    phi = 3.14159265359/6.0;     // tilt angle: 30 degrees
    sn = sin(phi);
    cs = cos(phi);

// initialize parameter
    theta = 0.0;

// main loop
    while (theta <= 6.28318530718) {
        s = sin(theta);
        c = cos(theta);
        x = a*c*cs-b*s*sn;
        y = a*c*sn+b*s*cs;
        cout << "(" << floor(x+0.5) << ", " << floor(y+0.5) << ")" << endl;
        dx = fabs(a*s*cs+b*c*sn);
        dy = fabs(a*s*sn-b*c*cs);

        if (dx > dy) theta += 1.0/dx;
        else theta += 1.0/dy;
    }
    return 0;
}