// The centers of the circles
Cartesian x = new Cartesian(1, 0, 0, false);
Cartesian y = new Cartesian(0, 1, 0, false);

// The two great circles
Halfspace hx = new Halfspace(x, 0);
Halfspace hy = new Halfspace(y, 0);

// The intersection of the two circles is a convex
Convex c = new Convex(new Halfspace[] { hx, hy });
c.Simplify();
Console.Out.WriteLine("Area: {0}", c.Area);
Console.Out.WriteLine(c);

// The union of the circles is a region
Region r = new Region();
r.Add(new Convex(hx));
r.Add(new Convex(hy));
r.Simplify();
Console.Out.WriteLine("Area: {0}", r.Area);
Console.Out.WriteLine(r);

Area: 10313.2403123548
CONVEX
 0 1 0 0
 1 0 0 0

Area: 30939.7209370645
REGION
 CONVEX
 0 1 0 0
 CONVEX
 0 -1 0 0
 1 0 0 0