--Given a set of points P and another Q in the plane, the question of whether a disk D exists with P inside D but Q outside D, is a linear programming problem, for each point xy we demand a*x*x+b*x*y+a*y*y+c*x+d*y+e > 0 (or <0)
+ b*x*y ??? I don't think so; the general equation of a circle is: A(x^2 + y^2) + Bx + Cy + D = 0 which forms a projective 3-space of possible circles. It looks like you have a 4-parameter family of conic sections instead. But, yes, your idea does generalise to determining whether there exists an algebraic curve (within a particular pencil) which separates the sets P and Q. -------- Returning to my original algorithm (just for discs), it is sufficient to check the interior points on the perimeter of the polyomino (for the same reason it is sufficient to check the exterior points adjacent to them). This reduces the running time from O(n^2) to O(n) for confirming a disc polyomino -- asymptotically, the best possible. Sincerely, Adam P. Goucher