Discriminant of Position Relationship between an Ellipse and a Quadratic Curve

Position relationship problem between two quadratic curves is usually discussed in collision detection problem between two coplanar objects.Combining with the resultant theory and the observation that the tangent point is not only an intersection point but also the closest point,several polynomial discriminants are obtained to classify all possible cases of the position relationship between an ellipse and a quadratic curve. Our method is very intuitive and simple where only simple operations such as addition,subtraction and multiplication are involved.The method could also be used in position relationship problem between two moving quadratic curves.Examples have been presented to show that the new method is robust and feasible in various applications.