The supporting ellipsoids and linear programming reflector design methods build upon the property of conics to address the inverse problem of finding the freeform surface that directs light from a point source to produce a prescribed target distribution. We review the properties and main computational limitations of the two methods and show that a fast flux estimation method based on contour detection can be used in combination with the supporting ellipsoid algorithm. Once the intersections between neighboring conic patches on the reflector are known, it is possible to estimate the collected flux using the vertices of the intersection boundary. The advantage of using the intersection method to estimate the flux instead of the more common approach—Monte Carlo ray tracing—is that there is no tradeoff between speed and accuracy. Examples of flux estimation with the intersection method for different target configurations are shown.