Cristina Canavesi, William Cassarly and Jannick P. Rolland published a paper, ‘Direct calculation algorithm for two-dimensional reflector design,’ in Optics Letters 37(18), 3852-3854 (2012)
Abstract: We have developed a fast algorithm to design two-dimensional reflector surfaces that ties together the supporting paraboloids, linear programming, and numerical integration methods. The algorithm builds upon the properties of conics and is shown to be several orders of magnitude faster than the supporting paraboloids and linear programming methods. The scalability and ease of implementation of the algorithm are discussed.
September 2012