Patent ID: 8630825

Claim:
A method of generating a convergent surface topology of two reflectors comprising the steps of: A. generating a convergence pattern of a forcing function in a complex space having at least two unsolvable areas by root approximation methods; B. determining a boundary edge of each of the unsolvable areas; C. selecting a starting point of one of the boundary edges of the unsolvable areas; D. iterating a convergence algorithm beginning with the starting point to create a stepping pattern in the complex space in the at least one unsolvable area; E. converting the stepping pattern into the real domain to form a topology pattern comprising a first and second set of coordinates of the surface topology; F. determining a first set of slopes corresponding to each of the first set of coordinates of the surface topology; G. fitting the slopes to a current iteration of a second set of coordinates corresponding to the first set of coordinates to generate at least one slope function; H. integrating the at least one slope function relative to the current iteration of the second set of coordinates to determine a reflector topology function; I. recording the current iteration of the second set of coordinates as a previous iteration of the second set of coordinates; J. determining a new iteration of the second set of coordinates corresponding to the first set of coordinates from the mirror topology function and setting the new iteration of the second set of coordinates to the current iteration of the of the second set of coordinates; K. determining that the reflector topology function represents the surface topology of the reflector when comparing the new iteration of the second set of coordinates to the previous iteration of the second set of coordinates satisfies a threshold; and L. repeating steps F-K if comparing the current iteration of the second set of coordinates to the previous iteration of the second set of coordinates does not satisfy a threshold.