one hundred twenty once the r theta point at the maximum height is known we can set our step sizes to calculate exactly one hundred fifty r theta points between u03c6 0 and the point of maximum height this is done between lines two hundred one and three hundred using the same numerical integration procedure again the points are read into arrays r i theta i in the end we are left with two arrays r i and theta i each with two hundred components specifying two hundred r theta points of the reflector surface these arrays can then be used for design specifications and ray trace applications in the case of a uniform beam design profile p u03b8 constant a typical set of parameters is also see fig1 in the case of an exponential beam profile p u03b8 ce a u03b8 a typical set of parameters is nonimaging illumination can also be provided by general optical sources provided the geometrical constraints on a reflector can be defined by simultaneously solving a pair of system the previously recited equations 1 and 2 relate the source angle and angle of light reflection from a reflector surface where l u03b8 i is the characteristic luminance at angle u03b8 i and g u03b8 i is a geometrical factor which is a function of the geometry of the light source in the case of a two dimensional lambertian light source as illustrated in fig6 a the radiated power versus angle for constant illuminance varies as cos 2 u03b8 for a three dimensional lambertian light source shown in fig6 d the radiated power versus angle for constant illuminance varies as cos 3 u03b8 considering the example of a two dimensional lambertian light source and tile planar source illustrated in fig6 b the concept of using.