Reflections From Multiple Surfaces Without Edges

An algorithm is presented for calculating the positions of the specular points that appear when a collection of reflecting surfaces is illuminated by an external source. The set of specular points is represented as the fixed point of a certain mapping, and this fixed point is calculated by the method of successive approximations (MSA). The MSA is an iterative technique which is essentially different from a search or shooting and bouncing ray technique. The latter require much larger numbers of functional evaluations, especially when the number N of reflecting surfaces is greater than unity. A search technique requires a number of function evaluations that varies exponentially with N, whereas the number of function evaluations required by the MSA varies linearly with N.