POINT-TO-CURVE RAY-TRACING

Point-to-curve ray tracing is an attempt at dealing with multiplicity of solutions to a generic boundary-value problem of ray tracing. In a point-to-curve tracing (P2C) the input parameters of the boundary-valu e problem (BVP), such as the ends of the ray, are allowed to vary alon g a curve. The solutions of the BVP automatically wander from one solu tion branch to another generating a nearly complete multi-valued solut ion of the BVPs. A procedure for transforming an arbitrary iterative a lgorithm, solving a ray tracing BVP to a corresponding P2C algorithm, is presented. Bifurcations of the solution curve of the P2C problem at caustics are studied and an algorithm for obtaining the bifurcating b ranches is developed. In particular, transition from real rays to comp lex rays in a caustic shadow offers an additional link between otherwi se disconnected solution curves of the P2C problem. The topological st ructure of a generic solution curve and its implications for the algor ithm are studied.