We present a fast algorithm for path computation of multiple diffracted rays relevant to ray tracing techniques. The focus is on double diffracted rays, but generalizations are also mentioned. The novelty of our approach is in the use of an analytical geometry procedure which permits to re-write the problem as a simple nonlinear equation. This procedure permits a convergence analysis of the algorithms involved in the numerical resolution of such nonlinear equation. Moreover, we also indicate how to choose the iteration starting point to obtain convergence of the (locally convergent) Newton method. As in previous works, explicit solutions are obtained in the relevant cases of parallel or incident diffraction edges.
A fast algorithm for determining the propagation path of multiple diffracted rays
BAGNERINI, PATRIZIA;
2007-01-01
Abstract
We present a fast algorithm for path computation of multiple diffracted rays relevant to ray tracing techniques. The focus is on double diffracted rays, but generalizations are also mentioned. The novelty of our approach is in the use of an analytical geometry procedure which permits to re-write the problem as a simple nonlinear equation. This procedure permits a convergence analysis of the algorithms involved in the numerical resolution of such nonlinear equation. Moreover, we also indicate how to choose the iteration starting point to obtain convergence of the (locally convergent) Newton method. As in previous works, explicit solutions are obtained in the relevant cases of parallel or incident diffraction edges.
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