Point-to-curve ray tracing |
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| Authors: | Andrzej Hanyga |
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| Institution: | (1) Institute for Solid Earth Physics, University of Bergen, Allégaten 41, N5007 Bergen, Norway |
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| Abstract: | 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-value problem (BVP), such as the ends of the ray, are allowed to vary along a curve. The solutions of the BVP automatically wander from one solution branch to another generating a nearly complete multi-valued solution of the BVPs.A procedure for transforming an arbitrary iterative algorithm, 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 branches is developed. In particular, transition from real rays to complex rays in a caustic shadow offers an additional link between otherwise disconnected solution curves of the P2C problem. The topological structure of a generic solution curve and its implications for the algorithm are studied. |
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| Keywords: | Ray tracing bifurcation complex rays diffraction |
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