非線形光線追跡のシミュレーション : シンプレクティック・レイトレーシング(<小特集>CGにおけるシミュレーション)

概要

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This paper describes a symplectic ray-tracing that is a novel method for non-linear ray-tracings. In general, non-linear ray-tracings require efficient numerical computation for solving differential equations numeri cally. However, numerical simulation techniques of the non-linear ray-tracings have not been improved in this decade. A symplectic ray-tracing which is described in this paper improves numerical calculation by introducing Hamiltonian dynamics and a symplectic integrator into computation of the non-linear ray-tracing. Main features of the symplectic ray-tracing are the followings. First, reusability of programs of the symplectic ray-tracing is very high. Secondly, researchers can implement the symplectic ray-tracing by any language easily. Thirdly, the symplectic ray tracing is able to integrate almost of non-linear ray-tracings into Hamiltonian dynamics and a symplectic integrator. Lastly, the symplectic ray-tracing can calculate efficiently with controlling accumulation error and estimating local error. The symplectic ray-tracing will be applicable to visualization and computer graphics by using many other dynamical systems.
2002-09-15