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An Analysis of Quasi‐Monte Carlo Integration Applied to the Transillumination Radiosity Method
Author(s) -
SzirmayKalos László,
Fóris Tibor,
Neumann László,
Csébfalvi Balázs
Publication year - 1997
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/1467-8659.00164
Subject(s) - radiosity (computer graphics) , monte carlo method , computer science , monte carlo integration , quasi monte carlo method , numerical integration , convergence (economics) , global illumination , mathematics , mathematical optimization , algorithm , monte carlo molecular modeling , mathematical analysis , computer graphics (images) , rendering (computer graphics) , markov chain monte carlo , statistics , economics , economic growth
This paper presents an enhanced transillumination radiosity method that can provide accurate solutions at relatively low computational cost. The proposed algorithm breaks down the double integral of the gathered power to an area integral that is computed analytically and to a directional integral that is evaluated by quasi‐Monte Carlo techniques. Since the analytical integration results in a continuous function of finite variation, the quasi‐Monte Carlo integration that follows the analytical integration will be efficient and its error can be bounded by the Koksma‐Hlawka inequality. The paper also analyses the requirements of the convergence, presents theoretical error bounds and proposes error reduction techniques. The theoretical bounds are compared with simulation results.