Title:
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Optimal sample weights for hemispherical integral quadratures
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Author:
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Marques, Ricardo; Bouville, Christian; Bouatouch, Kadi
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Abstract:
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Data de publicació electrònica:10-04-2018 |
Abstract:
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This paper proposes optimal quadrature rules over the hemisphere for the shading integral. We leverage recent work regarding
the theory of quadrature rules over the sphere in order to derive a new theoretical framework for the general case of hemispherical
quadrature error analysis. We then apply our framework to the case of the shading integral. We show that our quadrature
error theory can be used to derive optimal sample weights (OSW) which account for both the features of the sampling pattern
and the material reflectance function (BRDF). Our method significantly outperforms familiar QMC and stochastic Monte
Carlo techniques. Our results show that the OSW are very effective in compensating for possible irregularities in the sample
distribution. This allows, for example, to significantly exceed the regular O(N-1=2) convergence rate of stochastic Monte Carlo
while keeping the exact same sample sets. Another important benefit of our method is that OSW can be applied whatever the
sampling points distribution: the sample distribution need not follow a probability density function, which makes our technique
much more flexible than QMC or stochastic Monte Carlo solutions. In particular, our theoretical framework allows to easily
combine point sets derived from different sampling strategies (e.g., targeted to diffuse and glossy BRDF). In this context our
rendering results show that our approach overcomes MIS (Multiple Importance Sampling) techniques. |
Abstract:
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Ricardo Marques was supported by the European Union’s Horizon
2020 research programme through a Marie Sklodowska-Curie Individual
Fellowship (grant number 707027). |
Subject(s):
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-Monte Carlo techniques -Global illumination -Computing methodologies—Rendering -Ray tracing |
Rights:
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This is the peer reviewed version of the following article: Marques R, Bouville C, Bouatouch K. Optimal sample weights for hemispherical integral quadratures. Comput Graph Forum. 2018., which has been published in final form at http://dx.doi.org/10.1111/cgf.13392. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving. |
Document type:
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Article Article - Accepted version |
Published by:
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Wiley
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