Show simple item record

dc.contributor.authorMarques, Ricardoen_US
dc.contributor.authorBouville, Christianen_US
dc.contributor.authorBouatouch, Kadien_US
dc.contributor.editorChen, Min and Benes, Bedrichen_US
dc.date.accessioned2019-03-17T09:56:48Z
dc.date.available2019-03-17T09:56:48Z
dc.date.issued2019
dc.identifier.issn1467-8659
dc.identifier.urihttps://doi.org/10.1111/cgf.13392
dc.identifier.urihttps://diglib.eg.org:443/handle/10.1111/cgf13392
dc.description.abstractThis 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 bidirectional reflectance distribution function (BRDF). Our method significantly outperforms familiar Quasi Monte Carlo (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 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.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 Quasi Monte Carlo (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 convergence rate of stochastic Monte Carlo while keeping the exact same sample sets.en_US
dc.publisher© 2019 The Eurographics Association and John Wiley & Sons Ltd.en_US
dc.subjectMonte Carlo techniques
dc.subjectglobal illumination
dc.subjectComputing methodologies—Rendering
dc.subjectRay tracing
dc.titleOptimal Sample Weights for Hemispherical Integral Quadraturesen_US
dc.description.seriesinformationComputer Graphics Forum
dc.description.sectionheadersArticles
dc.description.volume38
dc.description.number1
dc.identifier.doi10.1111/cgf.13392
dc.identifier.pages59-72


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record