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Reinert B.,MPI Informatik | Ritschel T.,MPI Informatik | Ritschel T.,Saarland University | Seidel H.-P.,MPI Informatik | Georgiev I.,Solid Angle
Computer Graphics Forum | Year: 2016

We propose projective blue-noise patterns that retain their blue-noise characteristics when undergoing one or multiple projections onto lower dimensional subspaces. These patterns are produced by extending existing methods, such as dart throwing and Lloyd relaxation, and have a range of applications. For numerical integration, our patterns often outperform state-of-the-art stochastic and low-discrepancy patterns, which have been specifically designed only for this purpose. For image reconstruction, our method outperforms traditional blue-noise sampling when the variation in the signal is concentrated along one dimension. Finally, we use our patterns to distribute primitives uniformly in 3D space such that their 2D projections retain a blue-noise distribution. We propose projective blue-noise patterns that retain their blue-noise characteristics when undergoing one or multiple projections onto lower dimensional subspaces. These patterns are produced by extending existing methods, such as dart throwing and Lloyd relaxation, and have a range of applications. For numerical integration, our patterns often outperform state-of-the-art stochastic and low-discrepancy patterns, which have been specifically designed only for this purpose. For image reconstruction, our method outperforms traditional blue-noise sampling when the variation in the signal is concentrated along one dimension. Finally, we use our patterns to distribute primitives uniformly in 3D space such that their 2D projections retain a blue-noise distribution. © 2015 The Eurographics Association and John Wiley & Sons Ltd. Source


Kulla C.,Sony | Fajardo M.,Solid Angle
Computer Graphics Forum | Year: 2012

We introduce a set of robust importance sampling techniques which allow efficient calculation of direct and indirect Lighting from arbitrary light sources in both homogeneous and heterogeneous media. We show how to distribute Samples along a ray proportionally to the incoming radiance for point and area lights. In heterogeneous media, we Decouple ray marching from light calculations by computing a representation of the transmittance function that can Be quickly evaluated during sampling, at the cost of a small amount of bias. This representation also allows the Calculation of another probability density function which can direct samples to regions most likely to scatter light. These techniques are orthogonal and can be combined via multiple importance sampling to further reduce variance. Our method has very modest per-ray memory requirements and does not require any preprocessing, making it Simple to integrate into production ray tracing based renderers. © 2012 Sony Pictures Imageworks Inc. All Rights Reserved. Source


Urena C.,University of Granada | Fajardo M.,Solid Angle | King A.,Solid Angle
Computer Graphics Forum | Year: 2013

We present an area-preserving parametrization for spherical rectangles which is an analytical function with domain in the unit rectangle [0, 1] 2 and range in a region included in the unit-radius sphere. The parametrization preserves areas up to a constant factor and is thus very useful in the context of rendering as it allows to map random sample point sets in [0, 1]2 onto the spherical rectangle. This allows for easily incorporating stratified, quasi-Monte Carlo or other sampling strategies in algorithms that compute scattering from planar rectangular emitters. © 2013 The Author(s) Computer Graphics Forum © 2013 The Eurographics Association and John Wiley & Sons Ltd. Source

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