Combining analytic direct illumination and stochastic shadows

Heitz, Eric; Hill, Stephen; McGuire, Morgan

doi:10.1145/3190834.3190852

Cited by 34 publications

(26 citation statements)

References 25 publications

(22 reference statements)

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“…In addition, our formulations provide novel closed‐form expressions for the form factor between a differential surface element and a sphere [Sny96]. The form factor could be used to improve many‐light rendering techniques [HKWB09, SHD15, EK17] as well as direct illumination sampling with combined analytical and stochastic techniques [HHM18].…”

Section: Discussionmentioning

confidence: 99%

Stratified Sampling of Projected Spherical Caps

Ureña

Georgiev

2018

Computer Graphics Forum

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We present a method for uniformly sampling points inside the projection of a spherical cap onto a plane through the sphere's center. To achieve this, we devise two novel area‐preserving mappings from the unit square to this projection, which is often an ellipse but generally has a more complex shape. Our maps allow for low‐variance rendering of direct illumination from finite and infinite (e.g. sun‐like) spherical light sources by sampling their projected solid angle in a stratified manner. We discuss the practical implementation of our maps and show significant quality improvement over traditional uniform spherical cap sampling in a production renderer.

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Section: Discussionmentioning

confidence: 99%

Stratified Sampling of Projected Spherical Caps

Ureña

Georgiev

2018

Computer Graphics Forum

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“…Analytic integration of parts of the path integral has previously been proposed for a wide range of applications such as anti-aliasing [Jones and Perry 2000], visibility [Gribel et al 2010[Gribel et al , 2011Barringer et al 2012;Billen and Dutré 2016], depth of field [Tzeng et al 2012], single scattering [Sun et al 2005;Pegoraro and Parker 2009], and area lighting [Arvo 1995b,a;Arvo 2000, 2001;Belcour et al 2018]. These have also been combined with more general Monte Carlo integration using ratio [Heitz et al 2018] or control variates estimators [Belcour et al 2018]. Recent theoretical analyses [Sun et al 2013; have explained how such techniques reduce variance and improve convergence rate by smoothing the integrand prior to Monte Carlo integration.…”

Section: Related Workmentioning

confidence: 99%

Photon surfaces for robust, unbiased volumetric density estimation

et al. 2019

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We generalize photon planes to photon surfaces : a new family of unbiased volumetric density estimators which we combine using multiple importance sampling. To derive our new estimators, we start with the extended path integral which duplicates the vertex at the end of the camera and photon subpaths and couples them using a blurring kernel. To make our formulation unbiased, however, we use a delta kernel to couple these two end points. Unfortunately, sampling the resulting singular integral using Monte Carlo is impossible since the probability of generating a contributing light path by independently sampling the two subpaths is zero. Our key insight is that we can eliminate the delta kernel and make Monte Carlo estimation practical by integrating any three dimensions analytically, and integrating only the remaining dimensions using Monte Carlo. We demonstrate the practicality of this approach by instantiating a collection of estimators which analytically integrate the distance along the camera ray and two arbitrary sampling dimensions along the photon subpath (e.g., distance, direction, surface area). This generalizes photon planes to curved "photon surfaces", including new "photon cone", "photon cylinder", "photon sphere", and multiple new "photon plane" estimators. These estimators allow us to handle light paths not supported by photon planes, including single scattering, and surface-to-media transport. More importantly, since our estimators have complementary strengths due to analytically integrating different dimensions of the path integral, we can combine them using multiple importance sampling. This combination mitigates singularities present in individual estimators, substantially reducing variance while remaining fully unbiased. We demonstrate our improved estimators on a number of scenes containing homogeneous media with highly anisotropic phase functions, accelerating both multiple scattering and single scattering compared to prior techniques.

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“…Others, like shadow mapping, can be improved by ray tracing. Replacing a high number of shadowmapped lights by ray tracing remains a performance challenge, yet it already promises high-quality results [5].…”

Section: Discussionmentioning

confidence: 99%

Deferred Hybrid Path Tracing

Willberger¹,

Musterle²,

Bergmann³

2019

Ray Tracing Gems

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We describe a hybrid rendering approach that leverages existing rasterizationbased techniques and combines them with ray tracing in order to achieve realtime global illumination. We reduce the number of traced rays by trying to find an intersection in screen space and reuse information from previous frames via reprojection and filtering. Artificial lighting is stored in nodes of the spatial acceleration structure to ensure efficient memory access. Our techniques require no manual preprocessing and only a few seconds of precomputation. They were developed as a real-time rendering solution for architectural design but can be applied to other purposes as well.

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Combining analytic direct illumination and stochastic shadows

Cited by 34 publications

References 25 publications

Stratified Sampling of Projected Spherical Caps

Stratified Sampling of Projected Spherical Caps

Photon surfaces for robust, unbiased volumetric density estimation

Deferred Hybrid Path Tracing

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