Solid Angle Sampling of Disk and Cylinder Lights

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.

Section: Introductionmentioning

confidence: 99%

Stratified Sampling of Projected Spherical Caps

Ureña

Georgiev

2018

“…To avoid costly numerical inversion, we develop a practical mapping tabulation that introduces little overhead over traditional uniform area sampling [SC97] while significantly reducing the variance of the illumination estimate. Our mappings are also competitive to existing disk solid angle sampling techniques [Gam16], without imposing restrictions on the sample generator.…”

Section: Discussionmentioning

confidence: 99%

“…Area-preserving solid angle maps have been developed for triangles [Arv95] and rectangles [UFK13]. For sampling the solid angles of disks, Gamito [Gam16] proposed to use a rectangle map [UFK13] followed by rejection sampling. This technique cannot be used with fixed-size canonical point sets, and needs a low-discrepancy sequence capable of progressively generating stratified sample candidates.…”

Section: Problem Statement and Previous Workmentioning

confidence: 99%

“…Moreover, disk lights form the base for some approximate global illumination algorithms [HKWB09,SHD15]. So far, the only practical method for uniformly sampling the solid angle of disk lights is the work by Gamito [Gam16], who proposed a rejection sampling approach that generates candidates using spherical quad sampling [UFK13]. Unfortunately, achieving good sample stratification with this method requires special care.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Area‐Preserving Parameterizations for Spherical Ellipses

Guillén

Ureña

King

et al. 2017

We present new methods for uniformly sampling the solid angle subtended by a disk. To achieve this, we devise two novel area-preserving mappings from the unit square [0, 1] 2 to a spherical ellipse (i.e. the projection of the disk onto the unit sphere). These mappings allow for low-variance stratified sampling of direct illumination from disk-shaped light sources. We discuss how to efficiently incorporate our methods into a production renderer and demonstrate the quality of our maps, showing significantly lower variance than previous work.

“…Several techniques have thus been developed for uniformly sampling solid angles of e.g. triangular [Arv95], rectangular [UFK13], disk and cylindrical [Gam16], elliptical [GUK * 17], or polygonal [Arv01] luminaires.…”

Section: Luminaire Samplingmentioning

confidence: 99%

Monte Carlo Methods for Volumetric Light Transport Simulation

Novák

Georgiev

Hanika

et al. 2018

107

The wide adoption of path‐tracing algorithms in high‐end realistic rendering has stimulated many diverse research initiatives. In this paper we present a coherent survey of methods that utilize Monte Carlo integration for estimating light transport in scenes containing participating media. Our work complements the volume‐rendering state‐of‐the‐art report by Cerezo et al. [CPP*05]; we review publications accumulated since its publication over a decade ago, and include earlier methods that are key for building light transport paths in a stochastic manner. We begin by describing analog and non‐analog procedures for free‐path sampling and discuss various expected‐value, collision, and track‐length estimators for computing transmittance. We then review the various rendering algorithms that employ these as building blocks for path sampling. Special attention is devoted to null‐collision methods that utilize fictitious matter to handle spatially varying densities; we import two “next‐flight” estimators originally developed in nuclear sciences. Whenever possible, we draw connections between image‐synthesis techniques and methods from particle physics and neutron transport to provide the reader with a broader context.