Area‐Preserving Parameterizations for Spherical Ellipses

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...

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Bibliographic Details
Published inComputer graphics forum Vol. 36; no. 4; pp. 179 - 187
Main Authors Guillén, Ibón, Ureña, Carlos, King, Alan, Fajardo, Marcos, Georgiev, Iliyan, López‐Moreno, Jorge, Jarabo, Adrian
Format Journal Article
LanguageEnglish
Published Oxford Blackwell Publishing Ltd 01.07.2017
Subjects
CCS Concepts
Computing methodologies → Rendering
Ellipses
Illumination
Light sources
Production methods
Projection
Ray tracing
Sampling methods
Variance
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Summary: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.
ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.13234