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Stratified Sampling of Projected Spherical Caps
Author(s) -
Ureña Carlos,
Georgiev Iliyan
Publication year - 2018
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/cgf.13471
Subject(s) - ellipse , rendering (computer graphics) , sampling (signal processing) , computer science , solid angle , unit sphere , projection (relational algebra) , geometry , projection plane , square (algebra) , computer graphics (images) , mathematics , computer vision , algorithm , mathematical analysis , telecommunications , filter (signal processing) , detector , image (mathematics)
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.