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An Area‐Preserving Parametrization for Spherical Rectangles
Author(s) -
Ureña Carlos,
Fajardo Marcos,
King Alan
Publication year - 2013
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.12151
Subject(s) - parametrization (atmospheric modeling) , rectangle , rendering (computer graphics) , unit sphere , planar , mathematics , geometry , computer science , monte carlo method , mathematical analysis , computer graphics (images) , physics , optics , statistics , radiative transfer
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.