An Area-Preserving Parametrization for Spherical Rectangles
Article first published online: 18 JUL 2013
© 2013 The Author(s) Computer Graphics Forum © 2013 The Eurographics Association and John Wiley & Sons Ltd.
Computer Graphics Forum
Volume 32, Issue 4, pages 59–66, July 2013
How to Cite
Ureña, C., Fajardo, M. and King, A. (2013), An Area-Preserving Parametrization for Spherical Rectangles. Computer Graphics Forum, 32: 59–66. doi: 10.1111/cgf.12151
- Issue published online: 18 JUL 2013
- Article first published online: 18 JUL 2013
- I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism—Color, shading, shadowing, and texture
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.