Fast Equal-Area Mapping of the (Hemi)Sphere using SIMD

Abstract

We present a fast vectorized implementation of a transform that maps points in the unit square to the surface of the sphere, while preserving fractional area. The mapping uses the octahedral map combined with an equal-area parameterization and has many desirable features such as low distortion, straightforward interpolation, and fast inverse and forward transforms. Our SIMD implementation completely avoids branching and uses polynomial approximations for the trigonometric operations, as well as other tricks. This results in up to 9 times speed-up over a traditional scalar implementation. Source code is available online.