Abstract
In this paper, we present a simple multiresolution framework for curves on the surface of a sphere. Multiresolution
by subdivision and reverse subdivision allows one to decrease and restore the resolution of a curve, and is typically
defined by affine combinations of points in Euclidean space. However, translating such combinations to spherical
space is challenging. Several works perform such operations in an intermediate Euclidean space instead using
some mapping (e.g. the exponential map), but such mappings cause distortions and are often complicated. We
use a simple geometric construction for a multiresolution scheme on the sphere that does not require the use
of an intermediate space, which is based on a modified Lane-Riesenfeld algorithm (point duplication followed
by repeated averaging) that features an invertible averaging step. Such a multiresolution scheme allows one to
simplify/compress and reconstruct curves on the surface of a sphere-like object — such as the Earth — simply,
efficiently, and without distortion.
Refereed
No
