Multiscale NURBS curves on the sphere and ellipsoid

Abstract

In this paper, we introduce a framework that allows NURBS subdivision curves to be defined on the sphere and ellipsoid in a multiscale manner. This is achieved via modification of a repeated invertible averaging (RIA) framework for spherical B-Spline curves, which is constructed in terms of spherical linear interpolations. By incorporating vertex weights into the interpolation parameters of individual operations, and by generalizing the linear interpolations to other manifolds, we can define multiscale NURBS on several types of surfaces. We explore an application to the multiscale representation of geospatial vector data and present an optimization method that automatically assigns NURBS vertex weights to curve vertices.