Global change research has placed new demands on methods of spatial analysis. In particular, spherical methods for spatial interpolation are required when spatial analyses are performed over large areas of the Earth's surface. In this article, spherical spatial interpolation procedures are reviewed, compared, and evaluated. Three classesof spherical interpolants are evaluated in detail: distanc...

We investigate C1-smooth univariate curvature-based cubic L1 interpolating splines in Cartesian and polar coordinates. The coefficients of these splines are calculated by minimizing the L1 norm of curvature. We compare these curvature-based cubic L1 splines with second-derivative-based cubic L1 splines and with cubic L2 splines based on the L2 norm of curvature and of the second derivative. In ...

The convergence of the minimal energy interpolatory splines on the unit sphere is studied in this paper. An upper bound on the difference between a sufficiently smooth function and its interpolatory spherical spline in the infinity norm is given. The error bound is expressed in terms of a second order spherical Sobolev-type seminorm of the original function. §

We use splines on spherical triangulations to approximate the solution of a second order elliptic PDE over the unit sphere. We establish existence and uniqueness of weak solutions in spherical spline spaces and estimate convergence of the spline approximations. We present a computational algorithm and summarize numerical results on convergence rates. §

We propose a novel technique based on spherical splines for brain surface representation and analysis. This research is strongly inspired by the fact that, for brain surfaces, it is both necessary and natural to employ spheres as their natural domains. We develop an automatic and efficient algorithm, which transforms a brain surface to a single spherical spline whose maximal error deviation fro...

Spherical Jeans modeling is widely used to estimate mass profiles of systems from star clusters galactic stellar haloes galaxies. It derives the cumulative profile, M(<r), kinematics tracers potential under assumptions spherical symmetry and dynamical equilibrium. We consider application mapping dark matter distribution in outer reaches Milky Way using field halo stars. present a novel non-para...

Trivariate splines solve a special case of scattered data interpolation problem in the volume bounded by two concentric spheres. A triangulation ∆ of the unit sphere S is constructed based on the vertex set V. Given a partition P of the interval [1, R], let Sτ×ρ σ×δ be the space of the spherical splines of degree σ and smoothness τ over ∆ tensored with the univariate radial splines of degree δ ...