Geodesic interpolation on Sierpiński gaskets

Interpolation on spherical geodesic grids: a comparative study

Most operational models in atmospheric physics, meteorology and climatology nowadays adopt spherical geodesic grids and require “ad hoc” developed interpolation procedures. The author does a comparison between chosen representatives of linear, distance based and cubic interpolation schemes outlining their advantages and drawbacks in this specific application field. Numerical experiments on a st...

On the use of geodesic distances for spatial interpolation

Spatially distributed estimates of ecological variables are generally required for use in geographic information systems (GIS) and models when dealing with many environmental phenomena [2]. In particular, the quality of GIS products depends often on local properties that vary in space. In this context, increased interest has been demonstrated to geostatistics, or spatial statistics, as an analy...

Geodesic-Loxodromes for Diffusion Tensor Interpolation and Difference Measurement

In algorithms for processing diffusion tensor images, two common ingredients are interpolating tensors, and measuring the distance between them. We propose a new class of interpolation paths for tensors, termed geodesic-loxodromes, which explicitly preserve clinically important tensor attributes, such as mean diffusivity or fractional anisotropy, while using basic differential geometry to inter...

Generalized Geodesic Distances Applied to Interpolation and Shape Description

1 The grand tour via geodesic interpolation of 2 - frames

Grand tours are a class of methods for visualizing multivariate data, or any finite set of points in n-space. The idea is to create an animation of data projections by moving a 2-dimensional projection plane through n-space. The path of planes used in the animation is chosen so that it becomes dense, that is, it comes arbitrarily close to any plane. One inspiration for the grand tour was the ex...