Moebius-Invariant Natural Neighbor Interpolation

TL;DR

This paper introduces a Moebius-invariant interpolation method that uses natural neighbors and angle-based weighting to ensure consistent results under Moebius transformations.

Contribution

It presents a novel interpolation technique that maintains invariance under Moebius transformations using angle-based weights on natural neighbors.

Findings

The method achieves invariance under Moebius transformations.

It utilizes Delaunay circles to determine neighbor angles.

The approach improves consistency in geometric data interpolation.

Abstract

We propose an interpolation method that is invariant under Moebius transformations; that is, interpolation followed by transformation gives the same result as transformation followed by interpolation. The method uses natural (Delaunay) neighbors, but weights neighbors according to angles formed by Delaunay circles.