Distance Geometry for Kissing Spheres

TL;DR

This paper introduces a novel distance geometry framework for kissing spheres, extending classical Euclidean distance geometry to accommodate spheres tangent to a reference ball, with potential applications in geometric modeling.

Contribution

The paper develops a generalized distance geometry specifically for kissing spheres, expanding the scope of classical Euclidean distance geometry.

Findings

Generalization of Euclidean distance geometry to kissing spheres

Mathematical framework for tangent sphere configurations

Potential applications in geometric modeling and analysis

Abstract

A kissing sphere is a sphere that is tangent to a fixed reference ball. We develop in this paper a distance geometry for kissing spheres, which turns out to be a generalization of the classical Euclidean distance geometry.