Deciding whether two quadratic surfaces actually intersect

TL;DR

This paper addresses the problem of determining whether two quadratic surfaces intersect without explicitly computing their intersection points, providing a novel decision method for this geometric problem.

Contribution

The paper introduces a new approach to decide surface intersection without direct computation, solving an open question from 2007.

Findings

The method reliably determines intersection existence.

It improves computational efficiency over previous techniques.

The approach is applicable to various quadratic surface configurations.

Abstract

We answer an open question proposed by P\'{o}lik and Terlaky in 2007 that: {\it how we can decide whether two quadratic surfaces intersect without actually computing the intersections?}