On the Precision to Sort Line-Quadric Intersections

TL;DR

This paper investigates the minimal arithmetic precision needed to accurately determine the order of intersection points between quadrics along a line segment, proposing a method that reduces precision requirements compared to extended root calculations.

Contribution

It introduces a novel approach using resultants to determine intersection order with lower precision, improving efficiency in CAD modeling of neutron trajectories.

Findings

Resultant method reduces precision needs

Comparable accuracy to extended precision root calculations

Faster computation with maintained accuracy

Abstract

To support exactly tracking a neutron moving along a given line segment through a CAD model with quadric surfaces, this paper considers the arithmetic precision required to compute the order of intersection points of two quadrics along the line segment. When the orders of all but one pair of intersections are known, we show that a resultant can resolve the order of the remaining pair using only half the precision that may be required to eliminate radicals by repeated squaring. We compare the time and accuracy of our technique with converting to extended precision to calculate roots.