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{\bf Robust algorithms for the intersection of simplices}

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{\it Author and Presenter:}\\[0.5ex]

Conor McCoid (Universit\'e de Gen\`eve)

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& Martin J. Gander (Universit\'e de Gen\`eve)\\

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{\bf Abstract:} At times even the smallest of floating-point errors can cause intersection algorithms to destabilize.

The final result may then have an error several magnitudes larger.

Robust algorithms are then required to avoid such instabilities.

One way to achieve this is to write them parsimoniously \cite{fortune1989}, that is, by using the smallest number of direct calculations as necessary.

A given calculation may provide underutilized information that can eliminate the need for additional calculations.

In this talk we present methodology for maximizing information output of intersection calculations for $n$-simplices, with a focus on triangles \cite{mccoid2021} and tetrahedra.

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\bibitem{fortune1989} S.~Fortune,

Stable maintenance of point set triangulations in two dimensions.

Annual Symposium on Foundations of Computer Sicence (proceedings).

\bibitem{mccoid2021} C.~McCoid, M.~J.~Gander,

A provably robust algorithm for triangle-triangle intersections in floating-point arithmetic.

Transactions on Mathematical Software (in review).