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Preprint
English

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

Publication date2021
Abstract

Motivated by the unexpected failure of the triangle intersection component of the Projection Algorithm for Nonmatching Grids (PANG), this article provides a robust version with proof of backward stability. The new triangle intersection algorithm ensures consistency and parsimony across three types of calculations. The set of intersections produced by the algorithm, called representations, is shown to match the set of geometric intersections, called models. The article concludes with a comparison between the old and new intersection algorithms for PANG using an example found to reliably generate failures in the former.

Keywords
  • Graph enumeration
  • Computation of transforms
  • Consistency
  • Parsimony
  • Robustness
  • Software reliability
  • Mesh models
Notesubmitted to Transactions on Mathematical Software (TOMS)
Citation (ISO format)
MCCOID, Conor Joseph, GANDER, Martin Jakob. A provably robust algorithm for triangle-triangle intersections in floating-point arithmetic. 2021.
Main files (1)
Preprint
Identifiers
  • PID : unige:152653
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Technical informations

Creation06/25/2021 3:12:00 PM
First validation06/25/2021 3:12:00 PM
Update time03/16/2023 12:48:39 AM
Status update03/16/2023 12:48:38 AM
Last indexation05/06/2024 7:46:35 AM
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