A Provably Robust Algorithm for Triangle-triangle Intersections in Floating-point Arithmetic

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.

A Brief Survey of Clipping and Intersection Algorithms with a List of References (including Triangle-Triangle Intersections)

“…a line passes a vertex, a line touches a vertex, a line lies on an edge, etc. (Mccoid and Gander, 2022;Skala, 1989Skala, , 1990a.…”

“…A robust solution of triangle-triangle intersection in E 2 is described in Mccoid and Gander (2022). Other algorithms or modifications are described in Dimri (2015), Evangeline and Anitha (2014), Lu and Wu (2002), Lu et al (2002a), Tang and He (2009).…”

“…A deep analysis of possible situations is given in Lo and Wang (2004). Robust and reliable solution of the triangle-triangle intersection was developed by Mccoid and Gander (2022). Clipping triangular strips using homogeneous coordinates was described by Maillot (1991) in GEM II (Arvo, 1991).…”