Triangle-triangle intersections with different numerical representations

Garau, Luca

First

;Scateni, Riccardo

Second

;Cherchi, Gianmarco

Last

2025-01-01

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Abstract

The detection and classification of triangle intersections in virtual environments are key ingredients in many computer graphics and geometry processing applications, especially for 3D reconstruction, rendering, modeling, and mesh optimization. Current solutions often necessitate rewriting intersection algorithms when transitioning between numerical representation systems, such as floating-point and rational numbers, to maintain robustness and precision. This work-in-progress report introduces a tool designed to address the triangle-triangle intersection problem robustly and exhaustively. By breaking down the problem into lower-dimensional simplex intersections and utilizing robust geometric predicates, our approach aims to provide a flexible, efficient, and general solution. The tool, developed using C++ templates, will support multiple numerical representation systems, ensuring adaptability without compromising accuracy. Upon completion, it will be benchmarked against state-of-the-art methods and released as an open-source resource, offering a trustworthy foundation for future advancements in research and development.