A Robust Approach to Detect Intersections between Triangles with Different Numerical Representations

TL;DR

This paper introduces a versatile, open-source C++ algorithm capable of detecting and classifying triangle intersections across various numerical representations, simplifying integration into geometry processing workflows.

Contribution

It presents a generic, exhaustive intersection detection algorithm for triangles with floating point, rational, or implicit representations, easily integrable into existing systems.

Findings

Compared favorably with state-of-the-art methods

Supports multiple numerical representations

Open source implementation available

Abstract

The detection and classification of intersections between triangles are crucial tasks in a wide range of applications within Computer Graphics and Geometry Processing, including mesh Arrangements, mesh Booleans, and generic mesh processing and fixing tasks. Existing methods are hard-coded and deeply integrated into specific algorithms, and significant efforts are usually required to integrate them into new pipelines or to extend them to different numerical representations. This paper presents a versatile and exhaustive algorithm to identify and classify intersections between triangles with either floating points, rational numbers, or implicit representations. The proposed tool is implemented as a C++ templated and header-only code that is generic and easy to integrate into further algorithms requiring the triangle-triangle intersection detection step. The developed tool has been tested and compared with a state-of-the-art approach, and it is shared with the Geometry Processing community with an Open Source license.