An Implementation of Triangle-Triangle Intersection for Qualitative Spatial Reasoning

The intersection between 3D objects is ubiquitous in modeling. The objects are represented using the Boundary Representation (ANSI Brep) model in many applications such as CAD/CAM, collision detection, and spatial reasoning. Detection of possible intersection between objects can be based on the objects’ boundaries (approximate triangulations), computing triangle-triangle intersection. Usually there are separate algorithms for cross and coplanar intersections. The intersection detection is a byproduct of actual intersection computations. For qualitative spatial reasoning, intersection detection is sufficient, actual intersection is not necessary. Herein we present an implementation of a complete uniform integrated algorithm independent of cross and coplanar intersection. Additionally, we use barycentric coordinates for detecting and classifying intersections prior to computing precise 3D coordinates. This work is applicable to most region connection calculi, particularly VRCC-3D+, which uses intersection detection between 3D objects as well as their projections in 2D that are essential for occlusion detection.