A Generic Design for Implementing Intersection Between Triangles in Computer Vision and Spatial Reasoning

The intersection between 3D objects plays a prominent role in spatial reasoning, and computer vision. Detection of intersection between objects can be based on the triangulated boundaries of the objects, leading to computing triangle-triangle intersection. Traditionally there are separate algorithms for cross and coplanar intersection. For qualitative reasoning, intersection detection is sufficient, actual intersection is not necessary; in contrast, the precise intersection is required for geometric modeling. Herein we present a complete design and implementation of a single integrated algorithm independent of the type of intersection. Additionally, this algorithm first detects, then intersects and classifies the intersections using barycentric coordinates. This work is directly applicable to: (1) VRCC-3D+, which uses intersection detection between 3D objects as well as their 2D projections essential for occlusion detection; and (2) CAD/CAM geometric modeling where curves of intersection between a pair of surfaces are required for numerical control machines. Experimental results are provided.