Abstract: This paper discussed degeneracy and robustness issues in geometric computing by an example of two 3D triangle pairs intersecting ,especially the classification of their various relations. The first key to a problem is to describe this problem. Hence, the complete representation of degeneracies is an important foundation and support to design, improve as well as test a robust geometric computing algorithm. For the first time, this paper studies degeneracies for various triangle pairs in 3D space. Based on projecting reduction, their relationships are classified and a complete sample model is deduced to cover all kinds of degeneracies. The basic strategy is to establish a computed coordinate system. Then by projection, 3D relations are reduced to planar ones. Fixing one triangle, and changing the relative position and size of the other, various relations are classified in the clue of departed, contacted, intersected and overlapped. Consequently, all degeneracies can be got. The method proposed in this paper provides a new way to robustness 3D geometric computing algorithms not only for testing samples but also for algorithm reforming.

Key words: geometric computing, robustness, degeneracy, triangles intersection, projection and reduction