Information of high-level, topological contact states is useful and sometimes even necessary for a wide range of applications, from robotic tasks involving compliant motion to virtual prototyping and simulation. This paper addresses how to represent concisely and generate automatically graphs of contact states between 3D curved objects of a broad class, which may include smooth curved or planar surfaces. The approach is sound and complete if the step size of discretization is smaller than a finite threshold. By exploiting topological and geometrical constraints, it is also quite efficient. The implemented examples demonstrate the effectiveness of the approach.
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