Mesh editing with an embedded network of curves

We propose a new topological data structure for representing a set of polygonal curves embedded in a meshed surface. In this embedding, the vertices of the curve do not necessarily correspond to the vertices of the surface. The partition of the surface yielded by the intersecting curves is efficiently represented as a "cut-graph". The cut-graph stores combinatorial information of the network of curves. In our approach, the combinatorial form of information is systematically preferred to geometrical information since it improves both robustness and efficiency. Thanks to the topological data structure and algorithms, the cut-graph can be sketched through iterations of designing and erasing curves on the mesh surface in a "nondestructive" way, i.e. without modifying the mesh until the cutting operation is committed. We also demonstrate several prototype curve design tools inspired by 2D vector and bitmap graphics paradigms. We show how to sketch the cut-graph and how these tools can be mixedly used.