Generation of subdivision surface from network of curves

Abstract

Subdivision surfaces are usually used to construct freeform surfaces from network of curves for its ability and flexibility to deal with complex wireframes. In freeform surface designing, the designers usually draw at first some curves for describing the models conceived in their mind which form a curve network representing an object of arbitrary topology. Then 3D surfaces are computed to interpolate these curves in order to create a B-Rep model. If the subdivision surface is used in the workflow, its control polyhedrons generation from curves polygons could be a time-consuming stage. In this article, we develop an approach to generate automatically a control polyhedral mesh from an arbitrary topological curve network. One of common problems in interpolating surface patch using subdivision surfaces is how to determine the connectivity of control points. Arbitrary topological curve network has no restriction in topology structure, so another problem is that it has more ambiguousness in defining surface patches. There are three steps in our approach. Firstly, we compute a 1D mesh (a unique polygonal model) from curves. Secondly, we identify on the polygon different cycles that would be the boundaries of potential surface patches. Finally, in each identified cycle we apply an algorithm of quadrangulation to construct the control mesh of subdivision.