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Recent surface acquisition technologies based on microsensors produce three-space tangential curve data which can be transformed into a network of space curves with surface normals. This paper addresses the problem of surfacing an arbitrary closed 3D curve network with given surface normals. Thanks to the normal vector input, the patch finding problem can be solved unambiguously and an initial piecewise smooth triangle mesh is computed. The input normals are propagated throughout the mesh. Together with the initial mesh, the propagated normals are used to compute mean curvature vectors. We then compute the final mesh as the solution of a new variational optimization method based on the mean curvature vectors. The intuition behind this original approach is to guide the standard Laplacian-based variational methods by the curvature information extracted from the input normals. The normal input increases shape fidelity and allows to achieve globally smooth and visually pleasing shapes. Graphical abstractDisplay Omitted HighlightsA method for surfacing curve networks with prescribed normals is presented.The method does not require an extra parameter to control the magnitude of normals.The key insight is the decoupling of normals from positions before the extrapolation.The resulting shapes are globally smooth and visually pleasing.The method is fully automatic, and, at the same time, simple to implement.

International audience; 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.