Surfacing curve networks with normal control

• A 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.

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.

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