Reconstructing free-form surfaces from sparse data

We propose a scheme to recover general free-form surfaces from sparse data, and the data may contain unknown discontinuities. We use a global voting method to infer from sparse data three dense potential fields for surfaces, edges, and junctions. We then use a new model called “winged B-snakes”, which are deformable triangular B-spline surfaces embedded with active curves, to fit the surfaces and align the edges and junctions. A smooth C¹ surface with preserved discontinuity edges and junctions is obtained after the “winged B-snakes” have evolved and converged in the three potential fields using energy minimization. The triangular B-splines are state-of-the-art free-form surface representations and have good properties of arbitrary triangulation, lowest degree, local control, convex hull, automatic continuity, and affine invariance