B-Spline Approximation with Energy Constraints

This paper addresses the problem of reconstructing a free-form surface from measurement data. While the usual methods subdivide the point cloud and fit individual surfaces to these parts we fit a single integral tensor product B-spline surface to the entire point cloud. Holes in the point set, varying point densities, and free boundaries are handled. An effective algorithm is presented, which calculates a smooth approximation surface to a prescribed error tolerance with the help of energy terms.

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