Least-squares fitting of algebraic spline surfaces (Q1599379)

A new technique is described for fitting implicitly defined algebraic spline surfaces to scattered data in three-dimensional space. By approximating points and associated normal vectors estimated from the scattered data, a computationally simple method is obtained which requires the solution of a sparse system of linear equations. The method can be applied to data taken from arbitrary orientable 2-dimensional manifolds in 3-space. The potential applications include the reconstruction of free-form surfaces in reverse engineering. Furthermore, error bounds are established directly from the coefficients of the implicit representation.