Jüttler, Bert; Felis, Alf Least-squares fitting of algebraic spline surfaces. (English) Zbl 0997.65028 Adv. Comput. Math. 17, No. 1-2, 135-152 (2002). 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. Reviewer: Dana Petcu (Timişoara) Cited in 1 ReviewCited in 16 Documents MSC: 65D17 Computer-aided design (modeling of curves and surfaces) Keywords:spline surface; surface fitting; least-squares; scattered data; reconstruction of free-form surfaces; reverse engineering; error bounds × Cite Format Result Cite Review PDF Full Text: DOI