Least squares 2D bi-cubic spline approximation: Theory and applications. (October 2018)

• Record Type: Journal Article
• Authors: Amiri-Simkooei, A.R.; Hosseini-Asl, M.; Safari, A.
• Is Part Of: Measurement. Volume 127(2018)
• Page Start: 366
• Page End: 378
• Publication Date: 2018-10
• Subjects: Least squares 2D bi-cubic spline approximation (LS-BICSA) -- Continuity and differentiability conditions -- Constrained least squares -- Geoid height approximation; Weights and measures -- Periodicals; Measurement -- Periodicals; Measurement; Weights and measures; Periodicals; 530.8
• DOI: 10.1016/j.measurement.2018.06.005
• Languages: English
• ISSNs: 0263-2241

Abstract

Highlights: Theory of least squares 2D bi-cubic spline approximation (LS-BICSA) is developed. Continuity constraints are explicitly imposed by the user to pure bi-cubic splines. LS-BICSA is a generalized form of the 2D bi-cubic spline interpolation method. LS-BICSA is capable of approximating both regular and irregular data sets. Approximation accuracy is reached by using an appropriate size of surface patches. Abstract: Smooth surface approximation plays an important role in many applications. As an extension of the 2D bi-cubic spline interpolation, we propose the least squares 2D bi-cubic spline approximation (LS-BICSA). LS-BICSA, generally applicable to a set of irregular data, is formulated by the pure bi-cubic spline functions. The method is flexible because the user can impose the appropriate continuity and differentiability conditions at the boundary points using the available constrained least squares theory. Two scenarios having two and four knots at the boundary points are described in this paper. Two examples are presented to illustrate the theory. The first example approximates a known mathematical function on an irregular grid. The second example uses a real data set to approximate the geoid height. LS-BICSA can thus provide reliable results for many geoscience applications where it is required to approximate the function values using a smooth spline surface in the least squares sense.