Abstract Scattered data is, by definition, irregularly spaced. Uniform surface schemes are not well adapted to the locally varying nature of such data. Conversely, Triangular B‐Spline surfaces 2 are more flexible in that they can be built over arbitrary triangulations and thus can be adapted to the scattered data. This paper discusses the use of DMS spline surfaces for approximation of scattered data. A method is provided for automatically triangulating the domain containing the points and generating basis functions over this triangulation. A surface approximating the data is then found by a combination of least squares and bending energy minimization. This combination serves both to generate a smooth surface and to accommodate for gaps in the data. Examples are presented which demonstrate the eftectiveness of the technique for mathematical, geographical and other data sets.

Abstract Triangular B‐splines surfaces are a tool for representing arbitrary piecewise polynomial surfaces over planar triangulations, while automatically maintaining continuity properties across patch boundaries. Recently, Alfeld et al. [1] introduced the concept of spherical barycentric coordinates which allowed them to formulate Bernstein‐Bézier polynomials over the sphere. In this paper we use the concept of spherical barycentric coordinates to develop a similar formulation for triangular B‐splines, which we call spherical triangular B‐splines. These splines defined over spherical triangulations share the same continuity properties and similar evaluation algorithms with their planar counterparts, but possess none of the annoying degeneracies found when trying to represent closed surfaces using planar parametric surfaces. We also present an example showing the use of these splines for approximating spherical scattered data.