Strathprints logo
Strathprints Home | Open Access | Browse | Search | User area | Copyright | Help | Library Home | SUPrimo

Scattered data fitting by direct extension of local polynomials to bivariate splines

Davydov, O. and Zeilfelder, F. (2004) Scattered data fitting by direct extension of local polynomials to bivariate splines. Advances in Computational Mathematics, 21 (3-4). pp. 223-271. ISSN 1019-7168

[img]
Preview
PDF - Submitted Version
Download (3560Kb) | Preview

    Abstract

    We present a new scattered data fitting method, where local approximating polynomials are directly extended to smooth (C 1 or C 2) splines on a uniform triangulation (the four-directional mesh). The method is based on designing appropriate minimal determining sets consisting of whole triangles of domain points for a uniformly distributed subset of . This construction allows to use discrete polynomial least squares approximations to the local portions of the data directly as parts of the approximating spline. The remaining Bernstein-Bæ#169;zier coefficients are efficiently computed by extension, i.e., using the smoothness conditions. To obtain high quality local polynomial approximations even for difficult point constellations (e.g., with voids, clusters, tracks), we adaptively choose the polynomial degrees by controlling the smallest singular value of the local collocation matrices. The computational complexity of the method grows linearly with the number of data points, which facilitates its application to large data sets. Numerical tests involving standard benchmarks as well as real world scattered data sets illustrate the approximation power of the method, its efficiency and ability to produce surfaces of high visual quality, to deal with noisy data, and to be used for surface compression.

    Item type: Article
    ID code: 2172
    Keywords: scattered data fitting, bivariate splines, four-directional mesh, local polynomial least squares approximation, Bernstein-Bézier techniques, minimal determining set, Mathematics, Computational Mathematics, Applied Mathematics
    Subjects: Science > Mathematics
    Department: Faculty of Science > Mathematics and Statistics
    Related URLs:
      Depositing user: Strathprints Administrator
      Date Deposited: 04 Jan 2007
      Last modified: 04 Sep 2014 13:25
      URI: http://strathprints.strath.ac.uk/id/eprint/2172

      Actions (login required)

      View Item

      Fulltext Downloads: