Coefficient–Based Spline Data Reduction by Hierarchical Spaces

  • Cesare Bracco
  • Carlotta GiannelliEmail author
  • Alessandra Sestini
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10521)


We present a data reduction scheme for efficient surface storage, by introducing a coefficient–based least squares spline operator that does not require any pointwise evaluation to approximate (in a lower dimension spline space) a given bivariate B–spline function. In order to define an accurate approximation of the target spline with a significant reduction of the space dimension, this operator is subsequently combined with the hierarchical spline framework to design an adaptive method that exploits the capabilities of truncated hierarchical B–splines (THB–splines). The resulting THB–spline simplification approach is validated by several numerical tests. The target B–spline surfaces include approximations of functions whose analytical expression is available, reconstructions of geographic data and parametric surfaces.


Data reduction Quasi–interpolation Hierarchical splines THB–splines 



The support by MIUR “Futuro in Ricerca” programme through the project DREAMS (RBFR13FBI3) and by the Istituto Nazionale di Alta Matematica (INdAM) through Gruppo Nazionale per il Calcolo Scientifico (GNCS)—“Finanziamento Giovani Ricercatori” and “Progetti di ricerca” programmes—and Finanziamenti Premiali SUNRISE are gratefully acknowledged.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Cesare Bracco
    • 1
  • Carlotta Giannelli
    • 1
    Email author
  • Alessandra Sestini
    • 1
  1. 1.Dipartimento di Matematica e Informatica “U. Dini”Università di FirenzeFirenzeItaly

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