, 86:89 | Cite as

Adaptive quasi-interpolating quartic splines

  • Martin Hering-BertramEmail author
  • Gerd Reis
  • Frank Zeilfelder


We present an adaptive quasi-interpolating quartic spline construction for regularly sampled surface data. The method is based on a uniform quasi-interpolating scheme, employing quartic triangular patches with C 1-continuity and optimal approximation order within this class. Our contribution is the adaption of this scheme to surfaces of varying geometric complexity, where the tiling resolution can be locally defined, for example driven by approximation errors. This way, the construction of high-quality spline surfaces is enhanced by the flexibility of adaptive pseudo-regular triangle meshes. Numerical examples illustrate the use of this method for adaptive terrain modeling, where uniform schemes produce huge numbers of patches.


Triangular splines Adaptive approximation Quasi interpolation 

Mathematics Subject Classification (2000)

65D07 Splines 65D17 and 68U07 Computer aided design 65D18 Computer graphics and computational geometry 


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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Martin Hering-Bertram
    • 1
    Email author
  • Gerd Reis
    • 2
  • Frank Zeilfelder
    • 3
  1. 1.Fraunhofer ITWMKaiserslauternGermany
  2. 2.DFKIKaiserslauternGermany
  3. 3.Technical University of DarmstadtDarmstadtGermany

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