Verified Spatial Subdivision of Implicit Objects Using Implicit Linear Interval Estimations

  • Stefan Kiel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6920)


In this paper we describe the LIETree, a new data structure for verified spatial decomposition of implicit objects. The LIETree is capable of utilizing implicit linear interval estimations for calculating a verified enclosure of the implicit function’s codomain. Furthermore, it uses consistency techniques to tighten the object enclosure. Overall, it delivers improved accuracy and uses fewer nodes than common uniform subdivision schemes using interval or affine arithmetic for enclosure.


Interval Arithmetic Interval Extension Hierarchical Decomposition Interval Vector Spatial Subdivision 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Stefan Kiel
    • 1
  1. 1.University of Duisburg-EssenDuisburgGermany

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