Verified spatial subdivision of implicit objects using implicit linear interval estimations

Authors:
Stefan Kiel
Affiliations:
University of Duisburg-Essen, Duisburg
Venue:
Proceedings of the 7th international conference on Curves and Surfaces
Year:
2010

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Abstract

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.