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.
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Kiel, S. (2012). Verified Spatial Subdivision of Implicit Objects Using Implicit Linear Interval Estimations. In: Boissonnat, JD., et al. Curves and Surfaces. Curves and Surfaces 2010. Lecture Notes in Computer Science, vol 6920. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27413-8_25
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DOI: https://doi.org/10.1007/978-3-642-27413-8_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-27412-1
Online ISBN: 978-3-642-27413-8
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