On the volume of sets bounded by refinable functions

Jan Hakenberg and Ulrich Reif

Applied Mathematics and Computation, 2016, vol. 272, issue P1, 2-19

Abstract: We present a method for the precise determination of the volume of subsets of Rd which are bounded by a hypersurface parametrized by a set of refinable functions. The derivation is based on the linear refinement equations rather than on closed form expressions of these functions, which may not be available. In particular, our approach makes it possible to compute the area of planar domains bounded by subdivision curves or the volume of spatial domains bounded by subdivision surfaces.

Keywords: Volume; Subdivision surface; Area; Subdivision curve; Refinable function (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:272:y:2016:i:p1:p:2-19

DOI: 10.1016/j.amc.2015.06.050

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