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Journal Articles Theoretical Computer Science Year : 2016

An output-sensitive algorithm to compute the normal vector of a digital plane

Jacques-Olivier Lachaud
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Xavier Provençal
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Abstract

A digital plane is the set of integer points located between the parallel planes. We solve the following problem: how to compute the exact normal vector of a digital plane given only a predicate that answers the question “is a point x in the digital plane or not”. Our approach is iterative and “as local as possible”. We provide a worst-case complexity bound in O(ωlog⁡ω)O(ωlog⁡ω) calls to the predicate, where ω is equal to the arithmetic thickness parameter of the digital plane. Furthermore, our algorithm presents a much better average behavior in practice.

Dates and versions

hal-01294966 , version 1 (30-03-2016)

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Jacques-Olivier Lachaud, Xavier Provençal, Tristan Roussillon. An output-sensitive algorithm to compute the normal vector of a digital plane. Theoretical Computer Science, 2016, 624, pp.73-88. ⟨10.1016/j.tcs.2015.11.021⟩. ⟨hal-01294966⟩
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