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Approximation of Digital Surfaces by a Hierarchical Set of Planar Patches

Jocelyn Meyron Tristan Roussillon 1 
1 Origami - Origami
LIRIS - Laboratoire d'InfoRmatique en Image et Systèmes d'information
Abstract : We show that the plane-probing algorithms introduced in Lachaud et al. (J. Math. Imaging Vis., 59, 1, 23-39, 2017), which compute the normal vector of a digital plane from a starting point and a set-membership predicate, are closely related to a three-dimensional generalization of the Euclidean algorithm. In addition, we show how to associate with the steps of these algorithms generalized substitutions, i.e., rules that replace square faces by unions of square faces, to build finite sets of elements that periodically generate digital planes. This work is a first step towards the incremental computation of a hierarchy of pieces of digital plane that locally fit a digital surface.
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https://hal.archives-ouvertes.fr/hal-03769038
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Submitted on : Tuesday, September 27, 2022 - 9:39:09 AM
Last modification on : Monday, November 7, 2022 - 9:34:38 AM

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Jocelyn Meyron, Tristan Roussillon. Approximation of Digital Surfaces by a Hierarchical Set of Planar Patches. Discrete Geometry and Mathematical Morphology, Oct 2022, Strasbourg, France. pp.409-421, ⟨10.1007/978-3-031-19897-7_32⟩. ⟨hal-03769038⟩

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