Abstract
The aim of the paper is to define an algorithm for computing preimages - roughly the sets of naive digital planes containing a finite subset S of ℤ3. The method is based on theoretical results: the preimage is a polytope that vertices can be decomposed in three subsets, the upper vertices, the lower vertices and the intermediary ones (equatorial). We provide a geometrical understanding (as facets on S or S ⊝ S) of each kind of vertices. These properties are used to compute the preimage by gift-wrapping some regions of the convex hull of S or of S ⊝ S ∪ {(0,0,1)}.
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Gerard, Y., Feschet, F., Coeurjolly, D. (2008). Gift-Wrapping Based Preimage Computation Algorithm. In: Coeurjolly, D., Sivignon, I., Tougne, L., Dupont, F. (eds) Discrete Geometry for Computer Imagery. DGCI 2008. Lecture Notes in Computer Science, vol 4992. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79126-3_28
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DOI: https://doi.org/10.1007/978-3-540-79126-3_28
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