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            <title xml:lang="en">Gift-Wrapping based Preimage Computation Algorithm</title>
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              <p> Based  on  a classical convex hull   algorithm called Gift-Wrapping, the  purpose of the paper is to provide a new algorithm for computing the  vertices of a  polytope called preimage  - roughly the  set of naive  digital planes containing  a  finite subset $S$ of   $\mathbb{Z}^3$.  The    vertices of  the upper  hemisphere,    the ones of the  lower  hemisphere  and  at  last   the equatorial  vertices   are  computed  independently.  The  principle of the  algorithm is based on duality  and especially  on the  fact  that the   vertices  of the   preimage  correspond to faces  of  the input  set  $S$ or  of its  chords  set  $S\ominus S \cup \{(0,0,1)\}$.  It allows to  go from one  vertex to  another by gift-wrapping until the whole region of interest has been  explored.</p>
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