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                <term xml:lang="en">enclosure</term>
                <term xml:lang="en">additive manufacturing</term>
                <term xml:lang="fr">support</term>
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              <p>Additive manufacturing is a process by which a three dimensional object is created layer after layer, through selective deposition of material.It often requires the automated generation of auxiliary shapes, to temporarily support the object, to protect its surface, or to carve inner cavities and reduce material usage.In this context, we define a ``printable enclosure'' as a minimal volumeenclosing a given shape and whose boundary can be printed at the smallest possible thickness while ensuring proper bonding between layers.Such an enclosure is well suited to serve as auxiliary structure for additive manufacturing: it is easy to print and require little material. In thispaper, we demonstrate its use on three different applications: enclosing aprint within protective walls that are close to the surface; generating largeinner cavities whose walls are printable, and finally modeling support structures that provide a dense support to the downward facing surfaces while vanishing as quickly as possible below the supported object.We obtain the shape of an enclosure by considering constraints on its set of slices along horizontal planes. In practice, the set of slices is discrete and the constraints afford for an efficient sweep-like construction algorithm using morphological operations on the slices. We discuss the printability and optimality of the enclosures and their boundary walls.</p>
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              <p>La fabrication additive produit des objets en déposant un matériau en couchessuccessives.Cela requiert souvent la synthèse ou l'impression de formes additionnelles poursupport l'objet en cours de fabrication, protéger sa surface ou bien y creuserdes cavités afin de limiter la quantité de matériel utilisé.Dans ce contexte, nous définissons une "enceinte ajustée" comme le pluspetit volume contenant une forme donnée et dont le bord peut être fabriqué à laplus petit épaisseur possible tout en garatissant le bon maintient des couches dematière successives.Ces enceintes ajustées sont utiles pour la fabrication additive. Elles sontrapide à fabriquer et nécessitent peu de matériau. Cet article montre leurutilité dans trois applications~: la génération d'une paroi protectrice restantproche de l'objet à fabriquer, la génération de cavités aussi grandes quepossible à l'intérieur d'un objet et dont les parois restent fabriquables;enfin, la modélisation de structures de support denses dans le voisinageimmédiat des parties basses de l'objets et diminuant le plus rapidementpossible en dessous.Ces enceintes sont modélisées en considérant les contraintes s'opérant surleurs coupes transversales, par un plan horizontal. Nous décrivons unalgorithme par balayage permettant de modéliser rapidement ces enceintes àl'aide d'opérations morphologiques sur les coupes.</p>
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