Geometric Deformation by Merging a 3D-Object with a Simple Shape

Deformation techniques are often used to model the shape of geometric objects. This paper presents a new geometric deformation technique allowing local deformation of the shape of an object by merging the object with a simple 3D-shape (sphere, ellipsoid, ...). Two kinds of eeects can be obtained: the simple shape is used to produce either a bump or a dent on the object. The object is deformed so that it includes or it embeds the simple shape. In order to deform the object, the 3D-space where it lies is continuously deformed so that the object is bumped and the shape of the bump corresponds to the simple 3D-shape. If the surfaces of both the original object and the simple shape are smooth (continuously diierentiable), the surface of the deformed object is also smooth. Moreover, topological properties of the object are unchanged, and the volume variation of the deformed object is controlled by the volume delimited by the simple shape. An interactive deformation tool based on this technique is presented. It comprises a convex 3D-shape and a center (a 3D point included in the shape). The user can interactively control the deformation by changing the parameters of the tool shape and the position of the tool center. Control of the parameters is particularly intuitive. R esum e Les techniques de d eformation sont souvent uti-lis ees pour modeler la forme d'objets g eom etriques. Cet article pr esente une nouvelle technique de d efor-mation qui permet de d eformer localement un objet en le fusionnant avec une forme 3D simple (sph ere, ellipso de, ...). Deux types d'eeets peuvent ^ etre obte-nus: la forme simple est utilis ee pour produire une d e-formation en bosse ou en creux. L'objet est d eform e de faa con a inclure ou a englober la forme simple. AAn de d eformer l'objet, l'espace 3D dans lequel il est plac e est d eform e continument de telle faa con que l'objet soit bossel e et que la forme de la bosse cor-responde a la forme simple. Si les surfaces de l'ob-jet initial et de la forme simple sont lisses (continu-ment dii erentiables), la surface de l'objet d eform e l'est aussi. De plus, les propri et es topologiques de l'objet sont inchang ees et la variation de volume de l'objet d eform e est contr^ ol e par le volume d elimit e par …