Free Form Deformations or Deformations Non-Constrained by Geometries or Topologies

Free-form deformations are widely used to model 3D objects. In these methods “free-form” designates: “whatever the object is, whatever its description and topology, we are able to deform it”. They limit the user interaction to pull some points of an embedding rough mesh. From the user point-of-view, it does not matter if the object manipulated is 3-dimensional, of 0-genus or a parametric surface, he or she always uses the same process to model a complex object: load an initial object from a library and deform it via Ffd methods to follow his (her) needs. A large number of deformation methods have been published, allowing new deformations, new kinds of controls or enhancing the description of resulting objects. In fact advantage of deformation non-constrained by geometries is also a drawback: as it only manipulates points it could only result in points, so its necessary to use and maintain the neighborhood (the topology) or the surface expression on a second hand, as these methods do not care of object description. 1 Free-Form Deformations from the Beginning The work of creating an object from an empty scene is quite tedious, first methods of mesh manipulation [28, 31] highlight the future needs of user-oriented, efficient modeling methods. They first deform an object from a single vertex, diffusing the deformation on neighbors according to edges distance weights. The work of Barr [2] initiates free-form deformation techniques. It permits to deform an existing object globally (see Fig. 1), with mathematical functions (taper, bend, twist). Since it was not a “vertex by vertex” displacement method it simplifies the creation process. This method does not act on topology, keeping the neighbors as they were, with the edges R. Raffin (B) Aix-Marseille University, LSIS UMR 7296, Domaine universitaire de Saint Jérôme, Av. Escadrille Normandie-Niemen, Marseille Cedex 13397, France e-mail: [email protected] M. González Hidalgo et al. (eds.), Deformation Models, Lecture Notes in Computational 49 Vision and Biomechanics 7, DOI: 10.1007/978-94-007-5446-1_2, © Springer Science+Business Media Dordrecht 2013