3D OBJECTS MODELISATION USING PROFILED AND RAMIFIED GENERALIZED CYLINDERS AND JUNCTION PROBLEMS BETWEEN SURFACES RAISED BY THESE CYLINDERS
Generalized cylinders, frrst described at the beginning of the seventies, are frequently used in C.A.O., C.F.A.O., medical applications, robotics and shape recognition. A generalized cylinder is produced by moving a given contour curve along a given trajectory curve. In this thesis, sorne methods allowing to build 3D objects with the help ofthese generalized cylinders are described. In particular, sorne user defined parameters described by functions (profiles, orientation and deformation of the contour curve) allow to extend the family of the objects created by sweeping. A formai framework has been defmed for the functions associated to generalized cylinders, in order to provide, as most as possible, the validity of the created objects. Sorne simple and practical algorithrns have been developed, with control covering problems during the hilding of the generalized cylinders. In a somewhat unusuam way, a method allowing to define generalized cylinder through quaternions is presented. lt gives athe ability to înclude deformation parameters of the contour curve in a same mathematical framework. In the second part of this thesis, sorne methods allowing to build arborescent generalized cylinders are described. The notion of arborescent trajectory is introduced and we propose sorne systematic methods for difmed tubular parts of which the junction with G 1 continuity is leaning against. The achievement of this junctionis based on the theory of surfaces connections, because generalised cylinders are represented by means offiee form surfaces. Thus, the main connection techniques with G 1 continuity between rectangular and triangular Bézier patches are reminded and extended to B-splines patches. A conplete study of the constraints with the connecting functions is also described. In order to validate the previous methods in a given framework, a discussion on C and G continuity problems is proposed. lts purpose is to define a derivation method allowing to include the set of G-continuous functions into a set of C-continuous functions.