A Hybrid Models Deformation Tool for Free-Form Shapes Manipulation

This paper addresses the way models mixing various types of geometric representations (e.g. NURBS curves and patches, polylines, meshes), potentially immersed in spaces of different dimensions (e.g. NURBS patch and its 2D trimming lines), can be deformed simultaneously. The application domains range from the simple deformation of a set of NURBS curves in a 2D sketcher to the simultaneous deformation of meshes, patches as well as trimming lines lying in parametric spaces. The deformation itself results from the solution of an optimization problem defined by a set of geometric constraints and deformation behaviors. This new breakthrough on how geometric models can be manipulated has been made possible thanks to our linear mechanical model of deformation that can be coupled to manifolds of dimension zero (e.g. points, vertices) and one (e.g. edges, segments) whatever the spaces dimension. An extended constraints toolbox is also proposed that enables the specification of both characteristic points/curves and continuity conditions between the various geometric models. The link between the semantics of the deformation behaviors and the geometric models is ensured through the use of multiple minimizations. The approach is illustrated with several examples coming from our prototype software.