Research On Smooth And Coordinated Deformation Algorithm Of Complex Multi Surfaces Based On Rigid Frame Model

Geometric modeling technology is the kernel of Computer Aided Design/Computer AidedManufacturing (CAD/CAM), and surface deformation is an important part of geometric modelingtechnology. At present, free-form surface has widely been used in aircraft, automotive and otherindustrial areas of digital product design. In order to meet specific design requirments, repeatedediting and consciously changing works of the relevant surfaces are demanded. Therefore, practicaldeformation technology of surface can not only shorten product design cycle, but also become one ofthe key technologies in the rapid development and innovative design of digital products. In this paper,smooth and coordinated deformation of complex surface based on rigid frame model is studied; themain contents and research results are as follows:Based on the theory of rigid frame deformation, shape modification algorithm of the singlesurface under external load driven is researched. Because, single surface can perfectly express thesimple shape of some products, deformation design of single surface under external load is studiedfirstly, mainly including establishing rigid frame model, the effects on products shape as loadchanging, the predictability of surface shape modification and other issues. The content researched inthis part does some theoretical preparation for follow-up smooth and coordinated deformation ofcomplicated surface.Shape modification algorithm of the single surface under constrained optimization based on rigidframe model is discussed. The requirements of surface deformation design are abstracted to geometricconstraints (point constraints, point and normal vector constraints, and isoparametric line constraints,etc.) firstly, and then, appropriate optimizing objective function is presented, lastly, through solving aconstrainted optimization problem to obtain the size and direction of loads imposed on nodes. Surfacesatisfying the given geometric constraints after deformation can be achieved.On the basis of deformation design for single surface, a smooth and coordinated deformationalgorithm of complex surface based on rigid frame model is presented. The rigid frame model ofcomplex surface is established through merger and fracture of control mesh topology among thesurfaces. Shape deformation of multi-surfaces under load and geometric constraints is achieved byfinite element method. The deformed surfaces not only have “fine change” effect, but also keepsmooth connection as before.Example results show that the algorithm presented has achieved good results, and can be appliedto surface geometric modeling.