Research On Free-Form Deformation Modeling With Constrained Optimization Technology

We can design, edit or transform our models simply and conveniently because Free-Form Deformation (FFD), as a new method of geometry modeling in CAD /CAM system, makes great progress in the last 20 years. But some limitations still exist.After analyzing some classical algorithms, the direct manipulation of NURBS-based FFD is studied in detail. The common problem about pseudo-inverse matrix is solved through the constrained optimization method. The main research contents include as following:1. Sketch the development and present condition abroad and home about FFD. The whole process about FFD modeling system is mentioned, especially the direct manipulation of NURBS-based FFD and some classical algorithms.2. The method of penalty function multiplier is used successfully in the algorithm of the direct manipulation of NURBS-based FFD. The pseudo-inverse matrix is avoided, and some problems are solved through numeration method . The feasibility is proved in theory and the explicit solution is obtained in the conditions of changing the control points or weights.3. The uniform model of free-form deformation is studied. Based on the direct manipulation of NURBS-based FFD and the constrained optimization method, a uniform model which has a uniform skeleton structure is feasible, through separating the definition of deformation control methods and the definition of deformation spaces.4. A FFD modeling system is implemented, which includes Globe Deformation, FFD and the direct manipulation of NURBS-based FFD with constrained optimization method and a uniform model through which three kinds of control methods, curve control, surface control and geometry constrained control, could be joined together effectively.