SHAPE MODIFICATION OF NURBS CURVES

AND SURFACES BASED ON FORCE

DENSITY METHOD

WANG Qing  KE Yinglin  LI Jiangxiong

(College of Mechanical and Energy Engineering, Zhejiang University, Hangzhou 310027 )

Abstract: An effective solution for exact shape deformation, dealing with both curves and surfaces in NURBS form, is proposed based on the theory of force density method (FDM). Using an analogy between the control polyhedron and the bar network, four novel minimization models are constructed, i.e. minimization of the forces variation, minimization of the forces, minimization of the damped bars length, minimization of the nodes displacement, which represent different geometrical and physical properties. All objective functions are described by a uniform formula with the displacement of the control points and then the optimization problem is solved efficiently by using quadratic programming with linear constraints. For efficiency, a fast algorithm for evaluating the objective functions is applied and this makes the deformation suitable for realtime interactive design. Experimental examples show that the proposed method can be widely applied to complicated shape modeling, such as detail feature design, reverse modeling, etc.

Key words: Shape modification Force density method Constrained optimization Concept design Reverse engineering

CLC No: TP391

国家自然科学基金资助项目(50575098). Received 20060328, received in revised form 20060821