Deformation Of Parametric Curves And Surface Based On Extension Function Transformation

With the rapid development of science and technology, Geometric modeling technology of curves and surfaces has become a research hotspot. In order to accelerate the integration, unification and networking of Manufacturing Industries and Graphics Industries, Modeling technology of curves and surfaces has expended from the research of representation, intersection and blending curves and surfaces to space deformation of parametric curves and surfaces. Barr [1] was the scholar who firstly put forward the deformation thought into geometric modeling. Based on this, Sederberg et al [3] further proposed free-form deformation (abbr. FFD). In order to get better and more efficient deformation effect, a large number of experts and scholars at home and abroad have proposed different kind of FFD techniques from a different viewpoint,but these techniques need a strong theoretical knowledge, also has deficiencies in controlling deformation direction and deformation amplitude. In order to overcome these shortcomings, Some scholars put forward one effective deformation method-extension deformation method, it is simple in calculation and easy in operation. Considering these excellent properties, this paper has done the following work:1. According to 2D & 3D free-form deformation of parametric curves and free curves, a new algorithm based on polynomial extension function with platform is proposed. The new extension factor constructed by the function not only possesses perfect properties such as interval peak, peak value and symmetries, but also has the closure property; The global, local, periodic deformation effects are illustrated through plentiful examples.Considering free-form deformation of parametric surfaces, Inspired by curve deformation, a new algorithm based on binary polynomial extension factor with platform is put forward to solve the free-form deformation of parametric surfaces.2. Deformation matrices are built on the basis of the extension factor. Applying it on the equation of the surfaces, plentiful deformation surfaces can be achieved. Experiments show that the method is not only easy to compute, simple to manipulate, but also can be used repeatedly to obtain more practical and artistic deformation effects.3. In order to obtain plentiful modeling effects, a new extension factor which possesses single peak, domain peak and convex polygonal supported domain is constructed. First, an extension factor whose definition domain is an arbitrary convex polygonal area is introduced. Then, space deformation matrix is constructed on it. Experiments show that we can flexibly deform surfaces by adjusting some parameters...