Free Form Deformation Method of Parametric Surfaces on Rectangular Region

According to free form deformation of parametric surfaces, a new method based on extension function is proposed. It is made by piecewise polynomials and defined on rectangular region. Based on these, the new extension factor we constructed not only possesses perfect properties such as symmetry, single peak, linear peak and region peak, but also holds some parameters which have obvious geometric meanings. In real applications, the extension factor is very suitable for interactive design due to these properties and extraordinary parameters. Furthermore, the new extension factor is easy to construct and convenient to control because of its simple polynomial forms. Applying the deformation matrix constructed by the new extension factor to the original surfaces’ equations, plentiful deformation surfaces can be achieved. Deformation effects such as shearing, concave & convex, expand & contract and changing of deformation center can be obtained. With the help of superimposing, more complex deformation effects can be realized. Lots of numerical experiments are given at the end of paper which illustrate different kinds of deformation effects and plentiful adjusting effects of different parameters.