ISSN 1000-1239 CN 11-1777/TP

• 图形图像 •

### 矩形域上的参数曲面自由变形算法

1. 1(合肥工业大学数学学院 合肥 230009); 2(合肥工业大学计算机与信息学院 合肥 230009) (lizhang@hfut.edu.cn)
• 出版日期: 2016-05-01
• 基金资助:
国家自然科学基金-广东联合基金重点项目(U1135003)；国家自然科学基金项目(61472466,61100126)；安徽省自然科学基金项目(1508085QF116)；中央高校基本科研业务费专项资金项目(JZ2015HGXJ0175)；中国博士后科学基金项目(2015M571926)

### Free Form Deformation Method of Parametric Surfaces on Rectangular Region

Zhang Li1, Ge Xianyu1, Tan Jieqing1,2

1. 1(School of Mathematics, Hefei University of Technology, Hefei 230009); 2(School of Computer and Information, Hefei University of Technology, Hefei 230009)
• Online: 2016-05-01

Abstract: 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.