• 虚拟现实与数字媒体 •

### 基于结式的曲面拼接与三维造型

1. 天津职业技术师范大学 信息技术工程学院, 天津 300222
• 收稿日期:2015-04-24 修回日期:2015-06-30 出版日期:2015-10-10 发布日期:2015-10-14
• 通讯作者: 李耀辉(1968-),男,河北邢台人,教授,博士,主要研究方向:符号计算,philliplee@163.com
• 作者简介:武志峰(1974-),男,河北邯郸人,教授,博士,主要研究方向:智能算法、数据挖掘;宣兆成(1966-),男,黑龙江齐齐哈尔人,教授,博士,主要研究方向:可信计算。
• 基金资助:
天津市教委高校自然科学基金资助项目(20071311);天津工程师范学院自然科学基金资助项目(KJY12-09,KJ20080039);天津工程师范学院留学回国基金资助项目(RC14-50)。

### Surface blending using resultant and three-dimensional geometric modeling

1. School of Information Technology and Engineering, Tianjin University of Technology and Education, Tianjin 300222, China
• Received:2015-04-24 Revised:2015-06-30 Online:2015-10-10 Published:2015-10-14

Abstract: As many geometric modelings essentially are the problems of the surface blending with constrained conditions, a nonlinear homotopy mapping method was presented to compute the surface equation of three-dimensional modeling on the base of linear homotopy method. In the method, the interpolation polynomial was computed firstly by using the position of cross-over section or biological slices as the interpolation points. Then, this interpolation polynomial was regarded as the nonlinear continuous homotopy mapping function and substituted into the polynomials of primary surfaces and auxiliary surfaces respectively to get blending surface equation. Thus, two univariable equations were obtained when the interpolated variable in interpolation polynomial was used as the variable but the others in the equations of primary surfaces and auxiliary surfaces were used as parameters. Furtherly, Sylvester resultant was used to eliminate the interpolated variable in these two equations to achieve the modeling surface which satisfied the constraints. The proposed method can realize surface modeling with control points and geometric modeling with constraints, and it is more practical because it can redefine and change the the intermediate position and shape.