Periodic Deformation Based on Ridge Curves for Parametric Surfaces

Abstract

Abstract:

In order to obtain ideal modeling effects of parametric surfaces, a new polynomial extension factor was constructed. The new extension factor had excellence of the existed extension factors, and can achieve its maximum in the region. In the extended technique for free-form deformation of parametric surfaces, the original surface can be deformed by the ridge curves. Then the periodic deformation of a surface can be achieved by the ridge curves. Experiments show that the method is simple, intuitive and easy to control, and desired deformations can be achieved easily. It can be used in many fields such as geometric modeling, computer animation and CAD/CAM.

摘要：

为得到理想的参数曲面造型效果,构造了一种新的基于多项式的伸缩因子,它不仅具有已有伸缩因子的特性,还具有区域峰值性;同时引入脊曲线的概念,对曲面进行控制变形,从而对曲面进行雕刻;然后利用脊曲线实现对曲面的周期控制变形。实验结果表明,该方法计算简单、易于控制,可以得到丰富的变形效果,适用于几何造型、计算机动画、CAD/CAM等领域。


关键词: 参数曲面, 伸缩因子, 雕刻, 周期变形

CLC Number:

TP391

LIU You-Ta, WANG Zhi-Guo, ZHOU Lai-Shui, WANG Xiao-Beng. Periodic Deformation Based on Ridge Curves for Parametric Surfaces[J]. China Mechanical Engineering, 2012, 23(15): 1860-1864.

陆友太, 王志国, 周来水, 王小平. 基于脊曲线控制的参数曲面周期变形[J]. 中国机械工程, 2012, 23(15): 1860-1864.

References

[1]Barr A H. Global and Local Deformations of Solid Primitives[J]. Computer Graphics, 1984, 18 ( 3 ) : 21 - 30.
[2]Gudukbay U,Ozgiic B. Free-form Solid Modeling Using Deformations [J]. Computer & Graphics, 1990,14(3/4) :491-500.
[3]Sederberg T W,Parry R. Free-form Deformations of Solid Geometric Models[J]. Computer Graphics, 1986,20(4) : 151-160.
[4]Coquillart S. Extended Free-form Deformation: a Sculpting Tool for 3D Geometric Modeling[J]. Computer Graphics, 1990,24(4) : 187-196.
[5]Lazarus F,Coquillart S,Jancene P. Axial Deformation: an Intuitive Technique[J]. Computer- Aided Design, 1994,26(8): 607-613.
[6]Feng Jieqing,Ma Lizhuang,Peng Qunsheng. A New Free-form Deformation through the Control of Parametric Surfaces [J]. Computer & Graphics, 1996,20 (4):531-539.
[7]Au C K, Yuen M M F. Unified Approach to NURBS Curves Shape Modification[J]. Computer -Aided Design,1995,27(2) :85-93.
[8]Sdnchez R J. A Simple Technique for NURBS Shape Modification [J]. IEEE Transaction on Computer Graphics & Applications, 1997,17 ( 1 ): 52-59.
[9]Wang Xiaoping, Ye Zhenglin, Meng Yaqin, et al. Space Deformation of Parametric Surface Based on Extension Function [J]. International Journal of CAD/CAM, 2002,1 (1): 23-32.
[10]Wang Xiaoping, Zhou Rurong, Ye Zhenglin, et al. Periodic Deformation of Parametric Surface[J]. Chinese Journal of Mechanical Engineering, 2004, 17(3) :394-398.
[11]Wang Xiaoping, Liu Shenglan, Zhang Liyan. Con structing Surface Features through Deformation [J]. International Journal of Image and Graphics, 2010,10(1) :41-56.
[12]赵红星[1,2],叶正麟[1],宋文龙[1],郑红婵[1].基于仿射变换和B样条的参数曲面变形方法[J].西北工业大学学报,2006,24(3):384-388.
[13]宋来忠[1],彭刚[2],杨文颖[1],张先波[1].用于参数曲线自由变形的新的伸缩因子[J].工程图学学报,2009,30(3):87-93.
[14]刘植.CAGD中基于Bézier方法的曲线曲面表示与逼近[D].合肥工业大学,2009:
[15]宋来忠[1],彭刚[2],沈艳军[1].参数曲面多边形区域上变形的伸缩因子与实验[J].计算机工程与应用,2011,47(12):192-195.
[16]李靖谊.交互式计算机图形学[M].北京:航空工业出版社,2000..
[17]王国瑾等著.计算机辅助几何设计[M],2001:400.