摘要
为了得到理想的几何变形效果,将伸缩因子和toric退化理论作用到toric-Bézier曲线上,最终实现曲线的自由变形。首先给定提升函数构造出带参数t的权因子集,从而得到带参数t的toric-Bézier曲线;然后选取变形中心、变形区间以及变形区间边界光滑度,根据控制函数f(t)的选取原则选取适当的控制函数,确定伸缩因子进而构造出变形矩阵,再将其作用到上述带参数t的toric-Bézier曲线上;最后,当t趋于无穷大时,得到目标曲线,实现toric-Bézier曲线的自由变形,通过交互改变控制参数,可达到预期的变形效果,并可给出toric-Bézier曲线的变形动画演示。实验表明,该技术计算简单、易于控制,可兼顾整体与局部对曲线进行自由变形,具有可调性和预见性,叠加使用可得到丰富的变形动画效果,适用于几何造型和计算机动画等领域。
To gain ideal geometric deformation results,the expansion factor and the toric degeneration are applied to the toric-Bézier curve,realizing the free-form deformation of the curve.Firstly,the with parameter t weight factor was constructed by the given lifting function,thereby obtaining the with parameter t toric-Bézier curve.Secondly,according to the selected center of deformation,region of deformation,smoothness of deformation region boundary,and select rule of the control function f(t),the appropriate control function was selected,and the extension factor was determined,thus constructing the deformation matrix.Then,the deformation matrix acted on the with parameter t toric-Bézier curve.At last,when t tended to reach infinity,the target curve was obtained,and the free-form deformation of the toric-Bézier curve could be achieved.By changing the control parameters interactively,the expected deformation result could be attained,and the deformation animation demo of the toric-Bézier curve could be yielded.The experiments showed that the technique was simple and easy to control.The curve could be deformed freely both globally and locally,and the technique was of adjustability and foreseeability.Such a technique could be in repeated use,thereby generating the rich deformation animation results,which could be applicable to many fields,such as geometric modeling and computer animation.
作者
王涵
朱春钢
WANG Han;ZHU Chun-gang(School of Computer Science and Technology,Shandong Technology and Business University,Yantai Shandong 264005,China;School of Mathematical Sciences,Dalian University of Technology,Dalian Liaoning 116024,China)
出处
《图学学报》
CSCD
北大核心
2022年第6期1070-1079,共10页
Journal of Graphics
基金
国家自然科学基金项目(12001327,12071057)。
