凸多边形域上的参数曲面自由变形  

Free-Form Deformation of Parametric Surfaces on Convex Polygonal Domain

作　　者：张莉[1] 余慧芳[1] 檀结庆[1,2] 

机构地区：[1]合肥工业大学数学学院,合肥230009 [2]合肥工业大学计算机学院,合肥230009

出　　处：《计算机辅助设计与图形学学报》2015年第5期892-899,共8页Journal of Computer-Aided Design & Computer Graphics

基　　金：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(61472466;61100126)

摘　　要：为了获得丰富的曲面造型效果,构造了一种兼具单峰性和区域峰值性,支撑区域为任意凸多边形域的伸缩因子.首先引入基于凸多边形域的伸缩因子;然后构造了空间变形矩阵;最后将上述变形矩阵作用于待变形曲面的方程上,获得相应的变形效果.数值实例结果表明,通过调控支撑区域、峰值区域、变形中心、主方向、伸缩参数和光滑参数,可以灵活地对曲面变形;该方法不仅计算简单、易于控制,还能精确地控制变形的范围,迭加使用可以得到丰富的变形效果.In order to obtain plentiful modeling effects, a new extension factor which possesses single peak, domain peak and convex polygonal supported domain is constructed. First, an extension factor whose definition domain is an arbitrary convex polygonal area is introduced. Then, space deformation matrix is constructed and applied on the equation of the surface which is to be deformed. Ideal deformation effect can be achieved after a certain deformation matrix acts on the surface. Experiments show that we can flexibly deform surfaces by adjusting supported domain, peak domain, deformation center, principal direction, extension parameter and smoothing parameter. The method is not only simple in calculation, easy to control, but also high accuracy in control. Use it repeatedly; many and various deformation effects can be achieved.

关 键 词：参数曲面 伸缩因子 凸多边形域 自由变形 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]