Abstract: This paper presents a method of approximating swept volume of NURBS surfaces or solids. The method consists of (1)slicing the NURBS surfaces or solids by a series of plane and forming the sliced curves; (2)setting up the local moving coordinate system; (3)determining the singular points by obtaining local maxima and minima points at discrete frames during motion with respect to the local coordinate system; (4)using fast marching cubes method trimming the inside points of the swept volumes; (5)fitting each NURBS singular surface (envelope) by approximating or interpolating method. The errors of this method would be controlled by the number of slicing plane and the interval of the motion times in sweeping.

Key words: NURBS surfaces or solids, Swept volume, Marching cubes algorithm

摘要： 提供了一种NURBS扫描体的逼近方法。该方法主要步骤：(1)通过系列平面切割，把NURBS曲面(实体)进行降维处理，变成平面曲线；(2)为曲线设置局部标架；(3)在局部标架下求出每一曲线在每一时刻的极值点后将其转换成原曲线的奇异点；(4)使用marching cubes算法剔除扫描体内部点，保留扫描体边界上的奇异点；(5)由所有保留点拟合成奇异曲面。本算法能较好地逼近NURBS扫描体，其逼近精度可通过控制切割精度和扫描过程中时间间隔的选取而得到有效控制。

关键词: NURBS曲面(实体), 扫描体, marching cubes算法

CLC Number: 

• TP312