基于投影变换的Sweep曲面构造方法  

The Construction of Projected-Based Sweep Surface

作　　者：汪国平[1] 吴学礼[2] 林立新[3] 董士海[1] 

机构地区：[1]中国科学院计算技术研究所智能信息处理重点实验室 [2]河北科技大学电气信息学院,石家庄050001 [3]河北科技大学设备处,石家庄050001

出　　处：《中国图象图形学报（A辑）》2002年第2期150-154,共5页Journal of Image and Graphics

基　　金：国家自然科学基金重点项目 ( 6 0 0 330 2 0 ) ;教育部高等学校骨干教师基金项目

摘　　要：Sweep曲面通常用沿脊线的局部活动标架来刻划 ,但是活动标架的构造在很大程度上由脊线的几何性质决定 .因此提出 :构造 Sweep曲面是否一定需要用活动标架来确定截线的位置 ?为解决这个问题 ,提出了一种投影方法 ,它有两个优点 :首先 ,当脊线是直线段和圆弧时 ,Sweep曲面可以精确表示 ;第二 ,Sweep曲面可以直接用投影变换方法来构造 ,从而可以避免使用活动标架 ,进而可以不必考虑脊线的连续性对 Sweep曲面形状的影响 .另外 ,曲面的误差控制可以通过对脊线的 offset的误差控制来实现 .The Sweep surface is usually described by using the Local moving Frame along the spine. But the construction of the moving frame is strongly limited by the properties of spine. A problem is arisen: can we describe the Sweep surface to avoid using the moving frame? In this paper, a projected based approach is proposed which possesses two advantages: Firstly, the Sweep surface can be presented exactly if spine is line segment or arc curve. Secondly, the Sweep surface can be directly described by projected transform so we can avoid using the local moving frame, then the limitation of continuity of spine for the local moving frame is not necessary. On the other hand, the error control can be simplified to the error estimating of the offset of the spine. Three types of spine, such as line segment, arc curve and NURBS curve, are considered with different methods in the projection algorithm. Furthermore, 3D NURBS offset approximation algorithm is presented for 3D NURBS curve, and the projection algorithm of the sweep surface is introduced. Finally, the robustness and efficiency of the algorithm is verified by a lot of examples.

关 键 词：Sweep曲面 投影变换 几何造型 CAGD 投影算法 构造方法 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术] TP391.72[自动化与计算机技术—计算机科学与技术]