主法向方向单调自由曲面简易骨架图生成算法

Simple Skeleton Generation Algorithm for Free-form Surface with Main Normal Direction Monotonous

利用骨架图进行三维模型的相似性比较研究在工程中有着重要的应用,可以有效地解决检索与重用等问题。本文给出了一种用简易骨架图描述主法向方向单调自由曲面(沿曲面的主法向方向的任一直线与该曲面最多只有一个交点)的方法。首先,求自由曲面的总法向量,按照总法向量的反方向将自由曲面投影到二维平面上,得到投影曲面;然后,求取投影曲面的骨架点和骨架线;最后,将投影曲面的骨架线按照自由曲面的总法向量方向进行柱面拉伸与自由曲面产生交线,该交线就是自由曲面的简易骨架图。并将本文算法与MATLAB中求骨架算法进行比较,实验表明,本文所得的简易骨架图可以更好地描述主法向方向单调自由曲面的几何与拓扑特征,为比较自由曲面的相似性提供了理论技术基础。

The similarity study of three-dimensional models using skeleton diagrams has important applications in engineering,which can effectively solve problems such as retrieval and reuse.In this study,a simple skeleton diagram is used to describe the main normal direction monotonous free-form surface(any line along the main normal direction of the surface has at most one intersection with the surface).First,the total normal vector of the free surface is obtained.The free surface is projected onto the two-dimensional plane in the opposite direction of the total normal vector to obtain the projected surface.Then,the skeleton point and skeleton line of the projected surface is obtained.Finally,the skeleton line of the projected surface is stretched cylindrically in the direction of the total normal vector of the free surface and intersected with the free surface.The intersection line is a simple skeleton diagram of the free surface.The algorithm is compared with MATLAB′s skeletal algorithm.Experiments show that the simple skeleton diagram obtained in this paper can better describe the geometric and topological features of the mononormal free-form surface in the main normal direction,which provides a theoretical and technical basis for the similarity of free-form surfaces.