三维形体的形态学运算及应用

3D Object Morphology Operation's Computation and it's Application

本文首先讨论了边界表示的物体的形态学运算问题。文中讨论了任意形状的物体，包括凸物体和非凸物体；引入了负形体的概念；并提出了２Ｄ和３Ｄ连续物体的Ｍｉｎｋｏｗｓｋｉ运算的统一算法。利用这一算法，提出了３Ｄ任意形体间的变形新算法，把边界表示的物体的形态学运算的概念扩展到任意曲线和任意曲面上，并且介绍了３Ｄ物空间中曲线的概念和３Ｄ物空间双参数曲面的概念。文中任意形体的３Ｄ变形算法能很好地解决具有不同拓扑结构的３Ｄ边界表示的物体之间的变形问题。

In the paper, the problem of boundary-represented objects' morphology operations is first discussed. In this psper, arbitrary shaped objects include convex objects and non convex objects are discussed,the concept of negative shaped object is introduced and a unified algorithm to compute Minkowski operations of 2D and 3D continuous objects is presented. By using this algorithm, a new algorithm of deformations between 3D arbitrary shaped objects is presented, the concept of boundary-represented objects' morphology operations is expanded to arbitrary curve and arbitrary curved surface and the concept of curve in the 3D objects' space and biparametric patch in the 3D objects' space is introduced. The 3D morphing algorithm of arbitrary shaped objects in this paper can well resolve the problem of deformations between 3D boundary-represented objects having difference structure of topology.