基于旋转变换的平面体轴测草图三维重建方法

Algorithm for Reconstructing Polyhedral Objects from Single Axonometric Line Drawing Based on Rotation Transformation

为了提高单幅线图的三维物体识别重建效率,并保证优化算法的收敛性,基于划整为零、分而治之的策略,首先把单幅线图划分为若干封闭线框,然后按其连接关系进行分组,随后针对各组线框所表征的面片进行三维重建计算,把一个整体优化问题转化为若干局部优化计算问题.在此基础上,分析构造了适用于局部优化识别重建的计算准则,提出了基于旋转变换的分步求解方法.通过子面片绕其父面作旋转变换,利用局部优化准则完成同级子面片的重建计算,根据线图中各线框表征的面片之间的级联关系逐级向下传递,实现全部面片三维重建.算例测试表明,本文方法适于多面体的三维重建,且平均计算效率较全局优化方法高出20%.

The divide-and-conquer strategy is adopted to improve the efficiency of 3D reconstruction of a single line drawing and guarantee the convergence of the optimization algorithm for polyhedral objects. First, the single line drawing is divided into a lot of closed polygons, then all closed polygons are grouped according to their connection relationships, and finally all faces represented by the closed polygons in one group are reconstructed into 3D. In this way, a normal global optimization problem is resolved in a step-by-step fashion. Based on this strategy, several local optimization criteria are discussed, and a step resolving algorithm for 3 D reconstruction by use of the rotation transformation are proposed. By rotating the child face against its parent face until some local optimization criteria are met, all child faces in the same level can be resolved in 3D space. Utilizing the top-down linkage relationships among faces represented by the loops on the drawing, all the child faces will be reconstructed step by step. Case studies indicate that this method is suitable for 3D reconstruction of multi-face objects and the efficiency can be improved by 20% compared with typical global optimization methods.