Solution of Spatial Transformation Relationship of Similar Ruled Surfaces Based on Registration of Divided Regions

Abstract

Since the geometric transformation relationship of similar surfaces with complex features, such as local deformation and curvature changes, is hard to be solved through global registration, this paper proposes a method for solving the spatial transformation relationship of similar ruled surfaces based on registration of divided regions. First, an adaptive region division algorithm is proposed to divide similar surfaces, and then, an improved registration algorithm is proposed by adding two constraints which are the curvature feature and differential geometric features of point clouds. Through this improved registration algorithm, the geometric transformation relationship of each sub-region can be solved, and then the spatial geometric transformation relationship of the overall similar surface can be established. Moreover, the improved registration algorithm can ensure that the differential geometric properties of corresponding points are similar after registration, which may provide a basis for mapping and reuse of process knowledge between corresponding points on similar surfaces. Finally, two similar ruled surface blades are taken as examples for simulation verification, the results show that the maximum registration error of each sub-region is 0.025 mm, which is within the allowable error range, and the registration speed of the proposed algorithm is better than the S-ICP algorithm. This proves that the method in this paper is feasible and effective.