Computation of the Minimum One-sided Hausdorff Distance Between Plane Curves under a Similarity Transformation and Relevant Applications in Roundness Error Evaluation

Abstract

A two-stage (rough and accurate) computation strategy was developed in this study in order to accurately calculate the minimum one-sided Hausdorff distance between continuous plane curves under a similarity transformation. In the rough computation, a mathematical programming model based on the discretisation method was constructed to ascertain the minimum one-sided Hausdorff distance. In addition, the linearisation method in this model was elucidated. Based on that, the solutions were attained through a stable and efficient simplex method and 5 characteristic points were obtained. In the accurate computation, a local iterative accurate algorithm for computing the minimum one-sided Hausdorff distance was established after 4 similarity transformation parameters were separated from 10 curve parameters corresponding to 5 characteristic points. Similar results, which verify the feasibility of this algorithm, were obtained based on rough and accurate computations in a numerical example. Moreover, a roundness error evaluation programming model based on the minimum one-sided Hausdorff distance and relevant linear solution methods was also developed. Furthermore, the numerical examples based on this model were compared with those based on a conventional roundness error computation model. The results revealed that similar computation circle centre coordinates, roundness error, and characteristic points can be obtained based on both models. The computational efficiency can be significantly improved via the method proposed in this study.