A study of flatness digital measuring instrument models for algorithmic validation of minimum zone method

Abstract

To address the current lack of standardized evaluation systems and complete metrological traceability chains for flatness assessment algorithms, this study proposes a flatness digital measuring instrument model based on the minimum zone (MZ) method. By combining triangle and cross criteria, along with point cloud geometric feature analysis, barycentric coordinate methods, and projection techniques, a constraint framework satisfying the four fundamental sampling points is established. Based on rigorous mathematical and geometric derivations, a unified standard for constructing the flatness digital measuring instrument model is developed, and sampling procedures as well as reference model examples under different criteria are provided. Utilizing this model set and its implementation methodology, a series of validation experiments were conducted to assess the feasibility and applicability of various flatness evaluation algorithms and measurement software. Experimental results demonstrate that the proposed model is effective for verifying and evaluating flatness assessment algorithms, supporting accuracy validation down to 0.1 μm. This research provides a reproducible and traceable technical pathway for the standardized verification of flatness algorithms, supporting quality control in ultra-precision manufacturing.