Core calculation modules for "Estimating Sa and Sq directly from half the scan lines"
Abstract
Version 1.0.0 of the core Python calculation modules accompanying the manuscript Estimating Sa and Sq directly from half the scan lines. Software The package implements complete-grid, half-line and half-point sampling supports, coordinate-area and equal-observation weighting, separate weighted plane removal for each support, direct calculation of arithmetical mean height (Sa) and root mean square height (Sq), and relative discrepancy from the complete-grid calculation. Requirements: Python 3.10 or later, NumPy and SciPy. The README provides installation instructions and an example using evaluate_height_map. The archive contains seven core numerical modules, the README and dependency requirements. Associated manuscript abstract Surface topography instruments often acquire a complete height map even when the required measurands are only the arithmetical mean height (Sa) and root mean square height (Sq). We tested whether both parameters could be estimated directly from roughly half the complete scan lines without reconstructing the omitted heights. We selected one sampling pattern on 50 maps from the Surface Topography Challenge and applied it unchanged to 113 maps from four other batches. For all 45 maps labelled as contact based, the larger relative discrepancy in Sa or Sq did not exceed 0.5% under either weighting scheme. With area weighting, its median was 0.0034%, its observed maximum was 0.1241%, and every map remained below 0.2%. At a similar data volume, line sampling gave smaller discrepancies than point sampling on 35 of 45 contact maps, with no 0.5% exceedances compared with five. Across all 113 maps, line sampling exceeded 0.5% on six maps and reached 16.058%, which limits the finding to the contact group. The method halved line passes and recorded heights while retaining the full scan extent. Source data The associated study uses the public Surface Topography Challenge data, available separately at 10.5281/zenodo.15341939. Corresponding authors Zhiqiang Cao: zhiqiangcao@buaa.edu.cn Jine Zhang: zhangjine15@buaa.edu.cn Jiaqi Wei: weijiaqi@buaa.edu.cn Funding This work was supported by the Key R&D Program of Shandong Province, China (Project No. 2025CXGC010110), and the Taishan Scholars Foundation of Shandong Province (tsqn202507326). Competing interests The authors declare no competing interests. License Creative Commons Attribution 4.0 International (CC BY 4.0).
