Abstract Drag is a key criterion in assessing the quality of thermally cut sheet metal edges, which is critical to the reliability of the final product. The evaluation of drag has been described qualitatively and quantitatively, but the scientific literature lacks a methodical description of algorithmic tracking of the drag lines themselves. This absence of a standardized approach has hindered the objective determination of drag. With recent advances in the field towards automated quality assessment aimed at autonomous adaptation of process parameters, the need for consistent, fast and reliable assessment of drag lines has become apparent. To address this gap, this study introduces an innovative drag line tracking algorithm, inspired by the behavior of fluid flowing towards the lowest points, to compute a generalized drag line for an edge with a homogeneous cutting pattern. The algorithm utilizes the height data of the measured cut edges as a data base for the assessment of the drag lines. The results indicate that the drag lines identified by the algorithm are not only subjectively accurate, but also show a strong correlation with human-annotated drag lines across several metrics. This work lays the foundation for the objective evaluation of drag by not only describing an algorithm for the consistent determination of drag lines, but also by presenting a tool for human annotation and suitable customized metrics. As a result, it contributes significantly to the comprehensive evaluation of edge quality and represents a step forward in the automatic optimization of process parameters and the improvement of cutting edge quality.