In order to optimize turning processes, cutting forces need to be accurately predicted. This in turn requires accurate extraction of the geometry of tool-workpiece engagements (TWE) at critical points during machining. TWE extraction is challenging because the in-process workpiece geometry is continually changing as each tool pass is executed. This paper describes research on a hybrid analytical, solid modeler, and feature-based methodology for extracting TWEs generated during general turning. Although a pure solid modeler-based solution can be applied, it will be shown that because of the ability to capture different cutting tool inserts with similar geometry and to model the process in 2D, an analytical solution can be used instead of the solid modeler in many instances. This solution identifies features in the removal volumes, where the engagement conditions are not changing or changing predictably. This leads to significant reductions in the number of Boolean operations that are executed during the extraction of TWEs and associated parameters required for modeling a turning process. TWE extraction is a critical component of a virtual turning system currently under development.