Mathematical Approach in Complex Surfaces Toolpaths

This paper represents the focus on developing efficient algorithms that reduce the operations required to be employed in order to obtain complex surfaces milling finishing toolpaths for the three axis NC (Numerical Control) machine within the reverse engineering chain of processes. Direct machining is the process of generating efficient toolpaths directly from the digitized data, meaning the point cloud. The entire research is focused on determining the mathematical calculus able to interpret the data collected through the contact/noncontact 3D scanning process. In this direction, two algorithms were developed to generate ball-end mill finishing toolpaths for freeform surfaces using ordered/unordered point clouds. Practical work that validates author’s employed algorithms of obtaining finishing milling toolpaths uses the point cloud stored from the 3D scanning process in matrix found in ASCII files, which makes data interpreting easy.