LAUSR

Matching a five-axis toolpath and a vector field (VF) of preferred directions (VFPD) is increasingly popular in the five-axis machining industry. However, surfaces represented by industrial formats often produce irregular non-homogeneous VFPD. The current methods are often unable to match such complicated VFs. We propose a new technique based on an enhanced vector flow (EVF), similar to the gradient flow by Xu and Prince (1998. “Generalized Gradient Vector Flow External Forces for Active Contours.” Signal Processing 71 (2): 131–139) for image processing. The EVF keeps the high-rank vectors unchanged while extending them to unimportant regions, using a diffusion process based on a system of parabolic equations. The resulting enhanced vector field of statistically significant directions (EVFSD) is close to the original VFPD but is characterised by better continuity and regularity. Our second contribution is the clustering of the EVFSD using a prescribed library of templates by means of complex moments. The library includes three basic patterns: ‘parallel’-zigzag, ‘circular’-contour, and ‘star’-radial patterns. The toolpaths are generated by an extension of transfinite interpolation (TFI). Virtual and real machining shows the advantages of EVFSD with reference to the standard iso-parametric paths and several state-of-the-art VF-based methods. The experiments have been performed on a five-axis machining centre, Haas VF-2TR. A video, illustrating the proposed procedure is at https://drive.google.com/open?id=1qCrLZSSNKOpURs0JmbGpqV2oeJEUhBmT.