This paper presents a unified view that allows one to consider the global a
ccessibility question in the context of multi-axis machining, as well as gl
obally quantify and resolve this verification problem. No constraints are i
mposed on the possible orientations of the tool during the machining proces
s neither are any inflicted on the shape of the freeform surface. Being glo
bal, the presented method augments and complements contemporary multi-axis
tool positioning and verification schemes that were developed in recent yea
rs for 5-axis machining; schemes that identify and resolve the gouging prob
lem on a point by point basis for each individual point-location along the
tool path. Given a freeform surface to be machined, the orientation of the
tool at each surface location, and a check surface, the outcome of the prop
osed method is a global dichotomy that provides the regions of the freeform
surface that are accessible without gouging into the check surface. (C) 20
00 Elsevier Science Ltd. All rights reserved.