On the Formulation of Numerical Control Algorithms Using Computational Geometry - Yap, Kian-Tiong; Venkatesh, V.C. (CIRP annals, 1989)
Algorithms have been derived for computing 3D tool paths for planar and non-planar machined surfaces. Concepts from computational geometry such as vector solutions of line intersections with planes, spheres, cones and cylinders allow users the freedom to develop interfacing routines for complex NC machining which are not available in standard AFT packages. Using these algorithms, intersections of quadric surfaces are obtained as analytic solutions of 3D tool coordinates to serve as command inputs to NC processors. The algorithms must be guarded against cases of singularities and degeneracies and extensions to more general free-form machining are also addressed.