To improve efficiency of NC tool path generation for triangular Bézier surface and solve the interference issues of tool path, we proposed an algorithm of generating interference-free NC tool path based on triangular Bézier surface. The R*S tree is introduced into the algorithm and the dynamic spatial index structure of the triangular Bézier surface model is established by R*S tree; the intersection regions are acquired rapidly based on the R*S tree, so that the intersection triangular Bézier patches are located exactly; each intersection triangular Bézier patch is adaptively subdivided into many triangular planar patches in the scope of the tool path precision; the intersection curves are acquired through the intersection of triangular planar patches and cutting planes; the points on intersection curves are taken as the driving points, thus the interference-free cutter location points of triangular Bézier surface are obtained by the iterative calculation method, and then the interference-free cutter location points are connected rightly to generate NC tool path. It has been proved by examples that the algorithm of generating NC tool path based on triangular Bézier surface has strong adaptation to data type and that it can accurately and efficiently obtain the interference-free NC tool-path for the intricate triangular Bézier surface.
A third order partial differential equation for isotropic boundary based triangular Bézier surface generation
