Pencil curve detection from visibility data

The trajectory of the ball-center point of a ball-end mill slid along a concave-edge region on a part surface becomes a pencil curve, and the ball-end milling along the pencil curve is called pencil curve machining. Presented in the paper is a procedure for computing pencil curves for 3-axis sculptured surface machining. The proposed algorithm traces pencil curves from an offset triangular mesh having numerous intersections (self-intersections). Since the outer skin of an offset triangular mesh makes the valid CL-surface, pencil curves can be obtained by connecting valid intersections lying on the outer skin of the offset mesh. The underlying concept of the proposed algorithm is that visible intersections are always valid for pencil curves. To obtain the visibility data of intersections, the proposed algorithm uses a graphics board, which performs hidden surface removal at a rate of up to a million polygons per second. Various examples have been tested with implementation of the algorithm, and some examples are presented for illustration.