This paper presents a procedure to compute pencil curves from a triangular mesh which is offset with the radius of a given ball-end mill. An offset triangular mesh has numerous self-intersections caused by an abundance of invalid triangles, which do not contribute to the valid CL-surface. Conceptually, we can obtain valid pencil curves by combining all intersections tying on the outer skin of the offset triangular mesh, i.e., the valid CL-surface. The underlying concept of the proposed algorithm is that visible intersections are always valid for pencil curves, because visible intersections lie on the outer skin of the offset model. To obtain the visibility of intersections efficiently, the proposed algorithm uses a graphics board, which performs hidden surface removal on up to a million polygons per second.