Generalizing Bresenham's Algorithm to 3D Straight-Line

A 3D line segment can be defined with two endpoints，in which Δx ≥Δy ≥Δz ＞0，and then Bresenham’s 2D line algorithm is applied to the projections of line segment on xy and xz coordinate planes respectively，this results in the Bresenham’s algorithm for 3D straight-line．Case studies indicate that the performance of this algorithm is as perfect as 2D Bresenham’s algorithm and it is suitable for various CNC systems of machine tools and rapid prototyping machines．