直线Bresenham生成算法的三维推广

Generalizing Bresenham's Algorithm to 3D Straight-Line

直线 Bresenham生成算法仅适用于二维直线的生成 .文中巧妙地利用直线在两个坐标平面内的投影 ,将二维直线 Bresenham算法推广到三维 ,用于空间直线的生成 ,给出了一个具体实例 ,并分析了计算误差和算法效率 .结果表明 ,三维直线 Bresenham生成算法具有高效和高精度的特点 。

A 3D line segment can be defined with two endpoints, in which Δ x ≥Δ y ≥Δ z >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.