中点画线算法的三维推广

Generalizing Midpoint Algorithm to 3D Straight-Line

以往的中点画线算法仅适用于二维直线的生成。该文巧妙地利用直线在两个坐标平面内的投影 ,将二维中点画线算法推广到三维 ,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 ,三维中点画线算法具有高效和高精度的特点 ,可在实际工作中用于空间直线生成、空间直线插补和运动控制等方面。

A 3D line segment can be defined with two endpoints, in which Δx≥Δy≥Δz>0 , and then Midpoint 2D line algorithm is applied to the projections of line segment on xy and xz coordinate planes respectively, this results in the Midpoint algorithm for 3D straight-line. Case studies indicate that the performance of this algorithm is as perfect as 2D Midpoint algorithm.