关键词: 参数曲线, Hausdorff 距离, 近似折线

Abstract: In view of the general continuous parametric curves, a fast method of calculating the
Hausdorff distance between curves is proposed in this paper. Because a curve can be indicated by its
approximate polyline, many softwares use the approximate polyline to replace the original curve when
drawing curves. This paper proves that we can convert calculating the Hausdorff distance between
curves into the Hausdorff distance between polylines, and further into the distance between a point and
a segment under any given error range. In order to improve the computational efficiency, it also
supplement a pruning strategy and incremental algorithm. This method advantages in fast speed and
high degree of approximation, and basically solves the problem of calculating the Hausdorff distance
between parametric curves.

Key words: parametric curves, Hausdorff distance, approximate polyline