CAJ | 학술논문

为克服传统的针对平面曲线间 Hausdorff距离4种情况需分别求解不同非线性方程组的缺点，分两个步骤计算平面曲线间的 Hausdorff距离。首先将曲线A进行离散化处理，并计算各离散点到曲线B的最小距离，从中选择若干个距离较大，且满足曲线A上相邻点到曲线B 的距离呈“小大小”的点对作为近似解；然后根据各点对处曲线的特点，判断该点附近可能存在4种类型点的哪一种，建立相应的优化模型并进行局部寻优，选择优化结果中最大的距离值作为两平面曲线间的单向 Hausdorff距离。该法将平面曲线间 Hausdorff距离的计算转化为点到曲线的最小距离计算，计算过程简单有效。两个数值算例验证了该方法的正确性。
위극복전통적침대평면곡선간 Hausdorff거리4충정황수분별구해불동비선성방정조적결점，분량개보취계산평면곡선간적 Hausdorff거리。수선장곡선A진행리산화처리，병계산각리산점도곡선B적최소거리，종중선택약간개거리교대，차만족곡선A상상린점도곡선B 적거리정“소대소”적점대작위근사해；연후근거각점대처곡선적특점，판단해점부근가능존재4충류형점적나일충，건립상응적우화모형병진행국부심우，선택우화결과중최대적거리치작위량평면곡선간적단향 Hausdorff거리。해법장평면곡선간 Hausdorff거리적계산전화위점도곡선적최소거리계산，계산과정간단유효。량개수치산례험증료해방법적정학성。
The difficulty of computing the Hausdorff distance (HD)between planar curves lies in solving different nonlinear equations for four kinds of special cases which are encountered in this computing process.To simplify the process of calculation,a two-step method for computing the HD between planar curves is proposed.The first step of the method is sampling the curve A,and calculating the minimum distance between each discrete point on the curve A and the curve B.Then, selecting several points from the discrete points as the approximate solutions,which correspond to the larger minimum distance and the minimum distances of each point together with its adj acent two points obeying the 'small-large-small' order.The second step is identifying which case the approximate solution belongs to according to the shape and position of the curves,establishing corresponding optimization model and finding the local optimal solution.Comparing these local optimal solutions, the final directed HD with the largest minimum distance will be acquired.By using this method,the computing process of the HD between planar curves can be converted into the computation of the minimum distance between a point and a curve,which can improve the computational efficiency and stability of the algorithm. The feasibility of the algorithm has been verified by two numerical examples.