曲线简化中节点重要性度量方法比较及垂比弦法的改进

Abstract

在曲线简化过程中,一个最基础的问题是如何度量曲线上节点的重要性程度。该文简要回顾了现有的一些节点重要性度量方法,即角度度量法、面积度量法、弧比弦度量法和垂比弦度量法,指出其局限性。结合弧比弦度量法与垂比弦度量法的优点,提出了一种改进的垂比弦度量方法,并给出具体的评价方法。最后,根据曲线简化实验结果,发现相比于弧比弦度量法,改进后的垂比弦度量法选取的节点能较好地保持曲线的形状。 In the process of the curve simplification,a most basic question is how to measure the importance of all vertices in the curve.This is also a basis for selecting the vertices.In this paper,a brief review and evaluation of existing measure methods about the importance of the vertices was given,i.e.local angle measure,local area measure,local ratio measure of arc to chord length,and local ratio measure of perpendicular distance to chord length.Then,an improved method was proposed,which was obtained by a modification of neighborhood on the basis of classical ratio of arc to chord length,and the specific method of evaluation was provided.Through a practical example of curve simplification,it is found that the improved local measure method can maintain the shape of the curve well,compared with classical methods.That is to say,the improved method can measure the importance of vertices in the curve much better than existing ones.