摘要
平面上以任意方式放置的Ｎ个圆（Ｎ≥１）所覆盖区域面积的计算问题称为圆弧并面积的计算问题．该问题不仅具有很强的应用背景，而且是计算几何，ＣＡＤ／ＣＡＭ和计算机图形学中的一个基础算法．本文在给出有向多边形区域面积、约束圆弧所对圆心角计算公式的基础上，提出一个基于圆弧求交、平面有向多边形面积、扇形面积计算的动态计算圆弧并面积的一个新算法．该算法具有计算精度高，计算速度快，计算时间与圆的大小和计算精度无关，能统一处理圆弧并面积计算的各种情况，算法适用性和交互性好等特点．
The computing of the area covered by N circles placed randomly on a plane is called the computing of the area of the union of circular arcs. It is not only practical but also an important algorithm in Computational geometry, CAD/CAM and Computer graphics. Giving the formula for the computing of polygon area and central angle with constrain arc, based on the computing of intersection of arcs and polygon area and sector area, this paper proposed a new algorithm for computing the area of the union of circular arcs dynamically. This algorithm is characterized by its high speed and high accuracy. The computational time is not affected by the accuracy required and the size of the circle. It can be applied to all the cases for the computing of the area of the union of circular arcs and can be used widely with its user friendly interface.
出处
《计算机辅助设计与图形学学报》
EI
CSCD
北大核心
1998年第3期221-226,共6页
Journal of Computer-Aided Design & Computer Graphics
关键词
圆弧并面积
多边形区域
算法
计算几何
the area of union of circular arcs, the directed polygon area, the complexity of algorithm, computational geometry
