Calculate the intersection area of 3 circles

4 次查看（过去 30 天）

vatankhah 2013-8-9

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/84422-calculate-the-intersection-area-of-3-circles

评论： vatankhah 2014-1-13

We know center coordinate of three circles & also their radius. Now I want to know the intersection area of these three circle I know how to calculate the intersection area of two circle ,I want to calculate just the overlap area of these three How can I do this?

6 个评论
显示 4更早的评论隐藏 4更早的评论

Roger Stafford 2013-8-12

There is good reason no-one has answered this question as yet, Vatankhah. The problem you pose requires a more complicated matlab code than the usual kind which appear here in 'Answers'.

I assume we are taking about circles in the x-y plane. The region of points in the intersection of three circular disks can either be empty or consist of a convex shape bounded, 1) by a single complete circle, 2) by two circular arcs, 3) by three circular arcs, or 4) by four circular arcs in which two of these are parts of the same circle.

The "empty" case can occur if any pair of the circular disks do not touch, but it can also occur when each pair of disks intersect but with no common intersection in these pairwise intersections.

The method involved in finding the area of the non-empty intersection case is the same in cases 2), 3), and 4) above. The intersection region is composed of two, three, or four circular segments together with an enclosed polygon which is either a straight line segment, a triangle, or a quadrilateral. A circular segment area can be computed as the area of a circular sector with the area of the triangle composed of the circle center and the two arc endpoints either subtracted or added depending on whether the arc angle is less than or greater than pi.

Because of the necessity for distinguishing between all these different cases above, the resulting matlab code, however, would be excessive in terms of solution in this forum in my opinion.