确定三圈相交的正确解

问题描述

我有三个半径不准的相交圆。如何确定构成交叉区域的六个交点中的三个？我最初只想得到聚类点 - 它们之间距离最近的点。但是由于半径并不总是正确的，因此可能会出现这样的情况，即聚类点不是形成相交区域的点。任何想法？

解决方案

对于每一对圆，找到它们边界上的两个交点（如果它们存在）。然后测试这些点中的一个是否在第三个圆内（到中心的距离小于该圆的半径）。

这将识别三个拐角三重交点区域的点，至少在这样一个交点存在时。

顺便说一下，两个圆的交点实际上比线性问题更多二次方，正确接近。

I have three intersecting circles with inaccurate radii. How can I determine three out of six intersection points which form the intersection area? I was initially thinking of simply getting the cluster points - points which have smallest distances between them. But since the radii are not always correct, there might be cases where the cluster points are not the points forming the intersection area. Any ideas?

解决方案

For each pair of circles, find the two intersections (if they exist) on their boundary. Then test to see if one of these points is inside the third circle (distance to the center less than the radius of that circle).

This will identify the three "corner" points of the region of triple intersection, at least when such an intersection exists.

By the way, the intersection of two circles is really more of a linear problem than a quadratic one, properly approached.

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