I'm trying to do trilateration where I know the coordinates of three known points and the estimates of the radii - not guaranteed to be really precise. My question is, how can I check if the circles actually intersect each other? Does the checking step mentioned in this tutorial make sense, considering the estimate values?
How to check if circles intersect each other?
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0Thanks! I'll get back to you if there's any further issues. – 2011-06-02
1 Answers
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If by the checking step you mean the first three lines in the tutorial, it does make sense. It sounds like your center points are known well, even if the distances are not. For two circles, each with a range of radii, you can do two checks-one with the minimum radii and one with the maximum. For the most part, you will then know if they intersect none, some, or all of the time the radii are in that range. There are pathological cases where the intersection will disappear in the middle. One example would be center $(0,0)$, distance $(\frac{5}{8},\frac{7}{8})$ and center $(1,0)$ distance $(\frac{1}{2},\frac{7}{4})$. If the error in you distance estimates is small, this is unlikely.