I think for my problem, constructing the circle from three points should work

I'd love to see how you will pick the 3 points?

For your case, it should be trivial to vastly reduce the points set by excluding all those points that do not lie on the outer extremes of the grid. Eg.

        *---*
        |   | 
        +   +
        |   |
        +   +
        |   |
*---+---+   +---+---*
|                   |
*---+---+---+---+---*
    
    
*---+---+---+---*
|               |
+   +---+---+---+
|   |
+   +---+---+---+---*
|                   |
*---+---+---+---+---*

[download]

Picking out the *s and eliminating the +s is fairly easy, which reduces the points vastly. But picking just (the right) three of those is much harder.

However, I am also interested in the second way. I will not be dealing with more than 20.000 tiles,

My crude, naive implementation of SEC takes ~17 microseconds per 3-point trial. With 20,000 points and an O(n3) algorithm, you'd be looking at 20,000^3 * 0.000017 = 136e6 seconds or around 4.5 years! Its a non-starter.

Again, it is probably fairly trivial to vastly reduce the point set for consideration, but you'd be better to go looking at one of the implementations of the O(n) algorithms like: miniball and others.

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Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
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In reply to Re^7: Placeing Tiles in a Circle by BrowserUk
in thread Placeing Tiles in a Circle by janDD

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