# Unexpected behavior of minEnclosingCircle

I have recently used the function minEnclosingCircle of OpenCV (2.4.2) because I needed to measure the diameters of a blob of points.

After a while I realized that the results were not correct, so I decided to write a small routine that calculates the diameters of a really small set of points.

I tested the function against:

- 1 single point
- 2 - 4 points in a row
- Squares of different size formed by only 4 corner points

In the table below you can see the results of my tests:

```
Note Diameter Center Points
1x1 2.000 (1.0, 1.0) [[1, 1]]
2x1 2.000 (1.0, 1.5) [[1, 1], [1, 2]]
3x1 2.060 (1.0, 2.0) [[1, 1], [1, 2], [1, 3]]
4x1 3.090 (1.0, 2.5) [[1, 1], [1, 2], [1, 3], [1, 4]]
2x2 2.000 (1.5, 1.5) [[1, 1], [1, 2], [2, 1], [2, 2]]
3x3 2.913 (2.0, 2.0) [[1, 1], [1, 3], [3, 1], [3, 3]]
4x4 4.370 (2.5, 2.5) [[1, 1], [1, 4], [4, 1], [4, 4]]
6x6 7.283 (3.5, 3.5) [[1, 1], [1, 6], [6, 1], [6, 6]]
8x8 10.196 (4.5, 4.5) [[1, 1], [1, 8], [8, 1], [8, 8]]
9x9 11.653 (5.0, 5.0) [[1, 1], [1, 9], [9, 1], [9, 9]]
16x16 21.850 (8.5, 8.5) [[1, 1], [1, 16], [16, 1], [16, 16]]
10x10 13.110 (5.5, 5.5) [[1, 1], [1, 10], [10, 1], [10, 10]]
100x100 144.207 (50.5, 50.5) [[1, 1], [1, 100], [100, 1], [100, 100]]
1000x1000 1455.183 (500.5, 500.5) [[1, 1], [1, 1000], [1000, 1], [1000, 1000]]
```

I have already seen that the function does not return a radius smaller than 1, so the minimum diameter I get is 2.0.

Apart from that, the function is always returning a radius bigger than I would expect. For instance the 10x10 square would have a radius of about 12.726 instead of 13.110. The error increases with the size of the square: for a square of 1000x1000 I would expect 1412.5 instead of 1455.

Actually, I realized that the relative error is always about 3%.

How can I explain this strange behavior?