# [R-sig-Geo] Find a circle center with spatial points

Barry Rowlingson b.rowlingson at lancaster.ac.uk
Fri Mar 18 20:11:23 CET 2016

```On Fri, Mar 18, 2016 at 6:49 PM, Chris Reudenbach
<reudenbach at uni-marburg.de> wrote:
> Because it seems to be an arc and not a circle issue that you can solve the
> problem by
> picking arbitrary two points of your assumed "arc" then construct
> (calculate)  the perpendicular bisector of
> the line between them and do so for another arbitrary two points of the
> assumed "arc".
>
> The intersection of the perpendicular lines is the assumed center of the
> arc.
>
> If you iterate over all points this should be a pretty good estimation of
> the real center.

This is the  "sample 3 points and find the fitted circle" idea, you
are likely to get massive "outliers" and if you take the mean
coordinate it could fail horribly. See the paper I linked to for an
example. They use the median to get an initial "robust" estimate of
x,y,R, and then use some specialised optimisation to improve the
estimate - you can't just throw it into "optim"!

Not sure I understand the maths in it yet though....

Barry

```