Draft:Eriksson-Jemsson approximation

Background
The Eriksson-Jemsson approximation is an algorithm used for circle fitting in the context of LiDAR-data. The algorithm is mainly used for its simplicity and reduced time complexity over other fitting-algorithms such as the one described in Circle Fitting.

The algorithm
The algorithm fits a circle $$(x-x_0)^2+(y-y_0)^2=r^2$$ , where $$(x_0,y_0)$$ is the circle center and $$r$$ is the radius, to $$n $$ data points $$(x_i,y_i), i=1,...,n$$.

Given that the data points are order by ascending angle $$\theta_i = arg(x_i,y_i)$$, the circle center $$(x_0,y_0)$$ is calculated by

$$(x_0,y_0) = \left(\frac{x_1+x_n}{2},\frac{y_1+y_n}{2} \right)$$

and the radius

$$r = \frac{\sqrt{(x_n-x_1)^2+(y_n-y_1)^2}}{2}$$.