# Geometry Fitting (G Dataflow)

Version:

Determines the best spherical fit on a cloud of points in 3D.

## x

x coordinates of the points of the cloud.

## y

y coordinates of the points of the cloud.

## z

z coordinates of the points of the cloud.

## error in

Error conditions that occur before this node runs. The node responds to this input according to standard error behavior.

Default: No error

## x0, y0, z0

Calculated midpoints of the given cloud.

## r

Calculated radius of the given cloud.

## error out

Error information. The node produces this output according to standard error behavior.

## Algorithm for Calculating the Best Spherical Fit

The min-functional is to find x0, y0, z0 and r with

$\underset{i=1}{\overset{n}{\sum }}{\left({\left({x}_{i}-{x}_{0}\right)}^{2}+{\left({y}_{i}-{y}_{0}\right)}^{2}+{\left({z}_{i}-{z}_{0}\right)}^{2}-{r}^{2}\right)}^{2}=\mathrm{min}$

This leads to a simple linear equation in x0, y0, z0 where (xi, yi, zi) are the given points, (x0, y0, z0) is the unknown midpoint, and r is the unknown radius.

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported