# 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.

Standard Error Behavior

Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

error in does not contain an error error in contains an error
If no error occurred before the node runs, the node begins execution normally.

If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

Default: No error

## x0, y0, z0

Calculated midpoints of the given cloud.

Calculated radius of the given cloud.

## error out

Error information.

The node produces this output according to standard error behavior.

Standard Error Behavior

Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

error in does not contain an error error in contains an error
If no error occurred before the node runs, the node begins execution normally.

If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

## Algorithm for Calculating the Best Spherical Fit

This node calculates the best spherical fit by finding x0, y0, z0 and r that minimize the objective function:

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

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

Web Server: Not supported in VIs that run in a web application