# Cartesian Coordinate Rotation (2D Rotation) (G Dataflow)

Rotates a two-dimensional Cartesian coordinate system in the counterclockwise direction.

This node does not rotate points within a fixed coordinate system. This node rotates the coordinate system about the origin.

## x

X-coordinate.

This input accepts the following data types:

• Double-precision, floating-point number
• 1D array of double-precision, floating-point numbers

## y

Y-coordinate.

This input accepts the following data types:

• Double-precision, floating-point number
• 1D array of double-precision, floating-point numbers

Default: 0

## 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

## rotated x

Rotated x-coordinate.

This output can return the following data types:

• Double-precision, floating-point number
• 1D array of double-precision, floating-point numbers

## rotated y

Rotated y-coordinate.

This output can return the following data types:

• Double-precision, floating-point number
• 1D array of double-precision, floating-point numbers

## 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 Rotating Two-Dimensional Cartesian Coordinates

The following figure demonstrates how this node rotates two-dimensional Cartesian coordinates.

Before the rotation, the coordinate of point P is (x, y). After the rotation, the coordinate of point P is ( x', y'), which is defined by the following equation:

$\left[\begin{array}{c}x\prime \\ y\prime \end{array}\right]={R}_{\theta }\left[\begin{array}{c}x\\ y\end{array}\right]$

where θ is the rotation angle in radians, and ${R}_{\theta }=\left[\begin{array}{cc}\mathrm{cos}\theta & \mathrm{sin}\theta \\ -\mathrm{sin}\theta & \mathrm{cos}\theta \end{array}\right]$.

Where This Node Can Run:

Desktop OS: Windows

FPGA: This product does not support FPGA devices

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