# NRSDK Coordinate Systems

### NRSDK Coordinate Systems

This document describes the coordinate systems of the Xreal Glass used in the NRSDK for Unity. It also describes the corresponding interfaces for getting extrinsics between the glass components, camera image data, and camera intrinsics, as well as conversion to other definition of coordinate systems.Note that this document is applicable to the NRSDK for Unity only, and does not apply to other types of NRSDK.

## Unity-based Coordinate Systems

In the NRSDK for Unity, in terms of coordinate system's definition and the corresponding extrinsics, we use definition of the Unity coordinate system (left handed).

### XREAL Glass Components and Their Unity-based Coordinate Systems

The XREAL glasses consists of the following key components

2 x Grayscale Cameras

2 x Display Cameras

Head / IMU

RGB Camera

The placement of the above components and their corresponding coordinate systems, as defined in NRSDK for Unity, are as follows

The global coordinate frame of the tracking system is as follows

### Interface for Head Pose

The following Interface returns the 6dof head pose with respect to the global frame, as defined above.

### Interface for Extrinsics Between Components

The following Interface returns the 6dof extrinsics, as a transformation matrix, of a Device's coordinate frame expressed in the Head coordinate frame.

For example, given a vector's coordinate $P_{d}$ in the Device's coordinate frame, and using the extrinsic transformation matrix ${^{h}}{T}{_{d}}$ obtained as above, we can compute the vector's coordinate $P_{h}$ in the Head coordinate frame, by $P_{h}={^{h}}{T}{_{d}}*P_{d}$

#### Example 1: Getting the Extrinsics of RGB Camera From Head

The following example code gets the extrinsic transformation of RGB Camera in Head, and transforms a point's coordinate from the RGB camera frame to the Head frame.

## Converting to OpenCV-based Coordinate Systems

For computer vision algorithm developers, it is often convenient to handle quantities expressed in the OpenCV coordinate system (right handed). Hereafter, we describe how to convert the aforementioned Unity coordinate systems and their corresponding extrinsics to the OpenCV convention. We also describe the definitions and interfaces for image data and camera intrinsics.

### Xreal Glass Components and Their OpenCV-based Coordinate Systems

In the OpenCV convention, the Xreal Glass components and their corresponding coordinate systems are as follows

### Converting Extrinsics: From Unity to OpenCV

The definition difference between Unity and OpenCV coordinate systems for a camera is as follows

Note that only the y-axis needs to be negated between these two conventions. Therefore, given an extrinsic transformation defined under the Unity coordinate systems, we can obtain the equivalent transformation defined under the OpenCV, by using the following utility function

#### Example 2: Converting the Extrinsics of RGB Camera From Head to OpenCV

The following example code first gets the extrinsic transformation of RGB Camera in Head, under the Unity coordinate systems as described earlier, and then converts it to the OpenCV coordinate systems by using the above utility function.

#### Example 3: Getting the Extrinsics of Right Grayscale Camera From Left Grayscale Camera in OpenCV

The following example code shows how to get the extrinsic transformation between the two Grayscale cameras and convert it to the OpenCV coordinate systems.

### Image Pixel Coordinate System and Camera Intrinsics in OpenCV

The definition of the image pixel coordinates and the camera intrinsics in the NRSDK follows the OpenCV convention.

The image data is stored row-wise in memory as follows

The camera intrinsic matrix $K$ is composed of the focal lengths $f_x$ and $f_y$, and the principal point $c_x$ and $c_y$, expressed in pixel units.

The distortion parameters contain radial coefficients $k_1, k_2,k_3,k_4,k_5$ and tangential coefficients $p_1,p_2$. The order of NRDistortionParams is $(k_1,k_2,p_1,p_2,k_3,k_4,k_5)$.

### Interface for Camera Image Data

Raw image data can be obtained through NRRGBCamTexture or NRGrayCameraTexture for the RGBCamera or GrayCamera, respectively.

#### Example 4: Getting the RGB Camera's Image as Raw Byte Array

In the current version of NRSDK, one can use Texture2D to get the raw image data. The following example code uses GetRawTextureData to get raw data by accessing Texture2D from NRRGBCamTexture. The output raw data array stores the image pixel data row-wise as described above.

### Interface for Camera Intrinsics and Distortion

The interfaces for getting camera intrinsics, distortion parameters, and resolution are as follows

#### Example 5: Getting the RGB Camera's Intrinsic Parameters

The following example code gets the RGB camera's intrinsic matrix and distortion parameters as described above.