The Tobii documentation describes the 3D UCS as follows (highlights not in original):
User Coordinate System (UCS)
All the data available from Tobii Eye Trackers that describe 3D space coordinates are given in the so-called User Coordinate System or UCS for short. The UCS is a millimeter-based
system with its origin at the centre of the frontal surface of the eye tracker
(see Figure 1). The coordinate axes are oriented as follows: the x-axis points horizontally towards the user’s right, the y-axis points vertically towards the user’s up and the z-axis points towards the user, perpendicular to the front surface of the eye tracker.
To sum up: The unit is millimeters throughout, the origin point of the axes is the center of the eye tracker's front.
- lefteye (x,y,z) would reflect the left eye's position relative to the eyetracker.
- leftgaze (x,y,z) would reflect the left eye's gaze point on the calibration plane.
Hope this helps.