Documentation for Users
1.0.2
Perception Toolbox for Virtual Reality (PTVR) Manual

In a 3D cartesian coordinate system (aka XYZ system), the position of a point is defined by 3 coordinates as illustrated in Figure 1. In this example, the coordinates of the Point P are:
– X : 0.25 meters
– Y : 0.20 meters
– Z : 0.30 meters
Several different conventions for defining the axes directions of a 3D cartesian coordinate system are used in Mathematics and in Vision Science. The convention for the coordinate system displayed in Figure 1 is the lefthanded rule (see subsection below). This is the convention adopted by PTVR.
This xyz structure is used in some graphics programs (e.g. Unity, RenderMan). For users familiar with Unity, note that the correspondence between colors and axes is the same in PTVR and in Unity.
 
Figure 1: Representation of the lefthanded cartesian coordinate system used in PTVR (following Unity).  Figure 2: Animation (horizontal rotation) of figure 1 to allow you to build a better mental representation of the 3D structure of the figure (as if you were able to look at the static coordinate system from different angles). 
You can use this image as a mnemonic to remember the spatial configuration of a lefthanded coordinate system (Image from Primalshell, CC BYSA 3.0, via Wikimedia Commons).
Knowing if a system is left or righthanded is useful notably to specify the orientation of 3D objects (Wikipedia contributors. (2022, February 3)).
It does not really matter if you do not remember the formal definitions of right and lefthanded coordinate systems.
Try simply to remember the figure below.
The X axis points in the rightward direction,
The Y axis points in the upward direction,
And the Z axis points in the forward direction, i.e. "behind" the screen.
This spatial configuration will be used so often in the PTVR documentation that you should remember it quickly.
It can be helpful for those of you who are familiar with other coordinate systems to see how they relate with previous work. Only a few examples are presented among a multitude of studies.
In the field of stereovision, Read & Cumming (2006) use a headcentered space coordinates to describe an object's position relative to the head : "Z is the depth axis (Z increases with distance from the observer), Y is the vertical axis (Y increases as the object moves upward), and X is the horizontal axis (X increases as the object moves leftward). "
The latter system is therefore righthanded (in contrast to the PTVR RUF system).
Read, J. C. A., & Cumming, B. G. (2006). Does depth perception require verticaldisparity detectors? Journal of Vision, 6(12), 1. https://doi.org/10.1167/6.12.1
Wikipedia contributors. (2022, February 3). Righthand rule. In Wikipedia, The Free Encyclopedia. Retrieved 14:46, February 21, 2022, from https://en.wikipedia.org/w/index.php?title=Righthand_rule&oldid=1069678571