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

Note: If you really want to look at something in the present page: we recommend the introduction and Figures 1 and 2. The other figures are OK except that they display a purple full plane instead of a blue halfplane as correctly shown in Figures 1 and 2, and explaining text is still missing.
The 3D Harms coordinate system belongs to the class of spherical coordinate systems. The 3D Harms coordinate system is used specifically either by vision scientists, e.g. in the field of binocular disparity, or by ophthalmologists, e.g. in the field of strabology (Read & Cumming, 2008, Dysli et al., 2021).
This coordinate system is often called an azimuthlongitude / elevationlongitude system (Howard & Rogers, 2008  chapter 20, Schor's lab  chapter 3).
A previous section explains the different spherical coordinate systems used to specify the azimuth and the elevation of a point (Class of spherical coordinate systems).
In the Harms system, the 3D position of a point P is defined by 3 coordinates:
These 3 coordinates are described in details in the 3 following sections.
1. The azimuthlongitude
This is the dihedral angle between a vertical halfplane passing through P (purple plane in the figures below) and the zero azimuth halfplane (i.e. the YZ plane in PTVR).
The azimuthlongitude of Point P is 60° in figures 1 and 2 (180° < azimuthlongitude < 180°).
 
Figure 1: The point P has an azimuth angle of 60° (brown angle) with respect to the YZ halfplane (i.e. it lies on the purple halfplane). The elevation of point P is 19.96° (blue angle).  Figure 2: Animation (horizontal rotation about the Y axis) of figure 1 to allow you to build a better mental representation of its 3D structure (as if you were able to look at Figure 1 from different angles). 
2. The elevationlongitude
This is the dihedral angle between an elevated plane passing through the point and the zero elevation plane. [To be completed]
(from 90° to 90°) The elevationlongitude_poles_on_X_axis
 
Figure 3: .  Figure 4: [To be completed] Animation (horizontal rotation about the Y axis) of figure 3 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).. 
3. The radial Distance (in meters) – corresponds to the radius of the sphere on which P is lying (i.e. constant distance between Origin and P).
[To be completed]
 
Figure 5: elevation from 0° to 84° with constant azimuth (here 0°). Note the isoazimuth trajectory formed by the path of P on the 0° longitude going through the Y axis poles.  Figure 6: elevation from 0° to 84° with constant azimuth (here 60°). Note the isoazimuth trajectory formed by the path of P on the 60° longitude going through the Y axis poles. 
 
Figure 7: azimuth from 0° to 135° back and forth with constant elevation (here 0°). Note the isoelevation trajectory formed by the path of P on the 0° longitude going through the Z axis poles.  Figure 8: azimuth from 0° to 179° back and forth with constant elevation (here 30°). Note the isoelevation trajectory formed by the path of P on the 30° longitude going through the Z axis poles. 
 
Figure 9: Special case when P is on a tangent Screen: ie radial distance varies. [To be completed]  Figure 10: [To be completed] 
Schor, C. M. Chapter 3—KINEMATICS : COORDINATE SYSTEMS FOR DESCRIBING EYE POSITION. Retrieved July 30, 2021, from http://schorlab.berkeley.edu/passpro/oculomotor/html/chapter_3.html#coord
Howard, I. P., & Rogers, B. J. (2008). chap. 20. Classification of binocular disparity. In Seeing in Depth (Vol. 2). Oxford University Press. (Web link)
Wikipedia contributors. (2022, February 16). Spherical coordinate system. In Wikipedia, The Free Encyclopedia. Retrieved 15:18, February 21, 2022, from https://en.wikipedia.org/w/index.php?title=Spherical_coordinate_system&oldid=1072122604