C. Duke

Coordinate Systems used in GrISU, Kascade,
Eventdisplay and Vegas

Ground
System

Kascade/cherenkf
uses a ground coordinate system with z(down), y(South), and
x(East). This system differs from the standard ground system used
in grisudet, eventdisplay and vegas with z(up), y(North), and x(East).
Thus, for example, grisudet requires a coordinate system transformation
when reading photon records from cherenkf. Note that Corsika uses
x(North), y(West), and z(up).

Telescope System

With the telescope
in stow position, the telescope system used in grisudet, eventdisplay,
and vegas has: z(North), x(East), y(down). Thus, a 90-degree rotation
about the telescope's x axis will align the telescope coordinate system
with the ground-based coordinate system.

In grisudet, to
rotate the telescope to its pointing position, start with the telescope
aligned with the ground-based system. Rotate about telescope -z axis
through the azimuthal angle. Then, rotate about the telescope's new x
axis through the elevation angle. This sequence of rotations is
identical to the actual telescope rotation starting from its stow
position: rotation about the x(East) axis through the elevation angle
followed by a rotation about the downward pointing axis through the
aximuthal angle.

Camera System

The natural (in my
opinion, that is) camera coordinate system has its origin at the camera
center and its x and y axes parallel to the telescope-based
system. Thus, up to the latest release of GrISU, the GrISU telescope
configuration file which gives the x and y locations of the pixels on
our cameras uses this system.

However, our
standard camera coordinate system as specified in eventdisplay and
vegas has its y-axis antiparallel to the telescope y axis; that is,
when standing in front of the camera on the platform with the telescope
in stow position, the camera y-axis is up while the telescope y-axis is
down. The latest GrISU configuration version, 4.1.3, uses this
standard pixel coordinate system and is thus a change from prior
versions.

Since the camera
coordinate axes are not parallel to the telescope coordinate system
axes, our reconstruction algorithms require a coordinate transformation
so that the camera system axes are parallel to the telescope system
axes. This transformation is just a reflection of the y-axis; however,
it's easy to forget to do this.

So, we now have the same pixel, ground, and telescope coordinate systems in GrISU, eventdisplay, and vegas which should facilitate code comparisons.