Sensor Local System
S. Margetis, KSU
Definitions
STAR Global Coordinates
Wafer Local Coordinates
y (up)
n,β
d,α
x (South)
• 
• 
• 
t,γ
w (normal/away from ladder)
n,β
z (West)
d,α
v (along ladder +z)
t, γ
u (r-phi direction for RHS)
Local v (along ladder) is fixed and along global +z
Local w (normal to u-v [wafer] plane). Points away from exposed surface
Local u (r-phi on wafer plane) varies so it forms a RHS with v-w (u,w,v)
1
Wafer Local Coordinates Examples
w (normal/away from ladder)
n,β
d,α
v (along ladder +z)
t, γ
u (r-phi direction for RHS)
• 
We use the above RHS notation (u,w,v)
2
Local PXL system definitions (offline)
sensor
w (away)
v (West)
•  PXL Sector origin is the same as STAR global
•  use same convention as in SSD/IST (as a
whole) and IDS to simplify software
ladder
EAST
u
w
v
WEST
3
Survey Info in Db
Survey info stores position information of sensor,ladder etc center in STAR Global
Local-to-Global positioning is done in terms of TGeoHMatrix
d,n,t are unit vectors and α, β,γ the corresponding rotation angles in x,y,z [u,w,v]
directions [RHS] . dx is the unit vector d projection on the x-axis etc
• 
• 
• 
TGeoHMatrix definition
! x $ '
# G & )
# yG & )
#
&=)
z
G
#
& )
# 1 & )
"
% )(
d̂ x
n̂x
tˆx
dx
d̂ y
n̂y
tˆy
dy
d̂z
n̂z
tˆz
dz
0
0
0
1
*!
,#
,#
,#
,#
,#
,+"
xL $
&
yL &
&
zL &
1 &%
Local to Global transformation
definition
xGi = R ⋅ xLi + T i
(
y (up)
)
d,α
8.5cm
n,β
d,α
x (South)
xG = d̂ x ⋅ x L + n̂x ⋅ yL + tˆx ⋅ zL + d x
n,β
"
ˆ
$ d̂ x = cos20 n̂x = −sin 20 t x = 0 d x = −sin 20 *8.5cm = −2.91cm
$ d̂ = sin 20 n̂ = cos20 tˆ = 0 d = cos20 *8.5cm = 7.99cm
y
y
y
$ y
$
ˆ
d̂z = 0
n̂z = 0
tz = 1
dz = sensor − zC
$
$#
0
0
0
1
200
"
ˆ
$ d̂ x = −cos20 n̂x = sin 20 t x = 0 d x = −sin 20 * 2.5cm = −0.85cm
$ d̂ = −sin 20 n̂ = −cos20 tˆ = 0 d = cos20 * 2.5cm = 2.35cm
y
y
y
$ y
$
d̂z = 0
n̂z = 0
tˆz =1
dz = sensor − zC
$
$#
0
0
0
1
%
'
'
'
'
'
'&
4
%
'
'
'
'
'
'&