# Difference: ScanningTableCoordinateSystemAndProjections (1 vs. 3)

Revision 3
19 Mar 2015 - Main.TobiasHabermann
Line: 1 to 1

 META TOPICPARENT name="PulSAr"

# Scanning Table Coordinate System and Projections

Line: 37 to 37
Due to the position uncertainty in the PSD, the two trajectories do not cross, even if the two events originate from the same interaction position. Given one event from the side scan and one from the front scan, they "most likely" originate from the same interaction position, when the two signals differ only by noise. The "most likely" interaction position is given by the point that is 1/2 dist apart from each of the trajectories (cf. eg. http://de.wikipedia.org/wiki/Windschiefe):
Changed:
<
<
X = 1/2 [ b x ( b x d ) + d x ( b x d ) ]
>
>
X = 1/2 [ F1 + F2 ]

>
>
F1 = d (a. n1 - c. n1)/(d. n1) + c

F2 = b (c. n2 - a. n2)/(b. n2) + a

n1 = b x (b x d)

n2 = d x (b x d)

## -- TobiasHabermann - 21 Oct 2014

Revision 2
26 Nov 2014 - Main.TobiasHabermann
Line: 1 to 1

 META TOPICPARENT name="PulSAr"

# Scanning Table Coordinate System and Projections

Line: 21 to 21
The trajectories can be written as:
Changed:
<
<
T_Front(fy,fz) = (d1+d2,fy,fz) - λ (d2,fy,fz) = a - λb
>
>
T_Front(fy,fz) = (d1+d2,fy,fz) + λ (-d2,-fy,-fz) = a + λb

Changed:
<
<
T_Side(sx,sz) = (sx,d1+d2,sz) - λ (sx,d2,sz) = c - λd
>
>
T_Side(sx,sz) = (sx,d1+d2,sz) + λ (-sx,-d2,-sz) = c + λd

And the distance can be calculated via (cf. eg. http://en.wikipedia.org/wiki/Skew_lines#Distance):
Line: 33 to 33

dist = |(a-c).n|
>
>

Due to the position uncertainty in the PSD, the two trajectories do not cross, even if the two events originate from the same interaction position. Given one event from the side scan and one from the front scan, they "most likely" originate from the same interaction position, when the two signals differ only by noise. The "most likely" interaction position is given by the point that is 1/2 dist apart from each of the trajectories (cf. eg. http://de.wikipedia.org/wiki/Windschiefe):

X = 1/2 [ b x ( b x d ) + d x ( b x d ) ]

## -- TobiasHabermann - 21 Oct 2014

 META FILEATTACHMENT attachment="drawings1.png" attr="h" comment="Scanning Table Coordinate System" date="1413881398" name="drawings1.png" path="drawings1.png" size="14615" user="TobiasHabermann" version="1"

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