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All content in this area was uploaded by Stephen C. Kuehn on Mar 13, 2019

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Sample Number:

Input Coordinates Input Coordinates Output Coordinates

X Y X Y X Y

Reference 1 Particle 1 Particle 1 0.000 0.000

Reference 2 Particle 2 Particle 2 0.000 0.000

Reference 3 Particle 3 Particle 3 0.000 0.000

Particle 4 Particle 4 0.000 0.000

Particle 5 Particle 5 0.000 0.000

Particle 6 Particle 6 0.000 0.000

Particle 7 Particle 7 0.000 0.000

Particle 8 Particle 8 0.000 0.000

Particle 9 Particle 9 0.000 0.000

Particle 10 Particle 10 0.000 0.000

Particle 11 Particle 11 0.000 0.000

Input Coordinates Particle 12 Particle 12 0.000 0.000

Particle 13 Particle 13 0.000 0.000

Particle 14 Particle 14 0.000 0.000

X Y Particle 15 Particle 15 0.000 0.000

Reference 1 Particle 16 Particle 16 0.000 0.000

Reference 2 Particle 17 Particle 17 0.000 0.000

Reference 3 Particle 18 Particle 18 0.000 0.000

Particle 19 Particle 19 0.000 0.000

Particle 20 Particle 20 0.000 0.000

Particle 21 Particle 21 0.000 0.000

Particle 22 Particle 22 0.000 0.000

Particle 23 Particle 23 0.000 0.000

Particle 24 Particle 24 0.000 0.000

Particle 25 Particle 25 0.000 0.000

Particle 26 Particle 26 0.000 0.000

Particle 27 Particle 27 0.000 0.000

Particle 28 Particle 28 0.000 0.000

Particle 29 Particle 29 0.000 0.000

Particle 30 Particle 30 0.000 0.000

Scratch/note space:

Original Coordinate System Original Coordinate System New Coordinate System

New Coordinate System

040

0

2

4

6

8

10

12

Input Coordinates Reference Particles

X

Y

1011121314151617181920

0

2

4

6

8

10

12

Output Coordinates Reference Particles

X

Y

Formulas: inverse of:

X particle new = X ref 1 new X ref 2 new X ref 3 new X X ref 1 orig X ref 2 orig X ref 3 orig X X particle orig

Y particle new Y ref 1 new Y ref 2 new Y ref 3 new Y ref 1 orig Y ref 2 orig Y ref 3 orig Y particle orig

1 1 1 1

Calculations:

Reference points, original coordinate system

Top Left Right Particle 1, original coordinate system

X 0 0 0 X 0

Y 0 0 0 Y 0

1 1 1 1

Reference points, new coordinate system Reference points, original coordinate s ystem

Top Left Right Inverse of above

X 0 0 0 X #VALUE! #VALUE! #VALUE! = #VALUE! #VALUE! #VALUE!

Y 0 0 0 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!

Method of calculation based on matrix algebra described by Admon et al. (2005)

Reference Coordinate Transform

Particle 1 Particle 1

#VALUE! #VALUE! #VALUE! X 0 = #VALUE! x

#VALUE! #VALUE! #VALUE! 0 #VALUE! y

1

Particle 2 Particle 2

#VALUE! #VALUE! #VALUE! X 0 = #VALUE! x

#VALUE! #VALUE! #VALUE! 0 #VALUE! y

1

Particle 3 Particle 3

#VALUE! #VALUE! #VALUE! X 0 = #VALUE! x

#VALUE! #VALUE! #VALUE! 0 #VALUE! y

1

Particle 4 Particle 4

#VALUE! #VALUE! #VALUE! X 0 = #VALUE! x

#VALUE! #VALUE! #VALUE! 0 #VALUE! y

1

Particle 5 Particle 5

#VALUE! #VALUE! #VALUE! X 0 = #VALUE! x

#VALUE! #VALUE! #VALUE! 0 #VALUE! y

1

Particle 6 Particle 6

#VALUE! #VALUE! #VALUE! X 0 = #VALUE! x

#VALUE! #VALUE! #VALUE! 0 #VALUE! y

1

Particle 7 Particle 7

#VALUE! #VALUE! #VALUE! X 0 = #VALUE! x

#VALUE! #VALUE! #VALUE! 0 #VALUE! y

1

Particle 8 Particle 8

#VALUE! #VALUE! #VALUE! X 0 = #VALUE! x

#VALUE! #VALUE! #VALUE! 0 #VALUE! y

1

Particle 9 Particle 9

#VALUE! #VALUE! #VALUE! X 0 = #VALUE! x

#VALUE! #VALUE! #VALUE! 0 #VALUE! y

1

Admon, U., Donohue, D., Aigner, H., Tamborini, G., Bildstein, O., and Betti, M., 2005, Multiple-

Instrument Analyses of Single Micron-Size Particles: Microscopy and Microanalysis, v. 11, pp.

354–362. DOI: 10.1017/S1431927605050312

original

coordinat

e system

new

coordinate

system

Particle 10 Particle 10

#VALUE! #VALUE! #VALUE! X 0 = #VALUE! x

#VALUE! #VALUE! #VALUE! 0 #VALUE! y

1

Particle 11 Particle 11

#VALUE! #VALUE! #VALUE! X 0 = #VALUE! x

#VALUE! #VALUE! #VALUE! 0 #VALUE! y

1

Particle 12 Particle 12

#VALUE! #VALUE! #VALUE! X 0 = #VALUE! x

#VALUE! #VALUE! #VALUE! 0 #VALUE! y

1

Particle 13 Particle 13

#VALUE! #VALUE! #VALUE! X 0 = #VALUE! x

#VALUE! #VALUE! #VALUE! 0 #VALUE! y

1

Particle 14 Particle 14

#VALUE! #VALUE! #VALUE! X 0 = #VALUE! x

#VALUE! #VALUE! #VALUE! 0 #VALUE! y

1

Particle 15 Particle 15

#VALUE! #VALUE! #VALUE! X 0 = #VALUE! x

#VALUE! #VALUE! #VALUE! 0 #VALUE! y

1

Particle 16 Particle 16

#VALUE! #VALUE! #VALUE! X 0 = #VALUE! x

#VALUE! #VALUE! #VALUE! 0 #VALUE! y

1

Particle 17 Particle 17

#VALUE! #VALUE! #VALUE! X 0 = #VALUE! x

#VALUE! #VALUE! #VALUE! 0 #VALUE! y

1

Particle 18 Particle 18

#VALUE! #VALUE! #VALUE! X 0 = #VALUE! x

#VALUE! #VALUE! #VALUE! 0 #VALUE! y

1

Particle 19 Particle 19

#VALUE! #VALUE! #VALUE! X 0 = #VALUE! x

#VALUE! #VALUE! #VALUE! 0 #VALUE! y

1

Particle 20 Particle 20

#VALUE! #VALUE! #VALUE! X 0 = #VALUE! x

#VALUE! #VALUE! #VALUE! 0 #VALUE! y

1

Particle 21 Particle 21

#VALUE! #VALUE! #VALUE! X 0 = #VALUE! x

#VALUE! #VALUE! #VALUE! 0 #VALUE! y

1

Particle 22 Particle 22

#VALUE! #VALUE! #VALUE! X 0 = #VALUE! x

#VALUE! #VALUE! #VALUE! 0 #VALUE! y

1

Particle 23 Particle 23

#VALUE! #VALUE! #VALUE! X 0 = #VALUE! x

#VALUE! #VALUE! #VALUE! 0 #VALUE! y

1

Particle 24 Particle 24

#VALUE! #VALUE! #VALUE! X 0 = #VALUE! x

#VALUE! #VALUE! #VALUE! 0 #VALUE! y

1

Particle 25 Particle 25

#VALUE! #VALUE! #VALUE! X 0 = #VALUE! x

#VALUE! #VALUE! #VALUE! 0 #VALUE! y

1

Particle 26 Particle 26

#VALUE! #VALUE! #VALUE! X 0 = #VALUE! x

#VALUE! #VALUE! #VALUE! 0 #VALUE! y

1

Particle 27 Particle 27

#VALUE! #VALUE! #VALUE! X 0 = #VALUE! x

#VALUE! #VALUE! #VALUE! 0 #VALUE! y

1

Particle 28 Particle 28

#VALUE! #VALUE! #VALUE! X 0 = #VALUE! x

#VALUE! #VALUE! #VALUE! 0 #VALUE! y

1

Particle 29 Particle 29

#VALUE! #VALUE! #VALUE! X 0 = #VALUE! x

#VALUE! #VALUE! #VALUE! 0 #VALUE! y

1

Particle 30 Particle 30

#VALUE! #VALUE! #VALUE! X 0 = #VALUE! x

#VALUE! #VALUE! #VALUE! 0 #VALUE! y

1