Cocoa ME+1 Blessing

Preview:

DESCRIPTION

Cocoa ME+1 Blessing. James N. Bellinger University of Wisconsin-Madison 20-March-2009. Data used. 0T Distancemeter16-Nov average DCOPS11-Nov event Linkfrom Celso 3.8T Distancemeter1-4 Nov average DCOPS27-Oct event Linkfrom Celso PG - PowerPoint PPT Presentation

Citation preview

1

James N. Bellinger

University of Wisconsin-Madison

20-March-2009

Cocoa ME+1 BlessingCocoa ME+1 BlessingCocoa ME+1 BlessingCocoa ME+1 Blessing

James N. Bellinger 20-March-2009

2

Data usedData used

0TDistancemeter 16-Nov average

DCOPS 11-Nov event

Link from Celso

3.8TDistancemeter 1-4 Nov average

DCOPS 27-Oct event

Link from Celso

PGPG within disk UR-0058 (2006) (Oleg cleaned it up)

Supplementary UR-0103 (2008)

PG of disk UR-0124 (after Craft)

James N. Bellinger 20-March-2009

3

• Ideal– Ideal Geometry for Endcap+Link, default data

• 0T– Data from 0T, Link fit geometry/data from 0T

– Transfer plates from PG, rest of Endcap ideal

• 3.8T– Data from 3.8T, Link fit geometry/data from 3.8T

– Transfer plates from PG, rest of Endcap ideal

• Special– Data from 0T, Link fit geometry/data from 0T

– Transfer plates from PG, initial chamber pos PG

Cocoa Fit TypesCocoa Fit Types

James N. Bellinger 20-March-2009

4

Cocoa Ideal Fit vs DDDCocoa Ideal Fit vs DDD

• Only 6 entries. Cocoa Ideal minus DDD geometry

• Ring 3 only

• Cocoa Ideal geometry fit is fine: “chi-squared” is 1.4 with 872 “degrees of freedom”

Cocoa pos – DDD pos

Mean,

microns

RMS,

microns

X -17 69

Y -55 52

Z -7 1

James N. Bellinger 20-March-2009

5

Fit 0T- Fit Ideal

3.8T-Ideal

X Y Z X Y Z

ME+1/3/03 0.58 -2.17 -1.16 0.58 -2.14 -2.93

ME+1/3/09 2.31 -0.62 -4.38 2.2 -0.59 -4.39

ME+1/3/14 -0.32 -0.32 -3 -0.17 -0.17 -2.85

ME+1/3/20 0.11 -0.43 1.28 0.04 -0.13 -0.18

ME+1/3/27 1.03 -0.28 2.57 1.29 -0.35 -0.53

ME+1/3/33 -0.89 -0.88 8.33 0 0 -0.01

ME+1/2/02 0.9 -3.38 1.16 0.98 -3.66 -7.08

ME+1/2/08 3.46 -0.93 -0.54 3.51 -0.93 -7.89

ME+1/2/14 -0.07 -0.07 -0.93 0.07 0.07 -7.74

ME+1/2/20 -0.03 0.11 2.47 -0.1 0.37 -5.76

ME+1/2/26 0.92 -0.24 5.77 1.03 -0.28 -2.9

ME+1/2/32 -0.29 -0.27 5.3 -0.4 -0.4 -3.66

Chamber Z deviations Chamber Z deviations Cocoa 3.8T and 0T vs IdealCocoa 3.8T and 0T vs Ideal

Cocoa 3.8TCocoa 0TCocoa Ideal

Ideal fit uses ideal geom and nominal measurements

HSLM6 bad due to blocked IR target

James N. Bellinger 20-March-2009

6

Cocoa Fit 3.8T - Fit 0T

mm

Cocoa Fit 0T - P.G.

mm

ME+1/3/03 -1.76 -0.71

ME+1/3/09 -0.01 2.08

ME+1/3/14 0.15 2.27

ME+1/3/20 -1.46 -0.24

ME+1/3/27 -3.1 -1.88

ME+1/3/33 -8.33 3.27

ME+1/2/02 -8.24 0.16

ME+1/2/08 -7.36 2.46

ME+1/2/14 -6.81 0.25

ME+1/2/20 -8.23 -0.62

ME+1/2/26 -8.67 0.65

ME+1/2/32 -8.96 2.11

The Cocoa 0T fits are not far from the PG numbers

The 1_2 chamber deviations with field agree w/ Celso's numbers

The HSLM6 fits are bad because of a blocked IR target

Chamber center Z deviationsChamber center Z deviations

Rms=1.5

Rms=1.0James N. Bellinger 20-March-2009

7

Fit Ring Fit Ring (average of all chambers)(average of all chambers) Position Position Deviations from IdealDeviations from Ideal

0T-Ideal

X

0T-Ideal

Y

0T-Ideal

Z

3.8T-Ideal

X

3.8T-Ideal

Y

3.8T-Ideal

Z

+1/3 .74 -.76 -.94 .79 -.68 -2.18

+1/2 .98 -.98 1.59 1.10 -.97 -6.27

PG

(disk).58 -1.37 0.57 NA NA NA

James N. Bellinger 20-March-2009

8

ME+1/3/03 -0.5 1.53 2.03

ME+1/3/09 -0.83 1.99 2.83

ME+1/3/14 -1.14 1.09 2.23

ME+1/3/20 0.41 2.63 2.22

ME+1/3/27 -1.93 -0.69 1.25

ME+1/3/33 2.22 0 -2.22

AVERAGE -0.8 1.3 2.1

At disk bottom

At disk top

Tilts (mrad) determined from DCOPS Z positions at upper and lower ends of each chamber

0T 3.8T 3.8T-0T

ME+1/3 chamber tilts (mrad)ME+1/3 chamber tilts (mrad)

James N. Bellinger 20-March-2009

9

Uses the DCOPS PG targets to predict the DCOPS dowel positions for the Xfer DCOPS and the ME+1/3 DCOPSDifferent target holders at ME+1/3/09_outer and ME+1/3/27_outer?? Inconsistent

XFERPG Pred

1/3OutPG Pred

1/3InPG Pred

XFerCocoa

1/3OutCocoa

1/3InCocoa

XFer Coco-PG

1/3OutCoco-PG

1/3InCoco-PG

HSLM16823.54

6822.89

6823.74

6822.07

6821.67

6822.52

-1.47 -1.22 -1.22

HSLM26814.79

6809.68

6817.57

6819.28

6818.13

6819.57

4.49 8.45 2.00

HSLM36817.67

6816.99

6820.12

6819.78

6818.86

6820.82

2.11 1.87 0.70

HSLM46826.79

6825.80

6826.16

6825.68

6825.09

6824.39

-1.11 -0.72 -1.77

HSLM56826.27

6817.91

6828.22

6825.62

6824.18

6827.51

-0.66 6.27 -0.71

HSLM66829.10

6826.17

6828.15

6838.06

6833.60

6829.79

8.97 7.43 1.64

PG targets and Cocoa 0T Fits:PG targets and Cocoa 0T Fits:Z of DCOPS dowelsZ of DCOPS dowels

James N. Bellinger 20-March-2009

10

DCOPS from PG vs Cocoa 0T FitDCOPS from PG vs Cocoa 0T FitSummarySummary

DCOPS Dowel positions: 0T Cocoa fit – predicted from PG of DCOPS targets

Reference: mean= 0.67, rms=2.29mmME+1/3_outer: mean= 2.93, rms=3.83mmME+1/3_inner: mean= -0.20, rms=1.37mm

HSLM6 is not included

RMS is large, and at least partly attributable to PG problems

“Reference” = reference DCOPS on transfer plateJames N. Bellinger 20-March-2009

11

Deviations from IdealDeviations from Ideal

Chamber mounting errors: should not exceed a few mm

PG measurement errors: supposedly 300 microns but I don’t believe that anymore

Cocoa fitting errors

Real distortions because of the field

James N. Bellinger 20-March-2009

12

Cocoa Estimated ErrorsCocoa Estimated Errors

Cocoa returns some estimated errors for quantities in the coordinate system of the mother volume(Cocoa uses a hierarchical system description)

If I assume that off-diagonal entries are 0, I can transform this to the CMS coordinate system

I have no sense of how well Cocoa estimates errors

James N. Bellinger 20-March-2009

13

3.8T Cocoa ME+1/3 3.8T Cocoa ME+1/3 Chamber CentersChamber Centers

mm, Cocoa errors

X Y Z

ME+1/3_03 5593.20 ± .37 2033.34 ± .31 6864.52 ± .13

ME+1/3_09 1035.73 ± .30 5860.51 ± .38 6863.06 ± .13

ME+1/3_14 -3825.85 ± .25 4558.86 ± .23 6864.59 ± .37

ME+1/3_20 -5861.03 ± .16 -1033.74 ± .30 6867.26 ± .37

ME+1/3_27 -1032.27 ± .30 -5861.44 ± .38 6866.91 ± .13

James N. Bellinger 20-March-2009

14

Now Compare Cocoa to DDDNow Compare Cocoa to DDD

Cocoa errors and chamber mismounts both contribute to this

Remove overall disk rotation and translation to get a picture of the internal shifting

Only 6 chambers available for ME+1/2

Only 5 chambers for ME+1/3 (PT6 bad)

Does NOT display chamber tilts

James N. Bellinger 20-March-2009

15

ExpectExpect

Z shift of ring due to disk bending will be gone

Rotation of disk will be gone

Chamber mismounting, sensor mismeasure, and Cocoa fit error will remain

James N. Bellinger 20-March-2009

16

ME+1/3 deviation changes with fieldME+1/3 deviation changes with field

5 measured centers

Overall rotation and translation is removed

No more than a few dozen microns difference between the patterns found with field off and field onMax dev =1.6mm

Animated

cm

James N. Bellinger 20-March-2009

17

Cocoa EstimatesCocoa Estimates

Cocoa vs Ideal deviation RMSs are comparable to and smaller than (on the average) PG vs Ideal deviation RMSs: next slide’s tableCocoa better than PG?

Deviation averages aren’t always 0 because of missing measurements

BUT

Cocoa may be biased to finding things close to the ideal, since the ideal geometry is one of the inputs!

James N. Bellinger 20-March-2009

18

““Cocoa(0T) vs Ideal” Cocoa(0T) vs Ideal” vsvs “PG vs Ideal” “PG vs Ideal”Variation of DeviationsVariation of Deviations

Cocoa Cocoa PG Apin PG Apin

ME+1/2 ME+1/3 ME+1/2 ME+1/3

X devs 0 ± 1.2 0 ± 0.8 0 ± 0.7 0 ± 0.8

Y devs 0.1 ± 0.7 0.2 ± 0.6 0.2 ± 0.9 1.1 ± 1.5

Z devs 0 ± 0.4 -0.5 ± 0.8 3.1 ± 6.0 1.8 ± 5.5

James N. Bellinger 20-March-2009

19

Check for BiasCheck for Bias

Create a new 0T SDF file using PG measurements instead of Ideal geometry as the starting point for chamber positions

Compare fits from this special run to the normal 0T run

James N. Bellinger 20-March-2009

20

ME+1/3 0T Cocoa fits using PG startME+1/3 0T Cocoa fits using PG start

ME+1/3_03 5595.34 2033.7 6866.29

ME+1/3_09 1035.84 5860.48 6863.06

ME+1/3_14 -3826.75 4559.44 6864.58

ME+1/3_20 -5863.59 -1034.74 6869.03

ME+1/3_27 -1032.91 -5863.23 6870

ME+1/3_33 4558.73 -3827.16 6875.77

X Y Z

James N. Bellinger 20-March-2009

“Chi2” for ideal is 1593, special is 1643 for 866 “dof”

21

Special 0T – normal 0TSpecial 0T – normal 0T

X Y Z

ME+1/3_03 2.13 0.39 0.01

ME+1/3_09 0 0 0

ME+1/3_14 -0.76 0.73 0.13

ME+1/3_20 -2.64 -0.7 0.31

ME+1/3_27 -0.39 -1.86 -0.01

ME+1/3_33 0.52 -0.66 -0.01

PG notavailable

James N. Bellinger 20-March-2009

Rms=.15

22

Special 0T – normal 0T: notesSpecial 0T – normal 0T: notes

• The difference between using PG and Ideal geometry as a starting point has little effect on the Z fit: 10 microns in most places

• HSLM2 did not have good PG measurements for the alignment pins, so the Special run used Ideal measurements

• X and Y are not well constrained without the presence of the Transfer Lines.

• The fact that the Z measurement is bad at PT6 is irrelevant to this comparison, which studies fit stability

James N. Bellinger 20-March-2009

23

• Special 3.8T– Endcap data from 3.8T

– Initial chamber and transfer plate positions from PG

– Link and MAB fit geometry and data for 3.8T

5’th Cocoa Run5’th Cocoa Run

James N. Bellinger 20-March-2009

24

3.8T Fit Using Initial 3.8T Fit Using Initial Chamber Positions from Apin PGChamber Positions from Apin PG

X Y Z

ME+1/3_03 5595.336 2033.726 6864.532

ME+1/3_09 1035.726 5860.509 6863.053

ME+1/3_14 -3826.607 4559.585 6864.728

ME+1/3_20 -5863.667 -1034.446 6867.583

ME+1/3_27 -1032.655 -5863.300 6866.901

ME+1/3_33 4559.190 -3826.700 6866.523

James N. Bellinger 20-March-2009

25

Special 3.8T – Original 3.8TSpecial 3.8T – Original 3.8T

X Y Z

ME+1/3_03 2.136 0.388 0.016

ME+1/3_09 -0.003 0.000 -0.002

ME+1/3_14 -0.759 0.725 0.134

ME+1/3_20 -2.638 -0.703 0.319

ME+1/3_27 -0.385 -1.865 -0.012

ME+1/3_33 0.099 -1.085 -0.917

James N. Bellinger 20-March-2009

26

Cloud on the horizon:Cloud on the horizon:ME+1/2 chamber Z centersME+1/2 chamber Z centers

Fits My B=0 Celso B=0 Diff B=0 My B=3.8 Celso B=3.8

Diff B=3.8

ME+1/2_02 6770.64 6771.40 .76 6762.40 6763.18 .78

ME+1/2_08 6768.94 6769.58 .64 6761.59 6762.21 .62

ME+1/2_14 6768.55 6769.15 .60 6761.74 6762.28 .54

ME+1/2_20 6771.95 6771.75 -.20 6763.72 6763.46 -.26

ME+1/2_26 6775.25 6775.54 .29 6766.58 6766.84 .26

ME+1/2_32 6774.78 6774.91 .13 6765.82 6765.97 .15

James N. Bellinger 20-March-2009

27

Not sure yet

Change with field is the same

Why the difference?Why the difference?

James N. Bellinger 20-March-2009

28

ConclusionsConclusions

Cocoa fit for ME+1/3 chambers is stable with respect to initial conditions in Z

Photogrammetry includes spurious outliers

Cocoa deviations from the ideal are tighter than PG deviations, even if PG values were the starting point

James N. Bellinger 20-March-2009

29

Blessing for ME+1/3 chamber ZBlessing for ME+1/3 chamber Z

0T Pos mm 0T Tilt mrad 3.8T Pos mm

3.8T Tilt mrad

ME+1/3_03 6866.29 -0.5 6864.532 1.53

ME+1/3_09 6863.06 -0.83 6863.053 1.99

ME+1/3_14 6864.58 -1.14 6864.728 1.09

ME+1/3_20 6869.03 0.41 6867.583 2.63

ME+1/3_27 6870 -1.93 6866.901 -0.69

Average 6866.59 -0.8 6863.36 1.3

Δ from nominal

-0.85mm -0.8mrad -4.08mm 1.3mrad

James N. Bellinger 20-March-2009

30

Evaluate the PGEvaluate the PG

Photogrammetry errors for the Z of the alignment pins are not 300μ

Loveless says the pins were not inserted to nominal depth

James N. Bellinger 20-March-2009

31

• Targets on DCOPS (not used in next slide)

• Targets on alignment pins

• Coded targets on chambers

• Use alignment pins to define chamber axis

• Use X/Y of coded target to predict a Z

• Compare predicted w/ measured Z

PG targets on chambersPG targets on chambers

James N. Bellinger 20-March-2009

32

Coded Target Z – Predicted ZCoded Target Z – Predicted Z

mm

ME+1/3 chambers

Alignment pins used to predict Z of coded target given its X/Y

Rms=1.4mm

Looks like a single distribution, NOT a narrow one with a few typos

James N. Bellinger 20-March-2009

33

• Oleg says some were on wrong chambers

• Use his corrected table

• Look at deviation of coded target from alignment pin axis line

• Nothing looks badly wrong; largest deviation is 145mm from axis (min 75mm)

Crosscheck coded targetsCrosscheck coded targets

James N. Bellinger 20-March-2009

34

DCOPS targetsDCOPS targets

DCOPS on Transfer Plate, chamber 3 outer and chamber 3 inner have three 1.27mm PG targets on top.

These were included in the survey.

In the following table the three measurements were averaged for each of the 18 visible DCOPS

James N. Bellinger 20-March-2009

35

Variation of PG Z for DCOPSVariation of PG Z for DCOPS

Ref Ave

Ref Rms

3 out Ave

3 out Rms

3 in Ave

3 in Rms

HSLM1 -818.627 0.169 -819.137 0.097 -818.447 0.193

HSLM2 -821.44 0.037 -826.92 0.385 -820.46 0.198

HSLM3 -819.437 0.054 -820.387 0.067 -818.577 0.197

HSLM4 -817.093 0.040 -818.067 0.099 -817.37 0.169

HSLM5 -823.65 0.082 -831.597 0.737 -819.617 0.148

HSLM6 -819.76 0.092 -822.547 0.238 -818.847 0.302

PG target position 3-point ave/rmsJames N. Bellinger 20-March-2009

36

DCOPS PG Variation Along LineDCOPS PG Variation Along Line

HSLM1

HSLM2

HSLM3

HSLM4

HSLM5

HSLM6

Ave Z Rms Z

-818.737 0.292233

-822.94 2.842581

-819.467 0.739234

-817.51 0.409507

-824.954 4.977033

-820.384 1.573732

James N. Bellinger 20-March-2009

37

Evaluation of DCOPS targetsEvaluation of DCOPS targets

Consistency of measurement:The Transfer Plate DCOPS are measured

significantly better than the rest

HSLM5 outer DCOPS are not very consistent

Consistency along line:Chamber mounting variations contribute!

HSLM2 and HSLM5 show unreasonably large fluctuations

James N. Bellinger 20-March-2009

38

Chamber surface Z’s from PGChamber surface Z’s from PG

Apin outer

Apin inner Coded

DCOPS 3 outer

DCOPS 3 inner Diff outer Diff inner

HSLM1 -696.47 -696.93 -697.44 -697.497 -696.807 -1.02667 0.123333

HSLM2 NA -697.98 -699.06 -705.28 -698.82 NA -0.84

HSLM3 -696.89 -696.3 -698.39 -698.747 -696.937 -1.85667 -0.63667

HSLM4 -694.78 -695.64 -696.72 -696.427 -695.73 -1.64667 -0.09

HSLM5 -699.15 -697.15 -699.21 -709.957 -697.977 -10.8067 -0.82667

HSLM6 -700.4 -696.53 -697.45 -700.907 -697.207 -0.50667 -0.67667

Rms=.53 Rms=.37James N. Bellinger 20-March-2009

39

Z’s from PG vs dataZ’s from PG vs data

• HSLM5 outer chamber 3 DCOPS measurements are clearly out of line

• The DCOPS readings from HSLM5 correspond to corrected values shown at right.– Not much variation

XFer 3 Out 3 In 2

18.98 16.72 17.10 18.26

mm, corrected data values

James N. Bellinger 20-March-2009

40

PG ConclusionsPG Conclusions

Assuming the Alignment pin and coded target errors are comparable, the variation on these is 1mm and not 300 microns.If coded error=300μ, Apin error is 2mm

If the variation is due to random errors: for a DCOPS target atTransfer Plate: 140μOuter chamber edge: 470μInner chamber edge:350μ

Disregard PG measures with large disagreements with either other PG measurements or with data?

James N. Bellinger 20-March-2009

41

DisplaysDisplays

Omitting lines illustrating chamber surfaceTriangles show the slope well enough

PG information not displayedDiagram is very cluttered already

HSLM1-5 are animated to show 0 to 3.8T shifts

HSLM6 has bad data for the DCOPS at 3.8T and bad Z information for the distancemeter

James N. Bellinger 20-March-2009

42

Chamber surface estimates

Red=RealGreen=Sim

MAB ASPD

ME12 ASPD

ASPD P4

Distancemeter and dists

IR target

DCOPS dowels

Animated

James N. Bellinger 20-March-2009

43

Animated

James N. Bellinger 20-March-2009

44

Animated

James N. Bellinger 20-March-2009

45

Animated

James N. Bellinger 20-March-2009

46

Animated

James N. Bellinger 20-March-2009

47

3.8T is bad

IR target obscured, Z is bad

James N. Bellinger 20-March-2009

48James N. Bellinger 20-March-2009

Animated

49James N. Bellinger 20-March-2009

Animated

50James N. Bellinger 20-March-2009

Animated

51James N. Bellinger 20-March-2009

Animated

52James N. Bellinger 20-March-2009

Animated

53James N. Bellinger 20-March-2009

54

Blessing for ME+1/3 chamber ZBlessing for ME+1/3 chamber Z

0T Pos mm 0T Tilt mrad 3.8T Pos mm

3.8T Tilt mrad

ME+1/3_03 6866.29 -0.5 6864.532 1.53

ME+1/3_09 6863.06 -0.83 6863.053 1.99

ME+1/3_14 6864.58 -1.14 6864.728 1.09

ME+1/3_20 6869.03 0.41 6867.583 2.63

ME+1/3_27 6870 -1.93 6866.901 -0.69

Average 6866.59 -0.8 6863.36 1.3

Δ from nominal

-0.85mm -0.8mrad -4.08mm 1.3mrad

James N. Bellinger 20-March-2009

55

BACKUPMATERIAL

James N. Bellinger 20-March-2009

56

Method for Predicting Z from PGMethod for Predicting Z from PG

Get PG (X,Y,Z) wrt disk center from UR-0058 or UR-0103

Rotate disk as specified in UR-0124

Translate disk as specified in UR-0124

James N. Bellinger 20-March-2009

57

PG IssuesPG Issues

Photogrammetry is not always correct

James N. Bellinger 20-March-2009

58

PG errors and chamber mismountsPG errors and chamber mismounts

PG deviations from Ideal include 1. PG error, typos, and wrong targets

2. Real chamber mismount

3. Overall shifts and rotations of the disk

Subtract the overall shifts and rotations to get a better picture of the PG errors and mismount errors

In what follows PG Chamber centers are derived from alignment pin locations

James N. Bellinger 20-March-2009

59

PG vs DDD, ME+1/2PG vs DDD, ME+1/2

Chamber centers

Overall rotations and translations are removed

Deviations combine PG error and chamber mounting

cm

Max x/y dev is 2.2mm

James N. Bellinger 20-March-2009

60

PG vs DDD, ME+1/3PG vs DDD, ME+1/3

Chamber centers

Overall rotations and translations are removed

Deviations combine PG error and chamber mounting

cm

Max x/y dev is 2.6mm

Still a tilt?

James N. Bellinger 20-March-2009

61

PG to DDD summaryPG to DDD summary

Deviation of PG from standard geometry in the X/Y plane is at most 2.2mm for ME+1/2 and 2.6mm for ME+1/3.

RMS for X deviations is .7 for ME+1/2

.8 for ME+1/3

RMS for Y deviations is.9 for ME+1/2

1.5 for ME+1/3

RMS for Z is about 6. and 5.5mm

James N. Bellinger 20-March-2009

62

Z’s from PG vs dataZ’s from PG vs data

• The HSLM6 outer Z seems out of line with the rest in the line, but agrees with the alignment pin estimate

• Data shows O(4mm) deviation at 3 Outer also

• PG deviation is OK

XFer 3 Out 3 In 2

18.32 15.79 21.32 23.45

mm, corrected data values

James N. Bellinger 20-March-2009

63

Comparisons of Ideal with Cocoa Comparisons of Ideal with Cocoa RingsRings

James N. Bellinger 20-March-2009

64

0T ME+1/2 Cocoa vs Ideal0T ME+1/2 Cocoa vs Ideal

6 measured centers

Overall rotation and translation is removed

cm

James N. Bellinger 20-March-2009

65

0T ME+1/3 Cocoa vs Ideal0T ME+1/3 Cocoa vs Ideal

5 measured centers

Overall rotation and translation is removed

cm

James N. Bellinger 20-March-2009

66

3.8T ME+1/2 Cocoa vs Ideal3.8T ME+1/2 Cocoa vs Ideal

6 measured centers

Overall rotation and translation is removed

cm

James N. Bellinger 20-March-2009

67

3.8T ME+1/3 Cocoa vs Ideal3.8T ME+1/3 Cocoa vs Ideal

5 measured centers

Overall rotation and translation is removed

cm

James N. Bellinger 20-March-2009

Recommended