COMPUTER PROGRAM DOCUMENTATION

NUMBER 2

perspective Center Determination

John D. McLaurin

U.S. Geological SurveyTopographic DivisionMcLean, Virginia

May 1969

Program Number:Operating System: OS/360 vith HASP Equipment: IBM 360/65 Language: FORTRAN IV (G-Level)

Open-file Report

COMPUTER COirTRIBUTIOli

1. Weighted Triangulation Adjustment, by Walter L. Andersen, 1969

2. Perspective Center Determination, by John D. McLaurln, 1969

Free on application to the Chief, Computer Center Division, U. S. Geological Survey, Washington, D. C. 202k2

CONTENTS

Page

Abstract .......................... 1

Introduction ........................ 1

Description. ........................ 2

Restrictions ........................ 7

Input. ........................... 7

Program run preparation. .................. '13

Printed output ....................... 13

Diagnostic messages. .................... 16

Storage requirements .................... 16

Timing ........................... 17

Library routines ...................... 17

References ......................... 17

AttachmentsA. Program listing ................... 19B. Symbols and variables ................ 32C. Macro flowchart ................... 35D. Printed output. ................... UO

Figure 1. Control cards .................. 142. --Data deck files ................. 15

PERSPECTIVE uEJfeK DETERMINATION

by John D. McLaurin

ABSTRACT

This program determines coordinates of the perspective center of a stereoplotter projector by bringing two bundles of rays into a "best fit coincidence in a space-resection solution. One of the bundles of rays is defined by the perspective center and the grid intersections on a grid plate. The other bundle of rays is defined by the per­ spective center and the projected grid intersections in the model space.

The program is used with the independent-model method of semianalytical aerotriangulation, which requires the coordinates of perspective centers. It may also be used in checking the calibration of stereoplotters.

INTRODUCTION

Certain methods of independent-model aerotriangulation such as those described by Inghilleri and Galetto, Schut, Thompson, and Williams and Brazier require the coordinates of the perspective center of each projector so that the models can be joined in a strip. This documentation describes a computer program for determining the three-dimensional coordinates of these perspective centers.

DESCRIPTION

A grid of known precision is projected through a stereoplotter projector, and the coordinates of grid intersections in the model space are measured. Two "bundles of rays will then originate from the same theoretical point the perspective center. One bundle extends from the perspective center to grid intersections or image points on the precise grid plate; the other extends from the perspective center to projected grid intersections in the model space. After correcting systematic errors, the latter "bundle of rays is fitted to the other bundle in a least-squares space-resection solution.

Resection is based on the condition of collinearity, which requires that each Image, its object, and the perspective center lie on a straight line. The equations of collinearity have been derived in Harris, et al., and may be stated as follows:

x m (X-Xc) mll * (Y-Yc) mi2 + (Z-ZC ) *132 (x-xc ) *3i + (Y-YC ) m32 + (z-zc ) 0133

(x-xc ) *2i + (Y-YC ) "feg + (z-zc ) *23 (2)(X-XC ) m31 + (Y-YC ) m32 + (Z-ZC ) m33

In the equations, x and y are image coordinates of the grid inter­ sections based on the principal point as origin; z is the principal distance of the projector, considered to have a negative sign; X, Y, and Z are the model space coordinates of the projected grid intersections; Xc> Yc , and Zc are the unknown model space coordinates of the perspective center; and the m's are unknown direction cosines indicating the relative angular orientation of the image and model space coordinate axes.

The X and Y coordinates are measured with a digitized stereoplotter with the Z coordinate set at some constant value. The x and y values are derived from the grid plate calibration; the z comes from a previous calibration of the principal distance of the projector. Xc , Yc , and Zc are the unknown coordinates of the perspective center, and the three angles w , $ , and K are the unknown angular parameters . These last six parameters are the unknowns whose values will be determined in the resection.

The angles co, <j> , and K , are related to the m's as follows:

ml2

M =m31

cos 4> cos <

cos 4> sin

cosco sinK sino) since+sinu> sin<f> sin* -cosu) sin<f> cos K

coso) COSK 8inw cos*sin<l> sin* +cosu> sin<l> sin*

cos cos<t>

(3)

To solve the resection problem, the observation equations must "be linearized using a Taylor series expansion, and assumed values are used for the six unknown parameters. The resection is then solved iteratively for corrections to the unknowns until a satisfactory degree of convergence is achieved. The linearized observation equations, as modified for this program, are as follows:

vx = do, {x [ (Z-ZC ) m32 - (Y-Yc )m33 - z (Z-Zc )m12 - (Y-YC ) m13 )}(+l/R) (k)

+dk (z

- dX

- dY

- dZ

(X-XC ) n31 -i- (Y-Yc )n32

-I- (Z-Zc )n13 ] > (+1/R)

-i- Y-

{ x

( x

{ x

- z

(l/R)

(l/R)

- z[ (X-Xc )nu+ (Y-Yc )n12

-i- { x [(X-Xc )m31 + (Y-Yc )m32 -i- (2-

- (Y-Yc )m12 + (Z-Zc )m13 ]} (l/R)-z

and

vhere

R = (X-Xc )m31 + (Y-Yc )m32 -»- (Z-Zc )m33

mn = Q°s ^ cos K

m^2 = cos u) sin K + sin u> sin 4> cos K

m = s^n w s:*- n K " cos w sin cos K!3

= -cos <j> sin K

m22 = cos u> cos K - sin u> sin <j> sin

m23 = sin w cos K + cos w sin <J> sin

m32 ~ "snu) cos

moo = cosw cos

vy = d" fy[ (Z-Zc )m32 - (Y-Yc )m33 ] - z [ (Z-Z^rn^ - (Y-Y^m^]} (+1/B) (5)

+d* fyl (X-Xc )n31 + (Y-Yc )n32 + (Z-Zc )n33 l

-z [ (X-X^ng! + (Y-Yc )n22 + (Z-Z^oJ} (+1/R)

+dk{z [ (X-Xc )mil + (Y-Yc )m12 + (Z-Zc )m13 ]}

- dXc {y m31 - z m21

- dYc {y m32 - z m22

- dZc {y m33 - z m23

+ {y [(X-Xc )m31 + (Y-Yc )m32 + (Z-Zc )m33]

and

n!2

n...- = -cosw cos<|> COSK

sin*

cos<f> sinic

cos<j> sine

no^ as cos4>

no - sixu sixty

Initial approximations for the unknowns Xc , Yc , Zc, to, <^, and K are read as input to the program. These values are used during the first cycle. One set of observation equations is formed for each grid inter­ section read. The normal equations are formed from these observation equations, using the usual matrix algebra method. The coefficient matrix of the normal equations is inverted using the standard Gauss-Jordan method. Corrections to the unknowns are found using the following matrix equation:

X = (ATA)* ATL (6)

where X is the vector of unknowns

(ArA) is the inverse of the normal equations coefficient matrix

A is the coefficient matrix of the observation equations, and AT is the transpose of this matrix

and L is the vector of constant terms in the observation equations.

The following expression is computed:

TEST » ~\/dXj~ + dYc2 + dZc2

This value is compared with a tolerance read in with the data to dee if satisfactory convergence has been achieved. If TEST is larger than the tolerance, the computed corrections of the unknowns are added to the initial approximations of the unknowns, and the solution is iterated.

After the tolerance has been met or six cycles have been completed, the program proceeds to compute residuals on grid intersections in the model space. Using the values of unknowns computed in the resection, grid intersections are projected into the model space and compared with measured coordinates. In addition, the radial distance from the principal point to the grid intersection is computed for (l) the true position of the grid point on the grid plate and (2) the computed position found by transforming the measured position from the model space to the grid plate. /The difference between these radial distances is printed out as a radial distortion term.

The standard error of unit weight of the grid points is computed with the following equation:

STD =s\ /

2 n-y

where VY and vv are the X and Y residuals-A. JL

n is the number of points used

and V is the number of unknowns (usually 6).

The variance-covariance matrix is computed by multiplying the inverse of the normal equations coefficient matrix by the standard error of unit weight squared (unit variance). The standard errors of unknowns are computed from this matrix.

Multiple readings may be made on the projected grid intersections. The program counts the number of readings and computes the mean coordinates and standard deviation for each point. Then, if the coordinatoraraph of the digitized stereoplotter has been calibrated, the mean projected grid coor­ dinates will be corrected using X- and Y-scale and perpendicularity correc­ tion factors submitted as input.

Several sets of readings using the sane grid points and plate coordinates may be batched to run at once. The plate grid coordinates need only be placed in the data deck once, followed by the sets of projected coordinates. This is useful when projected coordinates are read at different Z levels.

RESTRICTIOBS

The program requires at least three grid points for the computation. Using many more than three points, however, provides a more satisfactory solution, since the method of least'squares is used in the adjustment. The maximum number of points that may be used is 50, but more may be used if the dimension statement is changed.

The projected grid coordinates must be arranged in the same order as the plate grid coordinates. If multiple readings are made on the projected points, all readings on each point must be grouped together. A different number of readings may be made for each point, if desired.

Input for this program must be on punched cards. Several sets of projected grid readings may be computed using the same plate grid points and coordinates.

Data for a new computation using different grid points and coordinates begin with a new card 1. As many groups of data as desired may be computed on one Job.

Card 1 Title

Input Item

Any alphameric information

Column Number

1-80

Format

2QAk

Program Variable

TITLE (l) thru TITLE (20)

Card 2 Input Format for Precise Grid Data

Input ItemColumn Number Format

Program Variable

Any desired format for reading pre­ cise grid data. Three fields must be provided In the following order:

Field 1--Point number

Field 2 x coordinate of point

Field 3 y coordinate of point

Example: (l^,2F10.0)

1-80 2Q/& 5M (l) thru FM (20)

Card 3 Input Format for Measured Coordinates

Input ItemColumn Number Format

Program Variable

Any desired format for reading measured coordinates. Four fields must be provided in the following order:

Field 1 Point number

Field 2 X coordinate of point

Fielfl. 3 Y coordinate of point

Field U Z coordinate of point

Example: (l4,3F10.0)

1-80 2QAU FMP (1) thru FMT (20)

8

Card k Specifications

Input Item

Number of grid points used

Number of sets of projected grid readings using the same plate grid points and coordinates.

Code indicating -whether projected grid readings are to be corrected for coordlnatograph errors.

1 corrections will be made; card 5 will be read.

0 = corrections will not be made; card 5 will not be read.

Principal distance of projector, written as a positive real number in millimeters.

Tolerance for testing convergence of the solution, written as a positive real number in millimeters.

Column Kumber

1-15

6-10

11-15

16-25

26-35

Format

15

15

15

F10.0

F10.0

Program Variable

NPTS

ICAIF

ICOR

FOCAL

GDIF

9 Card 5 Coordinatograph Correction Factors This card is read only if ICOR in columns 11-15(see card k) is equal to 1. These factors are used to correct projected grid coordinates for errors in the coordinatograph.

Input Item

X-scale correction factor

Y-scale correction factor

Nonperpendicularity correction factor.

Column Number

1-20

21-1*0

ltl-60

Format

D20.8

D20.8

D20.8

Program Variable

XSCAL

YSCAL

SIKALP

Card 6 thru 1-1 Precise Grid Coordinates (see fig. 2) One card is read for each grid intersection according to input format on card 2. The plate coordinate system is based on a positive plate the Z axis is considered positive upward so that the principal distance has a negative sign. Units of the coordinates are millimeters; the origin of the coordinate system is the perspective center.

Input Item

field. 1 Point number.(see card 2.)

Field 2 x coordinate of gridintersection.

Field 3 y coordinate of gridintersection.

Column Number

Columnnos . arespecifiedby formaton card 2.

Same asabove

Same asabove

Format

Integerwithlengthof fieldspecifiedby formaton card 2.

Real num­ber withlength offieldspecifiedby formaton card 2.

Same asabove

Program Variable

IDEKT(I)where Idesignatesthe Ith gridintersection.

PX(I) whereI designatesthe Ith gridIntersection.

PY(!)

10

Card I Initial Approximations to Unknowns The units for Xc , Yc , and Zc are in the same units as the projected coordinates,

Input Item

Initial value for w in minutes

Initial value for $ in minutes

Initial value for K in minutes

Initial value for Xc

Initial value for Yc

Initial value for Zc

Column Number

1-10

11-20

21-30

31-**0

1*1-50

51-60

Format

F10.0

F10.0

F10.0

F10.0

F10.0

F10.0

Program Variable

AOMEGA

APHI

AKAPPA

XE .

YE

ZE

Cards 1+1 thru M-l Projected Grid Coordinates (see fig. 2 ) Multiple readings may be made for each grid intersection according to input format on card 3- All readings for the same point are placed together in the deck. The program computes the mean coordi­ nates and standard deviations for each point. The Z coordinate is constant for each set of projected grid coordinate readings. Points must be placed in the same order as that for plate grid coordinates in the data deck.

Input Item.Column Number Format

Program Variable

Field I Point number Column nos. as specified by format on card 3-

Integer withlength of field specified by format on card 3

ID

11

Cards 1+1 thru M-l Projected Grid Coordinates (con't)

Input Item

Field 2--X coordinate of projectedgrid

I'ield 3 Y coordinate of projected grid

Tield k Z coordinate of projectedgrid

Column Number

Same asabove .

Same as above.

Same asabove.

Format

Realnumberwithlengthof fieldspecifiedby formaton card 3 (Singlepreci­ sion. )

Same as above.

Same asabove.

Program Variable

TMX(NRDG)where NRDGdesignatesthe order inwhich thereading wasmade.

MT(NEDG) (See item above.)

TMH(l) whereI designatesthe Ith gridintersection.

Card M, Flag End of projected grid coordinates (for one set of data). This card must be in the same format as cards 1+1 thru M-l.

Input Item

Field 1 Must be blank or zero

?ield 2 Not pertinent, but must not be an alpha character

Tield 3 Same as above

?ield k Same as above

Column Number

See card 3.

Not per­ tinent

Same as above

Same as above

Format

See card 3.

Not per­ tinent

Same as above

Same as above

Program Variable

ID

Not per­ tinent

Same as above

Same as above

12

PROGRAM RUN PREPARATION

The program is stored on disk on the 360/65 computer. The following deck setup (see figs. 1 and 2) includes the OS/360 control cards required to call the program from the disk. The OS/360 control cards (//'s in columns 1-2) must be as shown below. The JOB card is described in System Bulletin No. 1 of the Computer Center Division. All control cards must be punched in EBCDIC code. The symbol b denotes a blank card column, and <J> denotes a letter 0 to distinguish it from a zero.

PRINTED OUTPUT

The output of the program is in the following form. (See attachment D).

1. Title

2. Number of points and principal distance used in the computation.

3. Input data: point numbers, number of readings on each point, and grid coordinates.

h. Mean projected grid coordinates and standard deviations.

5. Values of unknowns after each cycle of the solution. The first line contains initial approximations to the unknowns. The final line contains values of the unknowns to be used in further com­ putations.

6. Residual and distortion values. Residuals are in the coordinate system of the projected points: distortion values are in plate coordinates.

7- Variance-covariance matrix.

8. Standard errors.

If more than one set of projected readings is used with the same set of grid coordinates, the output starts over again with item 2, number of points used and assumed principal distance. Output for an entirely new group of data starts at the top of a new page with the title. See attach­ ment D for output listing for sample problem.

13

// FT05F001bDDb*

// FT06F001bDDbSY50UT=A//bEXECbPGM = W5344

| //J0BUBbDDbDSNAME «SYS1. U^ADLIB,PISP^LD, KEEP)

USEP'S ufo CARD

Figure 1.-- Control cards

END 0F PROJECTED C^0RD3M\

PROJECTED GRID C00RDS

INITIAL APPROXIMATIONS

DATA FOR ONE GROUP WITH ONE

SET OF PROJECTED GRID COORDINATES

PRECISE GRID C00RD5

SPECIFICATIONS CARD

TITLE CARD

END0F PROJECTED C00RDS

PR0JECTED GRID C00RDS

INITIAL APPR0X1MATI0NS

END 0F PROJECTED C00RD5

PROJECTED GRID C00RDS

INITIAL APPROXIMATIONS

PRECISE GRID C00RDS

C00RDINAT0GRAPH C^RR£CT(0NS

SPECIFICATIONS CARD

FORMAT CARD-MEASURED

F0RMAT CARD-GRIDTITLE CARD

REPEATEDFOR

ADDITIONAL SETS

DATA FOR ONE GROUP

WITH RELATED SETS OF PROJECTED

GRID COORDINATES

Figure 2.--Data deck files

15

DIAGNOSTIC MESSAGES

The following error messages may be encountered when using this program:

ERROR - CARDS ARE OUT OF ORDER AT POINT NO.XXX -- This indicates that the projected coordinates are not in the same order as that of the plate grid coordinates. The number printed in XXX is the point number that should have appeared in the projected coordinate list. The program stops after printing this message. The input data deck should be checked, and the projected coordinates re­ arranged .

NORMAL EQUATIONS MATRIX IS SINGULAR -- This message indicates trouble in the matrix inversion routine, most likely caused by not having the data deck in the correct order or not using enough points in the solution. The program stops after printing this message.

SORRY - SOLUTION DOES NOT CONVERGE -- This message is printed if the test for convergence of the solution has not been met after six iterations, probably because the value for GDIF entered on card 3 was too small. For most uses a value of 0.01 or 0.001 is sufficient. It is also possible that initial approximations of the unknowns are too far from the correct values. The program proceeds through the computation of the residuals and standard errors after printing this message. Values of the unknowns, computed on the last iteration, are used.

STORAGE REQUIREMENTS

This program requires 21, J '36 bytes of internal storage as follows:

Main program 18,586 bytes

Subroutines:

RMSE 758

DMINV 2,092

21,^36 bytes

16

TIMING

Average HASP time required for running a typical solution is about O.b minute. This is the time required if using a card object deck. Calling the program from disk should require less time.

LIBRARY ROUTINES

The subroutine, DMIW, is included vith the program deck because this double-precision routine is not in the Scientific Subroutine .Package.

REFERENCES

Harris, W. D., Tewinkel, G. C., and Whitten, C. A., 1962, Analyticalaerotriangulation: U.S. Coast and Geodetic Survey,Technical Bulletin 21.

Inghilleri, G., and Galetto, R., 1967, Further developments of the methodof aerotriangulation by independent models: Photogrammetria,v. 22, no. 1, p. 13.

Karren, R. J., 1966, An evaluation of aerial camera calibration by themulticollimator method: MS Thesis, Ohio State University.

Keller, M., and Tevinkel, G. C., 1966, Space resection in photogrammetry:U.S. Coast and Geodetic Survey, Technical Bulletin 32.

Schut, G. H., 1967, Formation of strips from independent models: NationalResearch Council of Canada, Report NRC-9695.

Thompson, E. H., 1965, Review of methods of independent model aerialtriangulation: Photogrammetric Record, v. 5, no. 26, p. 72.

Williams, V. A., and Brazier, H. H., 1965, The method of adjustment ofindependent models, Huddersfield test strip: PhotogrammetricRecord, v. 5, no. 26, p. 123. '

17

ATTACHMENTS

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FORTRAN IV

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69106

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FORTRAN IV U

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MAIN

DATE -

69106

19/90/07

PAGE 0002

0043

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OExm

-xoEv

DtY(1)-YUEV

NRD(M*NRDG

TMX(1)«SUMX

TMYUI-SUMY

NKCG-1

130 IF

IILST.EQ. lOENTCIM GO TO 15

0 Il

-l-l

IF UUEO.O) 11-1

WRITE (6,140) ID

ENTl

I)

FORM

AT (1H0.5X,'ERROR - CARDS ARE OU

TOF ORDER*/5X.*AT POINT N0.*

t14

011

7) STOP

'150 11ST-1D

IF (lCOft.N

E.lt

GO TO

19

0 WRITE (6,160)

160

FORMAT UHO,5Xi*COGRDINATOGRAPH ER

RORS

CORRECTED*)

SMALX-DABS(AMXU))

SMALY«DABS(AMY(in

DO 17Q

I«2iN?TS

ABSV-DABSUMXil))

SMALX-OHIN1(SMALX,ABSV)

ABSV»DABS(AMYU) I

.170 SMALY-CMINK SMALY.ABSV)

00 180 1-1,NPTS

AMX(I»-XSCAL*((AMX(n-SMALX)*(AMY(I)-SMALY)*SlNALP»*$MALX

100 Af4Y(I)»(AMY(I)-SMALY)*YSCALtSMALY

190

WRITE 16.200) NPTS.FOCAL

20C

FORMAT (1HO,5X,'THE NUMBER OF

POINTS USED ON THIS PLATE IS

*tl4

/5Xf

1'

THE

ASSUMED PRINCIPAL DISTANCE USED IN THESE COMPUTATIONS IS*fF15

2.3) UR1TE (6,210)

inJtNTm,NRD(I),PXU),PYm,AMX(n,DEXm,AMY( D.DE

IY( I),TMHd ),!

-!,N

PTS)

210 FORMAT IIHO,5X|»COORDINATES OF INPUT

DATA*/T10,«NO. OF

,T21,'CAL1B

1RATEO GPI'D COORO',T54,'PROJECTED GRID COOHDI NATES'XIX, «PT NO',2X,«

2AEAOINGSS7X, «X«,12X,'Y',9X,'MEAN X«,3X,'X ST

D DEV ,

5X,

' MEAN Y«

,3X

3,'Y ST

D DtV',9X,'Z'/(I5,5X,I3,lX,3F13.3,2X,F8.3,2X,F11.3,2X,F8.3,2

4XrFll

f2)l

IT6K

-0

I FIN-0

WRIT

E (6,220) 1TER,XE,YE,2E,AOMEGA,APHI,AKAPPA

220 FORMAT (1

HO ,«ITER',6X,'X',10X, V',10X,«Z ,9X,»DX',8X,'DY«,8X.«D? t

16X|

OMEGA .6X1* PHI* ,6X.« KAPPA*/ 14 ,3F1U2,30X, 3F10.4)

ITEk

-1

SZ FOCAL

940

590

560

570

580

990

600

610

620

630

640

650

660

670

680

690

700

710

720

730

740

750

760

770

780

790

800

810

820

830

840

850

860

870

880

890

900

910

920

930

940

950

960

970

971 980

990

A1000

A1010

A1020

A1030

A1040

oo o o o o oo oooonopoo o o o o o<"» o o o o oooooooooooooooooooo o.o o oo. o ^-*-"* * *-«i ^-»-«»-»^-»-»»--»-'»--^«>->-> ^*i:-»-'»->^-l-*»-»» *- » ^->-§l-«»-»» H»^«OOOOOOOc>OOOOOO 3DM iy ^ ̂ »~ »~> * « »-* t-« » »- » » o o o o o o o o-o o *> <a «*> «> *o *> <o «* «o a> OP oe o> -4

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»-»l>^ u» t»c« *««»«-»?K*MOXX ^-»-»»«»-»->X.Jt»- m »«oo«

* t V» U» <"» X "^ < X»"V 0«O* U> fs» -V 6) > > O >3ooo'oDfM-»-«is»x4. m.m. m -H z oz o >>«- » >»*22*» -I"-V»-'* U»O Ut U* Z Ut Z «- OO

ix««*«ixxxr-Of>* r> -*. » i u* vt n N» i i < m *

x X 3t'»- v» Cn * f O»«-*j * * *~ no»-> o * * z «VM.^.^X2*rn»«>ii» vi on «

Z X 4- >-^- O

r» ^- IM mx

m m Oi- r-' Z r- r- mx r«»» o x r* r-on » i- oo 2X0 <ZZN>IM m +»< »»is> w i r> N» toi* * < »±± « C? O + K> O O. Om m O bi m m ^ 17 r-z * i-r- -<

z""o IMZ*"

(tf ^^ OJ ^^

5»x » ^- o-O O

mm o»

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oooooooooooooooooooooooooooooooooooooooooooooooooooo

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FORTRAN IV

G

LEVEL It

MCO 3

MAIN

DATE *

6*106

15/50/07

PAGE 00

0%

0136

C139

01

40

!8

0142

0143

0144

0145

0146

0147

0146

C149

0150

0151

C192

At *t

0154

0155

0156

C157

C158

01

59

ClbO

C161

C162

OU3

0164

0165

Olo

6

0167

Olt>

6 C

169

0170

0171

0172

C173

0174

0175

0176

C177

0176

C179

0160

Olel

0162

C183

C164

0165

OBSY(I,5)«R*(CM32*SY-CM22*SZ)

ObSY(I,6)«R*(CM33*SY-CM23*SZ)

260

OBSY(I,7)«SY-OBSX(I,3)

Nu»7

IF (IFIN.EQ.ll GO TO 430

00 270 K«1,NPTS

00 270 I»

1,NC

J00 270 J»I,NQ

270 N<

1 ,J)»M1 ,J)*OBSX(K,n*OBSX(K,J)+OBSY(K,n*OBSY<K,J>

00 2SO I»i»NO

OL 280 J«1.NQ

280 N(J,I)«NU,J)

ND-NU-l

00 290

I»l

, NO

OU 290

J«l,ND

NOW

THE

NORM

AL EQUATION COEFFICIENT

MATRIX IS

CONVERTED

TO AR

RAY

STORAGE

SO THE

SSP

INVERSION

ROUTINE

CAN

BE USED

'

CALL DMINV CUt6iDBT,Ll,Ml )

ir (uET.Nt.O.I Gu TO 310

WRITE (6i300)

300 FORMAT (1H0.5X, 'NORMAL EQUATION MATRIX IS SINGULAR*)

STCP

310 00 320 I-l.NO

SOL(I)«0.

,00 320 J»1,NU

320

SOLt

I)»SDL(1 )*U(IiJ)*N(JiNOI

OUM»SOL(1)

Df»Hl«SOL(2)

OKAP-SOLO)

DX*SOL(4)

OY«SOL(5)

OZ*SCJL(6)

XE»XE«-OX

YE«YE»OY

Zt»ZE*OZ

AOKEGA«AOMEGA*OOM*CONV

-^-

APHI«APHI*DPHI*CONV

AKAPP/k»AKAPPA*OKAP*CONV

WklTE (6,330) ITER,XE,YE,ZE,OX,DY,OZ,AOM6GA,APHI,AKAPRA

330 FORMAT

( 14 ,3F11.2» 6F10.4I

IF (SURT(DX*OX+DY*DY«-DZ*OZ).LT.GOIF) GO TO 360

IF (ITER.LT.6) GO TO 350

WRITE (6,340)

340 FORMAT QHO,' SORRY -

SOLUTION DOES NOT CONVERGE*)

*GO TO 410

350 IT

fcK*

lTER

+lGO TO 230

360 WRITE (6,370) GC1F

370 FORMAT

( 1HO,5X,

WITH IMIS ITERATION THE SQUARE ROOT Of OX2>OY2+DZ2

A 1570

A1580

A1590

A1600

A1610

A 1620

A1630

A1640

A 1650

A1660

A1670

A1680

A1690

A 1700

A1710

A1720

A1730

A1740

A1750

A1760

A1770

A1780

A1790

A1800

A1810

A1820

A1830

A1840

A1850

A1860

A1870

A1B80

A1890

A1900

A1910

A1920

A1930

A1940

A1950

A 1960

A1970

A1980

A1990

A2000

42010

A2020

A2030

A2040

A2050

A2060

A2070

A2080

FORTRAN IV G LEVEL I MOD 3

MAIN

DATE »

69106

IS/5

0/07

PAGE

00

05

0186

0186

169

C190

C191

0192

0193

0194

0195

0196

0197

CISfa

C199

0200

C201

C2C2

ro 0203

^1204

C205

0206

0207

020o

0209

0210

0211

C212

C213

0214

0215

0216

0217

0216

0219

C22C

C221

C222

0223

0224

0225

C2?6

0227

0226

390

400

410

420

430

440

450

460

470

480

490

500

1 IS

LE

SS

T

HA

N*,

F10.3

)»

RIT

E

(6,3

80

)M

jKrt

AT

liM

O,f

&,'C

OO

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INA

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S

OF

THE

P

ER

SP

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E

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13

,'Y

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FORMAT (4X,JF11.2)

rffcJTE

(6,400

)FOKMAT (1H1,T43,'STEHEOPLOTTER CALIBRATION INFORMATION*I

NO* COMPUTE RESIDUALS

WRITE (6,420)

FOKMAT (1H0.5X,'RESIDUAL AND DISTORTION VALUES*/lX,'POINT*,3X,*PRO

1JECTED»,12X,'PROJECTED',15X,'OBSERVED' ,7X

,'FIXED*,10X,'RADIAL'/2X,

2'NO.',bX,'X*,dX,'VX',10X,'Y',8Xt*VY'.IOX,'RADIUS*,8X,'RADIUS*t7X

t*

30ISTUKTION')

IFIN

-1GU TO 230

PUU-0,

PUO*0.

SCFAC-OELZ/SZ

00 460 1*1,NPTS

TbMX-0.

TEMY-C.

00 44C J»1,NO

TEMX-TEMX*ObSX(I,J)*SOL(J)

T£KY«TEMY*JB?Y(1,J)*SOL(J)

VX«(T£MX-OBSX(1,NO)I

VY»(TcMY-OBSY(I,NO))

ZP»VX*SCFAC

ZQ«VY*SCFAC

TP.UX»AMX(I)-ZP

TRUY*A,MY( I)-ZO

FXRAD*OSURT(PX(I)**2*PY(I)**2)

OBKAD*DSOKT((OBSX(I,NO»-PX(I))**2+<08SYII,NO)-PY(IM**2)

OS

TR

T»O

bR

AU

-FX

KA

DWRITE (0,450) IDENT(I),TRUX,ZP,TRUY,ZQ,OBRAD,FXRAD,DSTRT

FOKMAT (I5,2(F12.3,F4.3),5X,3(F9«3i5X|)

PUU*PUU*VX**2*VY**2

STO«OSOJ<T|PUU/(2*NPTS-NDI I

STDM«SURT( PUU/(2*NPTS-NOM

«(<ITc (6,470) i»TU

FORMAT (1HO

, IX

, 'STANDARD ERROR OF UNIT WEIGHT OF PLATE GRID COORDI

1NATES >',F8,5)

WRITE (6,4*0)

FOKMAT (1HO,5X,'VARIANCE-COVARIANCE MATRIX')

DC 490 1*

1, Ni)

CO

490 J»1,ND

VCV(I,J)*STb**2*U(I,J)

DC 500

1*1,6

WklTE (6,510) I,(VCV(I,J),J«1,6)

A2090

A2100

A2110

A2120

A2130

A2140

A 21-50

A2160

A2170

A2180

A219Q

A2200

A2210

A2220

A2230

A2240

A2250

A2260

A2270

A2280

A2290

A2300

A2310

A2320

A2330

A2340

A2350

A2360

A2370

A2380

A2390

A2400

A2410

A2420

A2430

A 2440

A2450

A2460

A2470

A2480

A2490

A2500

A2510

A2520

A2521

A2530

A 2 540

A2550

A 2 560

A2570

A2580

A2590

FORTRAN

0224

0230

C231

0232

0233

C

23*

C23

5 02

36

C23

7

0238

0239

IV

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6S106

15/5

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PAGE 0006

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A2650

A 26 60

A2670

A26B

OA2690

A2700

A2710

A2720

A27*

0A 27

50A2760

A2770

A 27 80

A2790

A2810

A 28

20-

FORTRAN IV

G

LEVEL It

MO

D 3

MAIN

DATE

«

6910

615/50/07

PAGE 0007

SYMBOL

XSCAL

SMALX

KFHI

AP

CM32

CN33

CM 12

OILY

S TEMX

CONV

FOCAL

b

AA

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| f,

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11

K DX

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1EO

208

230

258

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2A8

200

2F8

320

348

35C

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384

39d

3AC

3CO

304

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ICO

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210

238

2t»0

288

2bO

208

300

328

34C

36C

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i

38

6 39

C 30

0 3C

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C 400

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I TE

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STDK

LOCATION

1C8

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218

240

268

2<50

238

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308

330

350

364

37S

38C

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3B4

3C8

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sz B CMll

CN

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CN22

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LOCATION

100

1F8

220

248

270

298

2CO

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310

338

354

368

37C

390

3A4

3B8

3CC

3EO

3F4

SYMBOL

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C CM21

CN32

CN23

OELX

ft SCFAC

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APHI

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TKUY

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LOCATION

406

1E90

2420

26AQ

2A66

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SYMBOL

DCCS

SYMBOL

20

300

390

480

LOCATION

2Ab8

2ACC

LOCATION

2B64

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2EAC

2FE9

ARRAY MAr

LOCATION

590

1FBC

2470

2768

2AAO

SYMBOL

AMY

VCV

FMT

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SUBPROGRAMS CALLED

SYMBOL

LOCATION

SYMBOL

RMSE

2 AB

C DMINV

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FORMAT STATEMENT MAP

SYMBOL

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SYMBOL

3016

033

040

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2B6A

28

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20EB

2E

B5

30CC

40

200

340

420

520

LOCATION

720

1FEO

2538

2830

LOCATION

2ACO

2AD4

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2B9B

2C17

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DMIN1

SYMBOL

50

210

370

450

530

LOCATION

8BO

2100

2588

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LOCATION

2AC4

LOCATION

2BA6

2C90

2E22

2F6D

3126

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CN32

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SYMBOL

OBSY

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NRD

SYMBOL

DSIN

SYMBOL 90

220

380

470

LOCATION

108

200

^28

250

278

2AO

2Cd

2FO

318

340

35d

3*C

3 SO

394

3A8

3bC

300

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13AO

2290

25 08

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LOCATION

2AC6

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2ttAD

206C

2E60

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TOTAL MEMORY RECUIKEMENTS 0048A4 BYTES

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PA

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SUBROUTINE RMSE

t NUM ,XAR ,

YAR ,

XOEV, YOEV )

DIMENSION XAR(50), YAR(50»

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lh

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SYY=SYY*(YAR( l)-YMEAN)**2

XDLV'SUKTl SXX/I SN-l.O) )

10 20

30

40

50

60

70

80

90

B 100

B 110

B 120

B 13

0 B

140

B 150

B 160

B 170

B 180

B 190

B 200-

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FORTRAN IV

G

LEVEL If

MOO 3

RMSE

DATE *

69106

15/50/07

PAGE 0002

SYMdGL

suwx

a I YDfcV

LOCATION

A4

38

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SYMBOL

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ArtRAY MAP

SYMBOL

LOCATION

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LOCATION

SYMBOL

LOCATION

SYMBOL

LOCATION

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LOCATION

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06

SUBPROGRAMS CALLED

SYMBOL

LOCATION

SYMBOL

LOCATION

SYMBOL

LOCATION

SYMBOL

LOCATION

TOTAL MEMORY REQUIREMENTS 00030A BY

TES

FORTRAN iV 6

LEVEL It

MOO 3

OMINV

DATE «

69106

15/50/07

PAGE 0001

C001

0002

0003

000*

0005

OOC6

0007

cooe

C009

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0015

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1600

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C023

C024

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0027

C028

C029

0030

C031

0032

0033

0034

C035

0036

0037

0038

0039

00*0

0041

0042

0043

0044

C045

0046

0047

t04f

a0049

0050

0051

0052

SUBROUTINE OMINV (AlN,D,L,M)

DIMENSION Ad), L(l), Mil)

REAL*8 A,D,BIGA,HOLD

0»l.O

NK N

00 18

0 K«1,N

NK*NK+N

L(K»»K

M(K) *K

KK*NK+K

B1G4*A<KK|

00 20 J«K,N

U*N*(J-1)

00 20 1*

K,N

IJ-I

Ztl

10 bIGA»A<

IJI

!Ci2

0»20

A(K1)=A(JI)

A(JI)*HOLO

M(K»»J

20 CONTINUE

J=L(K)

IF (j

-Ki

30 KI»K-N

00 40 I-l.

NK1»KI+N

HOLO»-A(KI)

40

50

60 70 80

100

110

120

50,50,30

IF (1

-K)

60,80,60

JP»N*(I-1)

00 70 J»1,N

Ji»JP*J

HOLO*-A(JK>

A(JK)*A(JI)

A(JI)»HOLD

IF (D

1GA) 100^90,100

0=0.

RETURN

00 120

1*1, N

IF U-K) 110,120,110

IK«NK+I

Al 1K)«A( !K)/(-BlGA)

CONTINUE

CO 150

1*1, N

HOLO«A( IK)

DC 15

0 J-1,N

10 2030

40 50

60

70

80

90

C 100

C 110

C 120

C 130

C 140

C 150

C 160

C 170

C 180

C 190

C 200

C 210

C 220

C 230

C 240

C 250

C 260

C 270

C 280

C 290

C 300

C 310

C 320

C 330

C 340

C 350

C 360

C 370

C 380

C 390

C 400

C 410

C 420

C 430

C 440

C 450

C 460

C 470

C 480

C 490

C 500

C 510

C 520

FORTHAN

iv c

LEV

EL i

» MO

O 3

DMINV

DATE *

69106

15/50/07

PAGE 0002

0053

0054

0055

0056

0057

0056

0059

C060

C061

0062

0063

0064

0065

0066

0067

0066

00o9

0070

C071

C072

0073

G074

0075

0076

0077

0079

0050

0061

0082

0083

0084

0065

C086

0087

0086

130

140

150

160

170

180

IF (I

-K)

13C.15C.130

IF U-M 140,150,140

KJMJ-UK

A( IJ)»HOLD*A(KJ)«A(IJ)

CONTINUE

KJ*K~N

UU 170 J»1.N

IF IJ-KI 160,170,160

A(KJ)«A(KJ )/dlGA

CONTINUE

0«D*bIGA

A(KK)«l./bIGA

CONTINUE

0090

0091

190 K-K-1

IF (K)

260,260,200

200 I-L(K)

IF

( I-K) 230,230,210

210 JU»ft*(K-l)

JK«N*(I-n

00 22

0 J»

l ,N

JK«JU+J

HULC-A(JK)

240

AIK

I)--

A(J

»

250

A(J

I)«H

OL

OG

O

Tu

1

90

260

RE

TU

RN

END

MJM

A

(JI

I 220

AtJ

D-H

OL

D

230

J-M

(K)

IF U-M 190,190,240

KI-

K-N

DO

25

0 I-

l.N

KI-

KI+

NH

UL

O»A

(KM

C 530

C 54

0 C

550

C 560

C 570

C 580

C 590

C 600

C 610

C 620

C 630

C 640

C 650

C 660

C 670

C 680

C 690

C 700

C 710

C 720

C 730

C 740

C 750

C 760

C 770

C 780

C 790

C 800

C 810

C 820

C 830

C 840

C 850

C 860

C 870

C 880

C 890

C 900

C 910-

FORTRAN IV

G

LEVEL It MOO 3

UMINV

DATE *

69106

13/50/07

PAGE 0003

SYMt

fOL

0 K IJ IK

LOCATION

166

168

HC

1BQ

SYMB

BIGA

KK Ki KJ

SCALAR MAP

LOCATION

170

16C

m

SYMBOL

HOLD

J JI JQ

LOCATION

178

190

1A4

1B8

SYMBOL

NK 1Z JP JR

LOCATION

180

1A8

1BC

SYMBOL

N I JK

LOCATION

184

1AC

ARRAY MA

PSYMBOL

LOCATION

SYMBOL

LOCATION

SYMBOL

LOCATION

A IC

O L

1C*

M 1C

8SYMBOL

LOCATION

SYMBOL

LOCATION

TOTAL

MEMO

RY REQUIREMENTS 00083C BY

TES

F88-LEVEL LINKAGE EDITOR OPTIONS SPECIFIED LET,LIST,MAP

VARIABLE OPTIONS USED -

SIZ£«<94208,450561

lEhOOOO

NAHc

DEFAULT OPTION!SI USED

MODULE MAP

CCNT

ROL

SECT

ION

NAME

ORIGIN

MAIN

00RMSE

48A8

DMlfW

4db8

IhCLSCN *

53 F8

1HCFMAXD*

5678

IHCLSORT*

56c8

IHCFCOHH*

5830

IHCCOMH2*

6508

IHCSSQRT*

67B9

IhCFCVTH*

6900

IHCFINTH*

7A70

IHCFIOSH*

7E10

IhCTRCH *

8BF8

IHCU

OPT

* aeto

1HCUATBL*

8EE8

NTKV AOOKESS

UTAL LENGTH

LtNGTH

48A4

30A

33C

27C 6D 142

.DA1

IDS

149

116D 39 E

DEI

2E4 8

638

009520

ENTRY

NAME

DCOS

DMAX1

DSQRT

I8COM*

SEQDASD

SQRT

AOCON#

FCVIOUTP

ARITH*

FIOCS*

IHCERRM

LOCA

TION

NAME

LOCA

TION

NA

ME

LOCATION

NAME

LOCAT10

53F8

DSIN

5416

5678

DM

IN1

S68E

56E8

5830

FD

IOCS

tf

S8EC

INTSWTCH

65BE

66A6

67BO

6900

FCVAOUTP

69AA

FCVLOUTP

6A3A

FCVZOUTP

6B8A

6F16

FCVEOUTP

7418

FCVCOUTP

7632

INT6SMCH

7913

7A70

AOJSWTCH

7028

7E10

8BF8

NOW ADDED TO

DA

TA SE

T

B. SYMBOLS AND VARIABLES

TITLE

FM

FMT

NETS

ICALF

ICOR

FOCAL

GDIF

XSCAL, YSCAL, SINALP

ITEST

IDENT, IX, PY

AOMEGA, AHII AKAPPA

XE, YE, ZE

SUMX, SUMT, ID, ILST, XDEV, YDEV

NRDG

ID

TMX, TMY, TMB

Array containing title information.

Array containing the format for reading plate grid coordinates.

Array containing the format for reading projected grid coordinates.

Number of grid points used in computation.

Number of sets of data using the same set of plate grid points and coordinates.

Code indicating whether projected grid coordinates should be corrected for coordinatograph errors.

Principal distance of the projector.

Tolerance for testing the solution for convergence.

Coordinatograph correction factors.

Code to count the number of data sets that have been computed with the same grid points and coordinates.

Arrays containing the point number, and X and Y coordinates of the plate grid intersections.

Unknown angular elements in minutes.

Unknown coordinates of the perspective center.

Variables used in handling multiple reading data for each point.

Number of readings on a point.

Point number of projected grid reading.

Arrays containing the X, Y, and Z readings on a point,

AMZ, AMI

DEX, DEY

NRD

SMALX, SMALY, . ABSV

HER

SZ

ROMEGA, BIHI, RKAPPA

com

OBSX, OBSY

N

A, B, C, AP, BP, CP

own, CM12, cms,CM22, Cm3, CM32, CM33, GNU, CN12, CN13, GN21, CN22, CH23, CN32, GN33, R, S, T, DELX, DELY, DELZ

SX, SY

KD

NO

U

DET

Arrays containing the mean X and Y readings on the projected grid points.

Arrays containing the standard deviation of the X and Y readings for each point.

Arrays containing the number of readings on each point.

Variables used in correcting the mean readings for coordinatograph errors.

Number of present iteration.

The principal distance with a negative sign.

Unknown angular elements in radians.

Factor used to convert minutes to radians.

Matrices of the observation equations.

Augmented normal equations coefficient matrix.

Sines and cosines of the unknown angles.

Variables used in forming observation equations,

Plate grid coordinates.

Number of unknowns.

Number of unknowns plus one.

Normal equations coefficient matrix and later the inverse of the normal equations coefficient matrix.

Code indicating a correct return from the matrix inversion subroutine.

SOL Array containing corrections to unknowns.

DX, DY, DZ, DOM, DHII, DKAP

PUU, HJQ

VX, VY

ZP, ZQ

SCFAC

TRUX, TRUY

OBRAD

FXRAD

DSTRT

STD

STDM

VCV

STDX, OTDY, STDZ, STDO, STDP,

X, STD DEV Y, STD DEV

Corrections to unknowns.

Sum of the squares of the residuals.

x and y residuals in the plate grid coordinates,

X and Y residuals in the projected plane.

Scale factor for converting plate grid coordi­ nates to projected grid coordinates.

Computed projected grid coordinates.

Observed radius from principal point to grid.

True radius from principal point to grid intersection.

Radial distortion.

Standard error of unit weight of plate grid coordinates.

Standard error of projected grid coordinates in the model space.

Variance-covariance matrix.

Standard errors of the unknowns.

Standard deviations of readings of projected coordinates.

0START

TITLE AND FORMAT

CARDS C. MACRO FLOWCHART

STOP

READ [STEREOPLOTTER

CALIBRATION PARAMETERS

READCORRECTION

FACTORS

CORRECTION FOR COOKDINATOGRAPH

ERRORS

READGRID PLATE

COORD

'READ ESTIMATEDPROJECTOR

ORIENTATION PAKAMETERS

35

/READ MODEL-SPACECOORDINATES OF

GRID POINT

SAMEGRID POINT

NUMBER

COMPUTE MEAN VALUE* DEVIATION OF X & Y MODEL- SPACE COORDINATES

l-SMCE PT. NO. = GRID

PT. NO.

LASTMODEL-SPACE

POINT

USECOOROINAT06RAPH

CORRECTION

> NO ». WRITE ERROR-CARDSARE OUT Of

ORDER" K STOP

COMPUTE X-S.Y- SCALE AND NON-

PERPENDICULARITV CORRECTIONS

WRITE INPUT DATAL^rj

^ ADJUST MODEL SPACE X&Y COORDINATE

VALUES

©

SET

IFIN » O

WRITE ITER NOA PROJECTOR

ORIENTATION VAUJESl

ITER=1

FORMOBSERVATIONS

EQUATIONS

COMPUTE ADJUSTEDMODEL-SPACECOORDINATES

AND RESIDUALS

FORM NORMAL

EQUATIONS

(CALL PMINV

COMPUTE TRUE MODEL-SPACE COORDINATES

NO|?MAL EQUATIONS MATRIX |S SINGULAR

COMPUTE RADIAL

DISTORTION

STOP

COMPUTE NEW PROJECTOR ORIENT­ ATION PARAMETERS AND RESIDUALS

WRlTf RESIDUAL

ANDDISTORTION

VALUES

37

WRITEINTER NO. &PROJECTOR

ORIENTATIONVALUES

SUM OF RESIDUALS

EM7

THIS ITERATION THESQ.RIOF DX2+DY2+ on. is LESSi^-^KTHA«*

WRITE PERSPECTIVE

CENTER COORDINATES

WRITE * RESIDUAL S.DISTORTIOH

VALUES^

WRITE SORRY-SOL­ UTION DOES, NOTCONYEWt

COMPUTE STANDARD ERROR OF MODEL-SPACE

COORDINATES

iWRITE

STD. ERROROF

UNIT WEIGHT

COMPUTE VARIANCE-

COVARIANCE MATRl*

iWRITE

VARIANCE- C0VARIANCE

MATRIX

COMPUTE STANDARD ERROR OF PERSPECTIVE

CENTER PARAMETERS

WRITE STD. ERROR Ot PERSPECTIVE

CENTER BkRAMETERS

0.YES

1TEST-ITEST + 1

PERSPECTIVE CENTER DETERMINATION

A-7

NO.310 DATA FROM INTERNATIONAL TESTS -

HALLERT

ISP

SUO-CGMM 1YC4

COOROINATOGRAPH ERRORS CORRECTED

THE NUMBER OF

POINTS USED ON THIS PLATE IS

33

THE

ASSUMED PRINCIPAL DISTANCE USED IN THESE COMPUTATIONS IS

150.000

COORDINATES

PT NO 0 11 21 31 41 12 22 32 42 13 23 33 43 14 24 34 44 15 25 35 45 101

102

103

104

105

106

107

108

109

110

111

112

ITER 0 1 2

NO.

OFREADINGS

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

X50

0.00

500.

02500.02

OF IN

PUT

DATA

CALIBRATED GRID COORO

PROJECTED

GRID

X0.0

20.0

00-20.000

-20.000

20.000

40.0

00-40.000

-40.000

40.000

60.0

00-60.000

-60.000

60.0

0080

.000

-80.000

-80*000

80.0

00100.000

-100.000

-100.000

100.000

0.0

-60.000

-80.000

-100.000

-80.000

-60.000

0.0

60.0

0080

.000

100.

000

80.0

0060.000

Y50

0.00

499,

9949

9,99

Y 0,0

20,0

0020

,000

-20.000

-20.000

40.000

40.0

00-4

0.00

0-40.000

60.0

0060

.000

-60.

000

-60.000

80.0

0080

.000

-80.000

-80.000

100.

000

100.

000

-100.000

-100

.000

100.

000

80.0

0060

.000

0.0

-60.000

-80.000

-100.000

-80.000

-60.

000

0.0

60.0

0080

.000

Z300.60

300.14

300.

14

MEAN

X

X50

0.02

654

0. 054

460.017

459.999

540.

024

560.105

420.004

419.957

580.

040

620.112

380.002

379.

925

620.042

660.154

340.009

339.

930

660.054

700.

170

2 99'. 9 86

299.

892

700.

052

500.

096

380.

011

340.002

299.932

339.

932

379.922

499.962

620.035

660.C70

700.118

660.

138

620.

128

OX

DY

0.02

15

-0.0

091

0.0002

O.C001

STD

OEV

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

o.o

oz0.

1388

0.0002

COORDINATES

MEAN

Y

500.002

540.012

540.

034

460.005

459.978

580.032

580.

073

419.

983

419.958

620.042

620.

102

379.

981

379,934

660,058

660,132

340,000

339.900

700.072

700.

181

299,971

299.867

700,

114

660.120

620.118

500.052

380.004

339,977

299,932

339,

922

379,

910

499,950

620,

039

660,060

OMEGA

0,0

0.23

540.

2355

Y STD

OEV

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0 PHI

0.0

-0.0543

-0.0

543

Z0.

00.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

KAPPA

0.0

-0.9418

-0*9418

WITH TH

IS ITERATION TH

E SQUARE ROOT OF

OX2+DY2*OZ2 IS LESS THAN

COORDINATES OF THE PERSPECTIVE CENTER

0.001

500.02

Y 499.99

Z30

0,14

STER

EOPL

OTT

ER

CA

LIBR

ATI

ON

IN

FOR

MA

TIO

N

RESIDUAL AND

>OINT

NO. 0 11 21 31 41 12 22 32 42 13 23 33 43 14 24 34 44 15 25 35

45 101

102

103

104

10*

106

107

108

109

110

111

112

PROJECTED

X500.026

540.056

460.018

459.997

540.033

580.087

420.010

419.969

580.040

620.119

380.001

379.942

620.046

660.151

339.991

339.915

660.052

700.185

299.981

299.890

700.057

500.081

380.011

339.982

299.936

339.925

379.932

499.971

620.034

660.064

700.121

660.139

620.131

DISTORTION VA

LUES

VX-0

.000

-0*0

02-0

.002

0.002

-0.0

100.018

-0.0

06-0

.012

-0.000

-0.0

070.

001

-0.0

17-0

.004

0.00

20.017

0.014

0.002

-0.015

0.004

0.002

-0.005

0.015

o.oo

oO.C20

-0.004

0.007

-0.010

-0.009

0.001

0.005

-O.D03

-0.001

-0.003

PROJECTED

V500.011

540.019

540.041

460.004

459.982

580*028

580.071

419.998

419.953

620.038

620*102

3/9.993

379.925

660.049

660.134

339.988

339.898

700.060

700.166

299.985

299.871

700.113

660.123

620.113

500.066

380.004

339.977

299.928

339.909

379.914

499.957

620.027

660.059

VY-0.009

-0.007

-0.007

0.00 1

-0.004

0*004

0.002

-0.015

0.004

0.004

-0.001

-0.012

0.008

0.009

-0.002

0.012

0.002

0.01

10.015

-0.014

-0.004

0.00

1-0.003

0.005

-0.014

-0.000

-0.000

0.004

0.013

-0.004

-0.007

0.011

0.000

OBSERVED

RADIUS

0.005

28.281

28.282

28.283

28.283

56.576

56.571

56.578

56.567

84.852

84.852

04.86*

84. 84

8113.141

113.130

113.128

113.137

141.420

141.425

141.426

141.421

100.000

99.999

99.993

100.002

99.997

100.003

99.998

99.995

100.004

99.999

100.003

99.999

FIXED

RADIUS

0.0

28.284

28.284

28.284

28.284

56.569

56.569

56.569

56.569

84,853

84.853

04.053

84.853

113.137

113.137

113.137

113.137

141.421

141.421

141.421

141.421

100.000

100.000

100.000

100.000

100.000

100.000

100.000

100.000

100.000

100.000

100.000

100.000

STAN

DARD

ER

ROR

OF

UN

IT

WEI

GH

T O

F PL

ATE

G

RID

C

OO

RD

INA

TES

» 0.0

0447

RA

DIA

L D

IST

OR

TIO

N

O.C

05-0

.00

3-0

.002

-0.0

01

-0.0

02

0.0

08

0.0

03

0.0

10

-0.0

02

-0.0

01

-0.0

01

0.0

10

-0.0

04

0.0

04

-0.0

07

-0.0

09

O

.CO

O-O

.C01

0.0

04

0.0

04

-0.0

00

O

.OO

C-0

.001

-0.0

07

0

.00

2-0

.00

3

0.0

03

-0.0

02

-0.0

05

0.0

04

-0.0

01

0.0

03

-0.0

01

VA

RIA

NC

E-C

OV

AR

IAN

CE

MA

TRIX

1 0.

3773

6285

D-0

9 0

.559134130-1

4

0.1

73

01

68

10

-14

0.1

63760880-1

1-0

.135837510-0

6-

2 0

.55

91

34

13

0-1

4

0.3

77

40

40

9D

-09

-0.1

73

95

55

4D

-13

0.1

35

85

16

70

-06

-0.1

63

77

44

60

*1

13

0.1

73016810-1

4-0

.17

39

55

54

0-1

3

0.6

73942210-1

0-0

.653006120-1

1-0

.57

45

92

19

0-1

2-

4 0.1

63760680-1

1

0.1

35851670-0

6-0

.653006120-1

1

0.5

13218910-0

4-0

.45

45

16

56

0-0

95

-0.1

35837510-0

6-0

.163774460-1

1-0

.57459219D

-12-0

.454516560-0

9

0.5

13

17

04

20

-04

6 -0

.131821540-1

0

0.3

18442310-1

1-0

.2009B

546D

-15

0.1

12

68

44

50

-08

0.4

66

04

46

40

-08

STA

ND

AR

D

ERRO

RS

OF

THE

PER

SPE

CT

IVE

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