COMPUTER EVALUATION OF DOUBLE-THEODOLITE DATA by W. Gale Biggs Technical Report No. 4 ORA Project 03632 NATIONAL SCIENCE FOUNDATION GRANT G-11404 College of Engineering Department of Engineering Mechanics Meteorological Laboratories and Institute of Science and Technology Great Lakes Research Division Special Report No. 13 THE UNIVERSITY OF MICHIGAN ANN ARBOR, MICHIGAN April 1962 ABSTRACT Conventional methods of evaluating double-theodolite data involve numerical and/or graphical techniques that are laborious and time consuming. The following presentation offers a method whereby the electronic digital computer first computes the position of the balloon in space and then from this determines the wind vector. The program also makes provision for the problem of missing data. This computing technique is highly valuable when a large number of pilot balloon ascents must be processed. a While conducting field operations at the Enrico Fermi Nuclear Reactor Site during the summer of 1961, it was necessary to take double-theodolite balloon ascents as a means of evaluating the wind speed in the lower few thousand feet of the atmosphere. The basic approaches to evaluating double-theodolite data have been: 1) numerically to calculate the position of the balloon in space and time, and then to plot it on a winds-aloft plotting board to determine wind speed and direction; or 2) to use graphical methods throughout to determine wind speed and direction. Either of these methods requires the use of winds-aloft plotting boards and both methods are laborious and time consuming. Weedfall and Jagodzinski [1961] describe a graphical method in which they can evaluate a 30-interval run in about 25 min. The United States Weather Bureau Circular "O" describes a method which takes 70 min for a 30-interval run. When a large number of observations are to be evaluated, the high speed electronic digital computeroffers a much more convenient and rapid technique of analysis. The following method of analysis requires no plotting of data. The only work is in the conversion of the data from 1 tabular form to punched cards or any other convenient form of computer input. The data deck consists of one card containing the length of the baseline and the number of observations, followed by four sets of cards. The first of these contains the azimuth angles from station A (the balloon release point), the second contains the elevation angles from- station A, the third contains the azimuth angles from station B (the satellite station), and the fourth contains the elevation angles from station B. These angles are read into a three dimensional matrix A.., where in this ijk case i is the number of layers, j is the number of rows, and k is the number of columns. The output of the computer is in the desired form of the horizontal wind vector and the altitude of the balloon for each sounding. Also printed out are the horizontal radial distance of the balloon from-the launch site, the u and v components of the wind vector, and the x and y coordinates of the balloon. The mathematical basis for the method presented is simple and is easily handled by the digital computer. The use of two theodolites necessitates a baseline which is carefully surveyed. The baseline used was 2000 ft long and lay in an east-west direction. Since the terrain 2 is relatively flat, the two stations were at equal elevations, except for the two kilometer inland site which had seven feet difference in elevation. The other sites had less than a foot: difference in elevation. Communications were maintained through the use of two transistorized walkie-talkies. Five men were used, three at the balloon release station and two at the satellite station (figure 1). At the balloon release station one man tracked the balloon and read the two angles, one man recorded, and one man kept time. At the satellite station the radio was turned up so both could hear. One man tracked the balloon and read the angles while the second man recorded the data. This arrangement allowed for reading the theodolites at ten second intervals. Three sites were surveyed with 2000 ft baselines, one at the plant site, one at two kilometers inland, and one at four kilometers inland. Provisions were also made to survey an inland site at six kilometers which will be done during the spring of 1962. The two theodolites were adjusted so that both were reading north at 360~. As long as the balloon is not too near the vertical plane containing the baseline, the horizontal triangle ABC (figure 2) is solved first, to obtain the projection of the balloon and its horizontal distance 3 4.) A4.) ~0 $4 04 0 4r-, 40 r4 -4 d4J - 0 ( rO4JJ I *d OH Q0 4 0 - $q 4 "4) r4) 4 P Figure 2. Perspective of two theodolite triangulation. from the two stations. AB is the baseline of length b; P is the position of the balloon, and C is its projection on the horizontal plane through A. The angles measured from A are a and e, those measured from B, a' and E'. After the projection of the balloon (C) has been obtained, its height above the level of A is calculated by the relation Z = AC tan E, where e is the elevation angle measured at A. The elevation above B may be calculated as a check; it is given by Z' = BC tan '. It is seen from figure 2 angle ACB = a - a' 5 and by the sine law AC b sin a' sin (a - a') therefore b sin a' AC = sin (a - a') Similarly b sin a BC. - -—, sin (a - a ) also b sin a' tan e sin (a - a') and Z = b sin a tan E' sin (a - a') Since in all but one case, A and B are at the same elevation, Z and Z' should be equal. At the two kilometer site where A and B are not in the same horizontal plane, all the above formulae hold except for Z' where it will differ by h, where h is the difference in elevation of A and B ~ The analysis so far has described the position of the balloon in space in a cylindrical coordinate system (r, i, z), where r = AC., e = a. and z = z. For the 6 following approach this needs to be converted to a Cartesian coordinate system (x, y, z). This is done as follows: x = r cos e y = r sin e z = z The Cartesian coordinate system is set up by requiring that the x-axis coincide with the baseline used for the two theodolites and that the origin be at the theodolite where the balloon is released. The baseline was located on an east-west line thus making the y-axis on a north-south line (figure 3). y (Xl+a Yi,+l) N A (xi,yi) W ----- E S a - 4m. Alk X B A 0S i<n Figure 3. Diagram showing coordinate system used in equations. 7 The position of the balloon in the x, y plane is designated as xo, Yo for the)release position;, Yi as the first position, etc., to x, y as the n n n position; then in order to find the distance the balloon traveled in going from x., yi to x., y. the 1 -1+1 Yi+3 following formulae are used r = - x) + (y+ -y e = tan' [ ill Yi X. X. - 1+1 1 0 < i < n Thus, knowing r, the distance traveled, and t, the time between successive readings (for this program it was every 10 sec), the average wind speed U is simply r/t. The height of the balloon was previously calculated by the computer in order to describe its position in space. The U. S. Weather Bureau in computing its pibal soundings uses every other point in obtaining a wind speed and direction; this is very simply done by using xi+, Yi+2 instead of xi+ ' Yi+2 8 When the computer comes to a missing point, an average is taken by using the next point. This is also true if two consecutive points are missing. However, if three or more consecutive points are missing, then an average is not taken and the computer continues to test for missing data until points are again found and the averaging process starts again. Thus a segment of the run is considered missing only if three or more consecutive readings are missing. A problem also arises when the balloon crosses the baseline or travels along it. A small error in a or a will cause a large error in the computed position of the balloon. In this case it is better to solve the vertical triangles ABP and ACP (figure 4). It follows that P A B C Figure 4. Solution of vertical triangles. 9 sin e cos e AC = b ~ -- sin (e ~ e') cos c' sin e BC = b sin (e ~ e' ) sin e' sin e sin (e + c') The positive sign will be used when C lies in AB, the negative sign when it lies in AB produced. Once the position of the balloon in space is computed, the coordinates are converted to Cartesian and the wind speed and direction are computed as before. Since the angles as recorded by the theodolites are used only in sine and cosine functions, the fact that they go through 360~ makes no difference. The sine and cosine functions are symmetric and periodic, thus the sine 362~ ' sine 2~, and the same is true for the cosine. Since the arc tangent is multivalued, there is a question of which value to choose. This problem can be easily solved by looking at the combination of signs on the x and y values used to compute the arc tangent. If both are positive then the angle lies in the first quadrant; if y is positive and x is negative then the angle lies in the second quadrant; etc. This was even less of a problem for this program since 10 o the computer has a calling subroutine that will compute the arc tangent for values between 0 -> 2 T. Just before the results are printed out by the computer, the complement of each angle is taken and then rotated 270~0. The complement is taken since the program computes e in a counterclockwise direction, whereas it is standard practice to use e in a clockwise direction to express wind direction. The angle is then rotated 270~ because in the program 360~ is east, and the angle e defines the direction in which the balloon is traveling. Thus e is rotated 90~ to correspond to the concept of north being 360~ and then 180~ more to correspond to the concept of wind direction being given as the direction from whence the wind is blowing. Table 1 shows a comparison between the computer evaluation and the hand calculated values. As a means of showing the computer evaluation with missing data, two values were read in as zeros and the results compared. The first pair of columns presents the radial horizontal distance from the release point to the balloon (in feet). The second pair gives the height of the balloon above the theodolite (in feet) and the third gives the local wind speed (in feet per second). The fourth pair of columns shows the local wind direction (in 11 TABLE 1 Comparison of values obtained by the computer with those obtained by conventional methods. R z (ft) (ft) U e u v (ft/sec) (deg) (ft/sec) HC Comp HC Comp HC Comp Comp Comp HC Comp 0 70 116 178 0 0 722 875 1118 1306 1438 1588 0 70 116 178 0 42.3 64.3 96.3 0 A\ 722 875 1118 1306 1438 1588 u 0 42.3 64.3 96.3 329.0 382.3 422.3 453.8 509.3 7 5 6 18 15 11 13 19 13 7 5 6 69 94 75 18 75 76 17.5 69 92 75 6.6 4.8 6.0 2.5 -0.3 1.6 4.5 4.4 4.9 4.9 7.5 5.6 329.0 382.3 422.3 453.8 509.3 14 10 14 20 12 73 64 68 67 65 67 62 67 67 65 14.7 10.1 12.3 17.4 12.0 5.6 537.6 537.6 - -- R z U e u v Comp HC Radial horizontal distance Height of balloon (ft) Wind speed (ft/sec) Azimuth of wind (deg) of balloon from launch site (ft) x-comp of wind (as obtained by computer) (ft/sec) y-comp of wind (as obtained by computer) (ft/sec) Computer values Hand calculated values 12 degrees), and the last two columns give the local u and v components of the wind speed as evaluated by the computer. The method of evaluation used to obtain the hand calculated figures was as follows: first the position of the balloon in space was numerically calculated, and then this was plotted on a winds-aloft plotting board and a graphical analysis used to determine the wind speed and direction. The program, since it is a computer analysis, suffers from none of the human errors involved in a graphical analysis and is therefore exact. Thus the accuracy of the final result is determined only by the accuracy with which the original angles were recorded. The program has (as an external function) a system whereby a smoothing subroutine is incorporated in it. Any method of smoothing may be used in the subroutine, with the present smoothing function given by A. = Bi-. + B. + B. 1 J1-1 1 1+1 where 0 < i < n The smoothing subroutine also takes care of missing data. In the present program only the wind speed is smoothed. 13 The merit of the program is the great speed with which a large number of data can be analyzed. One program consisted of 10 pibal soundings, each sounding 10 min long with readings taken every 10 sec for a total of 600 points. The computer time involved was 1.5 min for the IBM 709; it required about 45 min of one person's time for punching the data on cards. This is to be compared with time for the method presented by Weedfall and Jagodzinski [1961] which A required about 25 min to complete one run of only 30 points and that for the Circular "0" method which requires 70 min for a 30-point run. The program was written in the MAD* language and is reproduced here in that form in the Appendix. The program can be broken into four main groups —the first group consists of reading in the data and converting to radians. The second group computes the location of the balloon in space. The third group tests for missing data, computes wind speed and direction, and smoothes the wind speed. The last group consists of input and output statements necessary for the MAD translator. * Michigan Algorithm Decoder 14 Since the MAD language may not be familiar to everyone, each MAD statement is given with its SAP* translation. Thus the program may be used in most of the standard computers available today. - -- -- -- Share Assembly Program 15 REFERENCES 1. Middleton, W. E. K., and A. F. Spilhaus, 1953: Meteorological Instruments (3rd ed.). Toronto, University of Toronto Press, 186-187. 2. Weedfall, R. O., and W. M. Jagodzinski, 1961: Comments on Double-Theodolite Evaluations. Bull. Amer. Meteor. Soc., 42, 322-324. 3. Hansen, F. V, and N. H. Taft, 1959: Another Method of Evaluating Double-Theodolite Runs. Bull. Amer. Meteor. Soc., 40, 221-224. 4. U. S. Weather Bureau Circular "O." 16 APPENDIX PRINT FORMAT JUMP. too X~TART RAD FORMKAT CONw,N,B, IArC62 PRINT FORMAT UU *003 -ktA FOMAT AT~A~lqql)..A(91'N' 004 READ FORMAT DATAA(1,1,1)...A(1,1,N). *0O5 READ FORMAT DATA, At(2,t1 tlL..'A (2,.1,IN) *006 READ FORMAT DATAA(2,2,1)...A(2,2,N) *007 EXECUTE ZERO.(C-(lk-..C(N)) *000 _______THROUGH S#,FOR I=1,1,I.G.N *-009 WHJNtE4-VER A(1,1,I).E.0.ORA(2,1,IL.E.0,TRANSFER TO 5 *010, ---------— A(l19lI1 )=(90.-A(Ll,lgI))*6.283185,3/360. --------------— 4 --- —-- 011 ------ A(1,2,I)=A(1,2,I)*6.2831853/360 *012 A(21,l,)=(90.-A(2,1,1))*6.2831853/360. *013 A(2,2,I)=A(2,2,I)*6.2831853/360 *014 C(I)=B/SIN.(A(1,1,I)-A(2,1,I)) *015 S CONTINUE *016 THROUGH SSFOR I=1,1,I.G.N -*011 AC(I)=C(I)*SIN.(A(2,1,I))- *018 8C=C(I)*SIN.(A(1,1,I)) *0019 ZA( I)=AC( I )*SIN. (At 1,2,1))/COS~. (A(l,2,I)) *020 LB(I)=BC*SIN. (A(2,,2,1IflICOS.jjj,2gjl) *021 XA( I)=AC( I )COS.(A( 1,1,1)). 022 Ss YA-(I-)=AC (I)*SI N'.(A(1,I )) q. -------------------------------- 02-3 EXECUTE ZERO.(C(1)... C(NW). *02-4 TRUH MM,FORJ=1,1,J.G.N --------— *025 ------ WlH..EN EVER XA-%(J).EO.AD.Y(J)E.O*02 WHENEVER XA(J+1).E.0.AND.YA(J+1).E.0 *027 WHENEVER XA(J+2).E.0.AND.YA(J+2).E.O0 *028 THROUGH AAFOR K=J+3,1,K.G.N *029 WHENEVER XA ( K).NE.0.OR.YA (K).NE.0 *030 J =K *031 TRANSFER TO0 MM *032' AA ENDOF CONDITIONAL *3 END OF CONDITIONAL ~*034 X=XA(J4-2)-XA(J —1)_.035 Y=YA(J+2)-YA(J-1l) '-036 J=J+2 ____*031 ----— TRANSFER ---1-0-NN --- —----------------------------------------------------------- --------— 03 END OF CONDITIONAL '*039 X=XA( J+I)-XA(J-1) ~*040 Y=AJ1-A(J-1) ~*041 J=J+1 *042 OTHERWISE *043 X=XA(J)-XA(J —1) *044 Y=YA (J)-.YA (J-1). *045 END OF CONDITIONAL *046. NN R=SQRT.(X*X+Y*Y) --- —--,*041 THETA=270.-ATN1.(YX)'360./6.2831853 -*048 WHENEVER THETA.L.0,THETA=360.+THETA *4049 PRINT FORMAT PPJRTEAL()Z()Z()Z(-)Z()L(*050 IJ-1),ZA(J)-ZB(J),X,Y,XA(J)YA(J) *050 C(J)=R *051 MM CONTINUE *052 PRINT FORMAT XX,AC(1)...AC(N) *053 PUNCH FORMAT DATA1,N,C()...C(N)..5.....4....... WHENEVER LIC.NE.O. *055 EXECUTE SMOTH.(C,ZB,N) --- -. *056 PRINT FORMAT XX,ZB(1)...ZB(N) *057 END UF CONDITIONAL......... *058 TRANSFER TO START *059 INTEGER N,I,J,K ' ----------. --- -—. 060__ VECTOR VALUES DIM=3,1,2,200 *061 VECTOR VALUES CON=$I5,2F10.O*$ __- -*062 VECTOR VALUES DATA=$IS5/(16F5.l)e$ *063 VECTOR VALUES DATA=$16F5.1*$ *064 VECTOR VALUES XX=$l1HO/(1H,14F8.1,F7.1)i$ *065 VECTOR VALUES UU=$lH4,S4,1HJtS7,1HRtS9,UlHOUS8,2HZAS8,2HZBS7......-_ *066 1,5HZA-ZA,S5,5HZB-ZBtS5,5HZA-ZBS7,1HU,-S9,1HV,S9,1HX,S9,LHY/1H *066 2+,S22,1H-S$._ ---_- - -- — _ -*066 VECTOR VALUES PP=$SH,15,11FIO.l*$ *067 DLHMENSItN A(IQOO.IOM)C.(200),XA(.20Q)YA(200).ZA(Q2 000). ',Z200 -*068 1AC(200) *068 VECTOR _VALUES JUMP=SlHl$ --- - -.*069 --- - - - - - - - - - - -- - - - - - - - - - - - - --- -----— ^- ^ ^ ^ END OF PROGRAM *070 - - - - - - - - - - - - - - - - - - - - h.3) MAD PROGRAM,TYPE 12 MAR 1962 (ALL NUMBERS ARE OCTAL) --------------------------- ------------------— _ 'NO. OF LOCATIONS 05601 TRA VECTOR SIZE 00013 TRA VECTOR STARTS 00000 ENTRY PT. 04351 ERASABLE STARTS 77777 VARIABLE STORAGE AA 00013 CON 02301 I 02623 MM 02630_ S 02637 -_XA 03175 ZA 04025 AC 00324 A 02275 BC 02276 B 02277 C 02612 DATAi 02614 DATA 02616 DIM 02622. J 02624 JUMP 02,25 K 02626 LIC 02621 ____ NN 02631 ____N 02632 PP 02635 _____ R _____02636 SS 00013 START 02640 THETA 02641 UU 02664 X 03176 XX '03202 YA 03513 Y 03514 ZB 04336 FUNCTION DICTIONARY ATN1 00000 COS.READ 00005 SIN ZERO 00012 -, -...................... 00001 00006.MTX 00002 SMOTH 00007.PRINT 00003 PUNCH 0000PUNCH 00004 SORT 00010 SYSTEM 00011 _____ ABSOLUTE CONSTANTS. 04337 +0000000000006 04344 +203622077324 '04340 +0do00006 00001 04341 +000000000002 04342 +000000000003 04343-+000000000550 04345 +207550000000 04346 +211416000000 04347 +211550000000 04350 +233000000000.. I STATEMENT DICTIONARY 02630 TXL -305531005530 02631 TXL -305416005404 02637 TXL -304745004744 02640 TX~L -304362604354.. 0PRO{GRAM "-........................ --- —----- ---— T-X ---3- -- PRINT FORMAT JUMP '*001 04351 TSX +0 07400 4 00003 04352 STR -1 00001 0 02625 04353 STR -1 00000 0 00000 START READ FORMAT CONN,BLIC *002 04354 TSX +0 07400 4 00005 04355 STR-1 00001 002301 04356 STR -1 00000 0 02632 --- 04357 STR - 00000 0- 02277 04360 STR -1 00000 0 02627 04361 STR -1 00000 0 00000 rKINT FORMAT UU *003 04362 TSX +0 07400 4 00003 04363 STR -1 00001 0 02664 04364 STR -1 00000 0 00000 READ FORMAT DATA,~A(lt,1,1)...A(Itl,,N) *004.04365 TSX +0 07400 4 00005 04366 STR -1 00001 0 02616 04367 TSX +0 07400 4 00002 04370 TXH +3 02622 0 02275 04371 TXH +3 00000 0 04340 04372 TXH +3 00000 0 04340 04373 TXH +3 00000O 0 02632 04374 SUB +0 40200 0 04375 04375 TXH +3 00000 0 02275 04376 ALS +0 76700 0 00022 04377 STD +0 62200 0 04410 04400 TSX +0 01400 4 00002 04401 TXH +3 02622 0 02275 04402 TXH +3 00000 0 04340 04403 TXH +3 00000 0 04340 04404 TXH +3 00000 0 04340 04405 SUB +0 40200 0 04406 04406 TXH +3 00000 0 02275 04407 STA +0 62100 0 04410 04410 STR -1 00000 0 00000 04411 STR -1 00000 0 00000 READ FORMAT DATAA(L.,2,L)...A(1,?2N) *005 04412 TSX +0 07400 4 00005 04413 STR -1 00001 0 02616 04414 TSX +0 07400 4 00002 04415 TXH +302 0622 6221~5 04416. TXH +3 00000 0 04340 04417 TXH +3 00000 0 04341 04420 TXH +3 00000 0 02632 04421 SUB +0 40200 0 04422 04422 TXH +3 00000 0 02275 04423 ALS +0 76700 0 00022 04424 STD +0 62200 0 04435 04425 TSX +0 07400 4-00002 04426 TXH +3 02622 0 02275 04427 TXH +3 00000 0 04340 04430 TXH +3 00000 0 04341 04431 TXH +3 00000 0 04340 04432 SUB +0 40200 0 04433 04433 TXH +3 00000 0 02275 04434 STA +0 62100 0 04435 04435 STR -1 00000 0 00000 - -— 04436 SI —R- — 1 00000 0 00000 --- —---— ~~ ~_ _ — READ FORMAT DATAA(2,1,iT)...A(2,1,N) * 006 04437 TSX +0 07400 4 00005 04440 STR -1 00001 0 02616 ' 04441 TSX +0 07400 4 00002 04442 TXH +3 02622 0 02275 04443 TXH +3 0000 0 0 04341 04444 TXH +3 00000 0 04340" 04445 TXH'+3 00000 0 02632 04446 SUB +0 40200 0 04447 04447 TXH +3 000000 02275 04450 ALS +0 76700 0 00022 04451 STD +0 62200 0 04462 04452 TSX +0 07400 4 00002 04453 TXH +3 02622 0 02275 04454 TXH +3 0000 0 04341 04455 TXH +3 00000 0 04340 04456 TXH +3 00000 0 04340 04457 SUB +0 40200 0 04460 04460 TXH +3 00000 0 02275 04461 STA +0 62100 0 04462 04462 STR -1 00000 0 00000 04463 STR -1 00000 0 00000 READ FORMAT DATA,A(2,2,1)...A(2,2N4)- *007 04464 TSX +0 07400 4 00005 04465 STR -1 00001 0 02616 04466 -T-SX +0'07400 4 00002 04467 TXH +3 02622 0 02275 04470 TXH +3 Q000.0 0 004341 04471 TXH +3 00000 0 04341 04472 TXH +3 00000 0 02632 0447.3 SUB +0 40200 0 04474 04474 TXH +3 00000 0 02275 04475 ALS +0 76700 0 00022 04476 STD +0 62200 0 04507 04477 TSX +0 07400 4 00002 04500 TXH +3 02622 0 02275 04501 TXH +3 00000 0 04341 04502 TXH +3 00000 0 04341 04503 TXH +3 00000 0 04340 04504 SUB +0 40200 '0 04505 04505 TXH +3 00000 0 02275 04506 STA +0 62100 0 04507 04507 STR -1 00000 0 00000 04510 STR -1 00000 0 00000 ~~~~~EXEUTE LEHI(C(L~lt(N)) ~ '~1' --- —-— 1 --- —--— ~ --- —--- EXECUTE ZERO.(C(l)...C(N ) 04511 CLA +0 50000 0 02632 04512 SUB +0 40200 0 04513 04513 TXH +3 00000 0 02612 04515 STD +0 62200 0 04517 04516 TSX +0 07400 4 0001 004517 TIX +2 00000 0 02611 THROUGH SFOR I=l,lI,.G.N *( 04520 C-LA +0 50000 0 04340 04521 STO +0 60100 0 02623 0.4522" TRA +0 -020000 —04526 04524 ADD +0 40000 0 04340 04525 STO +0 60100 0 02623 04526 CLA +0 50000 0 02623 04530 TZE +0 100000 064532 04531 TPL +0 12000 0 04745 WHENEVER A(1,1,I).E.O.OR.A(2,1,I).E.O,TRANSFER TO S __ 008 309 04514 ALS +0 76700 0 00022 04523 CLA +0 50000 0.02623 04527 SUB +0 40200 0 02.632 I -r-7 04532 TSX +0 07400 4 00002 04533 TXH +3 02622 0 02275 04534 04536 TXH +3 00000 0 02623 04537 PAX +0 73400 1 00000 04540 04S4 FAD +0 30000 " 04350 ' 04543 CHS +0 760000 000002 04544 04546 TSX +0 07400 4 00002 04547 TXH +3 02622 0 02275 04550 04552- TXH +3 '00000 0 02623 04553 PAX +0 73400 1 00000 0-''4554 04556 FAD +0 30000 0 04350 04557 CHS +0 76000 0 00002 04560 04562 TRA +0 020CO 0 02637 A(1,1,I)=(90.-A(1,1,I))*6.2831853/360. '04563 —SX- +0 074C00 4 00002 04564 TXH +3 02622 0 02275 '- 04565 04567 TXH +3 00000 0 02623 04570 PAX +0 73400 2 00000 04571 04573 STO +0 60100 0 05576 04574 LDQ +0 56000 0 05576 04575 04577 STQ -0 60000 0 05576 04600 TSX +0 07400 4 00002 04601 04603 TXH +3 00000 0 04340 04604 TXH +3 00000 0 02623 04605 04607 STO +0 60100 1 02275 A(1,2,I)=A(1,2,I)*6.2831853/360 04610 TSX +0 07400 4 00002 04611 TXH +3 02622 0 02275 04612 04614 TXH +3 00000 0 02623 04615 PAX +0 73400 1 00000 04616 04620 STO +0 60100 0 05576 04621 CLA +0 50000 0 04343 04622 04624 STO +0 60100 0 05577 04625 CLA +0 50000 0 05576 04626 04630 TSX +0 07400 4 00002 04631 TXH +3 02622 0 02275 04632 04634 TXH +3 00000 0 02623 04635 PAX +0 73400 1 00000 04636 A(2,1,I)=(90.-A(2,1, I))6.2831853/360. 04640 TSX +0 07400 4 00002 04641 TXH +3 02622 0 02275 04642 04644 TXH +3 00000 0 02623 04645 PAX +0 73400 2 00000 04646 04650 STO +0 60100 0 05577 04651 LDQ +0 56000 0 05577 04652 04654 STO -0 60000 0 05577 04655 TSX +0 07400 4 00002 04656 04660 TXH +3 00000 0 04340 04661 TXH +3 00000 0 02623 04662 04664 STO +0 60100 1 02275 A(2t2, )=A(22,2, I)*6.2831853/360 04665 TSX +0 07400 4 00002 04666 TXH +3 02622 0 02275 04667 04671 TXH +3 00000 0 02623 04672 PAX +0 73400 I 00000 04673 04675 STO +0 60100 0 05577 04676 CLA +0 50000 0 04343 04677 04701 STO +0 60100 0 05576 04702 CLA +0 50000 0 05577 04703 04705 TSX +0 07400 4 00002 04706 TXH +3 02622 0 02275 04707 04711 TXH +3 00000 0 02623 04712 PAX +0 73400 1 00000 04713 C(I)=B/SIN. (A(l1, I)-A(2,1,I) ) 04715 TSX +0 07400 4 00002 04716 TXH +3 02622 0 02275 04717 04721 TXH +3 00000 0 02623 04722 STO +0 60100 0 05577 04723 04725 TXH +3 00000 0 04340 04726 TXH +3 00000 0 04340. 04727 04731 LXA +0 53400 2 05577 04732 CLA +0 50000 1 02275 04733 04735 TSX +0 07400 4 00006 04736 TXH +3 00000 0 05577 04737 04741 FDP +0 24100 0 05577 04742 LXA +0 53400 1 02623 04743 S CONTINUE 04744 TRA +0 02000 0 04523 THROUGH SS,FOR I=t1, I.G.N 04745 CLA +0 50000 0 04340 04746 STO +0 60100 0 02623 04747 04751 ADD +0 40000 0 04340 04752. STO +0 60100 0 02623 04753 04755 TZE +0 100Q00 0 04757 04756 TPL +0 12000 0 05146 _ AC(I)=C(I)*SIN.(A(2,,I)) 04757 TSX +0 07400 4 00002 04760 TXH +3 02622 0 02275 04761 04763 TXH +3 00000 0 02623 04764 SUB +0 40200 0 04765 04765 TXH +3 00000 0 04341 CLA +0 50000 0 04337 ADD +0 40000 1 02275 TXH +3 00000 0 04340 CLA +0 500000 0 4337 ADD +0 40000 1 02275 D3 10 04535 04541 04545 04551 04555 04561 TXH ORA TZE TXH ORA TNZ TXH CLA FMP TXH PAX TXH LDQ ORA FDP TXH CLA TXH CLA FMP TXH PAX +3 +0 +0 +3 +0 *011 00000 0 04340 04566 TXH +3 000000 04340 50000 0 04345 04572 FSB +0 30200 2 02275 26000 0 04344 04576 FDP +0 24100 0 04347 02622 0 02275 04602 TXH +3 00000 0 04340 73400 1 00000 04606 CLA +0 50000 0 05576 *012 +3-00000 0 04340 04613 TXH +0 56000 1 02275- 046'17 —MP -0 50100 0 04350 04623 FAD +0 24100 0 05577 04627 STQ +3 00000 0 04340 04633 TXH +0 56000 0 05577 04637 STO *013 +3 00000 0 04341 04643 TXH +0 50000 0 04345 04647 FSB +0 26000 0 04344 04653 FDP +3 02622 0 02275 04657 TXH +0 73400 1 00000 04663 CLA +3 00000 0 04341 +0 26000 0 04344 +0 30000 0 04350 -0 60000 0 0557-T +3 00000 0 04341 +0 60100 1 02275 +3 00000 0 0 4340 -0 50100 0 04350 +0 10000 0 04562 +3 00000 0 04340 -0 50100 0 04350 -0 10000 0 04563 +3 +0 +0 +3 +0 0oo00 30200 24100 00000 50000 0 2 0 0 0 TO O 04340 02275 04347 04341 05577 *014 TXH +3 00000 0 04341 04670 TXH +3 LDQ +0 56000 1 02275 -04674 FMP +0 ORA -0 50100 0 04350 04700 FAD +0 FDP +0 24100 0 05576 04704 STQ -0 TXH +3 00000 0 04341 04710 TXH +3 CLA +0 500000 005577 04714 STO +' 0_15 TXH +3 00000 0 04341 04720 TXH +3 TSX +0 07400 4 00002 04724 TXH +3 TXH +3 00000 0 02623 04730 PAX +0 FSB +0 30200 2 02275 04734 STO +0 STO-+O 601000 05577 0 04740 CLA +0 STO -0 60000 1 02612 *016 00000 0 04341 26000 0 04344 30000 0 04350 60000 0 05577 00000 0 04341 60100 1 02275 00000 02622 73400 60100 50000 0 0 1 0 0 sO 04340 02275 00000 05577 02277 TRA +0 02000 0 CLA +0 50000 0 *017 04753 02623 04750 CLA +0 50000 0 02623 04754 SUB +0 40200 0 02632 04762 TXH +3 00000 0 04340 04766 STA +0 62100 0 04770 *016 TXH'+3 00000 0 04341 TXH +3 00000 0 02275 04767 TSX +0 04773 LDQ +0 04777 05003 05007 05013 05016 05022 05026 05032 05036 05042 05046 TSX TXH TSX LD1 TSX TXH TSX TXH SUB TXH FMP +0 +3 +0 +0 +0 +3 +0 +3 +0 +3 +0 05052 TSX +0 05056 TXH +3 05062 TSX +0 05066 TXH +3 05072 SUB +0 05076 TXH +3 05102 FDP +0 05105 TSX +0 05111 TXH- +3 05115 TSX +0 05121 LDQ +0 SS 05125 TSX +0 05131 TXH +3 05135 TSX +0 05141 LDQ +0 05145 TRA +0 — 05146 CLA +0 05152 STD +0 05155 CLA +0 05161 ADD +0 07400 4 00006 04770 TXH +3 00000 0 00000 56000 1 02612 04774 FMP +0 26000 0 05577 BC=C( I)*SIN.(A(,1_,I )) 07400 4 00002 05000 TXH +3 02622 0 02275 0000 0 02623 05004 SUB +0 40200 0 05005 07400 4 00006 05010 TXH +3 00000 0 00000 56000 1 02612 05014 FMP +0 26000 0 05577 ZA( I )=AC( I )*SIN. (A(1i2, I )I/COS. (A( 1,2,I ) 07400 4 00002 05017 TXH +3 02622 0 02275 00000 0 02623 05023 SUB +0 40200 0 0502,4 074C00 4 00001 05027 TXH +3 00000 0 00000 0262t1 0 022-7-5 05033 TXH +3 00000 0 04340 40200 0 05037 05037 TXH +3 00000 0 02275 00000 0 00000 05043 LXA +0 53400 1 02623 26000 0 05576 05047 FDP +0 24100 0 05577 ZB( I )=BC*SIN. (A(2,2, I) )/COS. (A(2,2, I)) 07400 4 00002 05053 TXH +3 02622 0 02275 00000 0 02623 05057 SUB +0 40200 0 05060 07400 4 00001 05063 TXH +3 00000 0 00000 02622 0 02275 05067 TXH +3 00000 0 04341 40200 0 05073 05073 TXH +3 00000 0 02275 00000 0 00000 05077 STO +0 60100 0 05576 24100 0 05577 05103 LXA +0 53400 1 02623 XA( I )=AC( I )*COS. (A( 1, 1,- I )) 07400 4 00002 05106 TXH +3 02622 0 02275 00000 0 02623 05112 SUB +0 40200 0 05113 07400 4 00001 05116 TXH +3 00000 0 00000 56000 1 00324 05122 FMP +0 26000 0 05577 YA( I )=AC( I )*SIN. (A( 1,1, I ) ) 07400 4 00002 05126 TXH +3 02622 0 02275 00000 0 02623 05132 SUB +0 40200 0 05133 07400 4 00006 05136 TXH +3 00000 0 00000 56000 1 00324 05142 FMP +0 26000 0 05577 02000 0 04750 EXECUTE ZERO.(C(1)...C(N)) 50000 0 02632 05147 SUB +0 40200 0 05150 622C0 0 05154 05153 TSX +0 07400 4 00012 THROUGH MM,FORJ=1,1,J.G.N 50000 0 04340 05156 STO +0 60100 0 02624 40000 0 04340 05162 STO +0 60100 0 02624 04771 LXA +0 53400 1 02623 04775 LXA +0 —534001 02623 *019 04772 STO +0 60100 0 05577 -04776 STO +0 60100 ' 00324 05001 TXH +3 00000 0 04340 05002 TXH +3 00000 0 04340 05005 TXH +3 00000 0 02275.05006 STA +0 62100 0 05010 05011 LXA +0 53400 1 02623 050fi2 STO +0 601o0 0 05577 05015 STO +0 60100 0 02276 *020 05020 TXH +3 00000 0 04340 05021 TXH +3 00000 0 04341 05024 TXH +3 00000 0 02275 05025 STA +0 62100 0 05027 05030 STO +0 60100 0 05577 05031 TSX +0 07400 4 00002 05034 TXH +3 00000 0 04341, 05035 TXH +3 00000 0 02623 05040 STA +0 62100 0 05042 05041 TSX +0 07400 4 00006 05044 STO +0 60100 0 05576 05045 LDQ +0 56000 1 00324 05050 LXA +0 53400 1 02623 05051 STQ -0 60000 1 04025 *021 05054 TXH +3 00000 0 04341 05055 TXH +3 00000 0 04341 05060 TXH +3 OOOOD 0'O 02275 05061 STA +0 62100 005063 05064 STO +0 60100 0 05577 05065 TSX +0 07400 4 00002 05070 TXH +3 00000 0 04341i- 05071 — TXH-+3 00000 0 02623 05074 STA +0 62100 0 05076 05075 TSX +0 07400 4 00006 05100 LDQ +0 56000 0 02276 05101 FMP +0 26000 0 05576 05104 STQ -O 60000 1 04336 *022 05107 TXH +3-00000 0 04340 05110 TXH +3 00000 0 04340 05o13 TXH +3 00000 0 02275 05114 STA +0 62100-0-05116 05117 LXA +0 53400 1 02623 05120 STO +0 60100 0 05577 05123 LXA +0 53400 1 02623 05124 STO +0 60100 1 03175 *023 05127 TXH +3 00000 0 04340 05130 TXH +3 00000 0 04340 05133 TXH +3 00000.0 02275 05134 STA +0 62100 0 05136 05137 LXA'+0- 53400 02623 05140 STO -+0 60v100 0 05577 05143 LXA +0 53400 1 02623 05144 STO +0 60100 1 03513 ~> I n. *024 05150 rxT-+3'06060 0 02612 05154 TIX +2 00000 0 02611 -- - -- -- - _0-2....5-.. *025 05157 TRA +0 02000 0 05163 05163 CLA +0 50000 0 02624 - - - - - - - - - - - -----— ~- - - -_.. _ — - - - -- -- *026 05171 ORA -0 50100 0 04350 05175 TNZ -0 10000 0 05366 05201 FAD +0 30000 0 04350 05165 TZE +0 10000 0 05167 05166 TPL +0 12000 0 05531 WHENEVER XA(J).E.O. AND. YA(J) E. 0 05167.LXA +0 53400 1 02624 05170 CLA +0 50000 0 04337 05173 CHS +0 76000 00002 05174 ADD +0 40000 1 03513 05177 CLA +0 50000 0 04337 05200 ORA -0 50100 0 04350 05203 ADD +0 40000 1 03175 05204 TNZ -0 10000 0 05366 WHENEVER XA(J+1 ).E.O.AND.YA(J+1).E.0 705205 CLA +0 50000 0 02624 05206 ADD +0 40000 0 04340 05211 ORA -0 50100 0 04350 05212 FAD +0 30000 0 04350 05215 TNZ -0 10000 0 05336 - 05216 CLA +0 50000 0 02624 05221 CLA +0 50000 0 04337 05222 ORA -0 50100 0 04350 05225 ADD +0 40000 1 03175 05226 TNZ -0 10000 0 05336 WHENEVER XA(J+2).E 0.AND.YA(J+2 ).E.0 05227 CLA +0 50000 0 02624 05230 ADD +0 40000 0 04341 05233 ORA -0 50100 0 04350 05234 FAD +0 30000 0 04350 05237 TNZ —0 10000 0 05306 05240 CLA +0 50000 0 02624 05243 CLA +0 50000 0 04337 05244 ORA -0 50100 0 04350 05247 ADD +0 40000 1 03175 05250 TNZ -0 10000 0 05306 1HROUGH AA,FOR K=J+3,1,K.G.N 05251 CLA +0 50000 0 02624 05252 ADD +0 40000 0 04342 05151 ALS +0 76700 0 00022 05160 CLA +0 5-0000 0 02624 05164 SUB +0 40200 0 02632 05172 FAD +0 30000 0 04350 05176 LXA +0 53400 1 02624 05202 CHS +0 76000 0 00002 05207 05213 05217 05223 05231 05235 05241 05245 PAX CHS ADD FAD +0 +0 +0 +0 73400 16000 40000 30000 73400 76000 40000 30000 *02 1 0 00002 0 04340 0 04350... ---- - --- - - - - - 05210 CLA +0 05214 ADD +0 0522&-( PAX' +0 05224 CHS +0 50000 40000 73400 76000 50000 40000 73400 76000 0 04337 1 03513 1 '00000 0 00002 PAX +0 CHS +0 ADD +0 FAD +0 1 0 0 0 *026 00000 00002 04341 04350 05232 CLA 05236 ADD 05242 PAX 05246 CHS +0 +0 +0 +0 0 1 1 0 04337 03513 00000 00002 *029 05253 STO +0 60100 0 02626 05254 TRA +0 02000 0 05260 05255 CLA +0 50000 0 02626 05256 ADD +0 40000 0 04340 05257 STO +0 60100 0 02626 05260 CLA +0 50000 0 02626 0-)5261i —S-B —+0)-40200b —0-0263~2......05262 TiZE +0 00 05i~iO-O-S2647 0...3S263- TPL —+0 —2-00O-C -b05306? WHENEVER XA(K}.NE.O.OR.YA(K)kNE.O '030 05264 LXA +0 53400 1 02626 05265 CLA +0 50000 0 04337 05266 ORA -0 50100 0 04350 05267 FAD +0 30000 0 04350 05270 CHS +0 76000 0 00002 05271 ADD +0 40000 1 03513 05272 TNZ -0'10000 0 05302.05273 LXA +0 53400 1 02626 05274 CLA;+0 50000 004337 05275 ORA -0 50100004350 05276 FAD +0 30000 0 04350 5277 CHS +0 76000 0 00002 05300 ADD +0 40000 1 03175 05301 TZE +0 10000 0 05305 J=K *031 05302 CLA +0 50000 0 02626 05303 STO +0 60100 0 02624 TRANSFER TO MM *032 05304 TRA +0 02000 0 02630 AA END OF CONDITIONAL *033 05305 IRA +0 02000 0 05255 END OF CONDITIONAL *034 X=XA(J+2)-XA(J-1) *035 05306 CLA +0 5000 0 02624 05307 SUB +0 40200 0 04340 05310 STO +0 60100 0 05577 05311 CLA +O 50000 0 02624 05312 ADD +0 40000 0 04341 05313 PAX +0 73400 1 00000 05314 LXA +0 53400 2 05577 05315 CLA +0 50000 1 03175 05316 FSB +o 30200 2 03175 05317 STO + 60100 0 03176 Ys=YA(J+2)-YA( J-1) *036 05320 CIA +- 50-5-000 0 02624 05321 SUB +'- 460200 0 04340 05322 STO +0 60100 0 05577 05323 CLA +0 50000 0 02624 05324 ADD +0 40000 0 04341 05325 PAX +0 73400 1 00000 05326 LXA +0 53400 2 05577 65327 CLA +0 50000 1 03513 05330 FSB +0 30200 2 03513 05331 STO +0 60100 0 03514 J=J+2 *037 05332 CLA +0 50000 0 02624 05333 ADD +0 40000 0 04341 05334 STO +0 60100 0 02624 TRANSFER TO NN *038 05335 TRA +0 02000 0 02631 END OF CONDITIONAL *039 X=XA(J+1)-XA(J-1) *040 05336 CLA +0 50000 0 02624 05337 SUB +0 40200 0 04340 05340 STO +0 60100 0 05577 05341 CLA +0 50000 0 02624 05342 ADD +0 40000 0 04340 05343 PAX +0 73400 1 00000 05344 LXA +0 53400 2 05577 05345 CLA +0 50000 1 03175 05346 FSB +0 30200 2 03175 05347 STO +0 60100 0 03176 Y=YA(J+1)-YA(J-1) *041 05350 CLA +0 50000 0 02624 05351 SUB +0 40200 0 04340 05352 STO +0 60100 0 05577 05353 CLA +0 50000 0 02624 05354 ADD +0 40000 0 04340 05355 PAX +0 73400 1 00000 05356 LXA +0 53400 2 05577 05357 CLA +0 50000 1 03513 05360 FSB +0 30200 2 03513 05361 STO +0 60100 0 03514 J=J+. *042 05362 CLA +0 50000 0 02624 05363 ADD +0 40000 0 04340 05364 STO +0 60100 0 02'624 OTHERWISE *043 05365 TRA +0 02000 0 05404 X=XA(J)-XA(J-1) *044 05366 CLA +0 50000 0 02624 05367 SUB +0 40200 0 04340 05370 LXA +0 53400 1 02624 05371 PAX +0 73400 2 00000 05372 CLA +0 50000 1 03175 05373 FSB +0 30200 2 03175 05374 STO +0 60100 0 03176 Y=YA(J)-YA(J-1) *045 05375 CLA +0 50000 0 02624 05376 SUB +0 40200 0 04340 05377 IXA +0 53400 1 02624 05400 PAX +0 73600 2 00000 05401 CLA +0 50000 L 03513 05402 FSB +0 30200 2 03513 05403 STO +0 60100 0 03514 END OF CONDITIONAL *046 NN R=SQRT. (X*X+-Y*Y) *047 05404 LDQ +0 56000 0 03514 05405 FMP +0 26000 0 03514 05406 STO +0 60100 0 05577 05407 LDQ +0 56000 0 03176 05410 FMP +0 26000 0 03176 05411 FAD +0 30000 0 05517 05412 STO +0 60100 0 05577 05413 TSX +0 07400 4 00010 0b54-14- Ti-XH —+3 000000-" 05577..05 — 415'-S —TO06 0 02636 THETA=270.-ATN1.a(Y,X)*360./6.2831853 *048 05416 TSX +0 (+74-00 4 00000 05417- -TXH"+3 00000 0 03514' 05420 TXH +3 00000 0 03176 05421 STO +0 60100 0 05577 05422 LD +0 56000 0 05577 05423 FMP +0 26000 0 04347 05424 FOP +0 24100 0 04344 05425 STQ -0 60000 0 05577 05426 CLA +0 50000 0 04346 05427 -FSB + — -— 3-02'0 —005577 05-430 STO +0 60100-O-O2-641'. WHENEVER THE'TA.L.0,THETA=360.+THETA *049 S-'0" CLA —'+d-50000 0"04337' - 05432-RA -0 50100 0 0350 0.5433 FAD +0 300 ----0b 04350 -5434 CHS +0 76000 0 002 — 05435_. A.oD +0 40000 0 _02641 0...54_3_6_ TZE +0 10000 0 05443 05437 TPL +0 12000 0 05443 05440 CLA +0 50000 0 04347 05441 FAD +0 30000 0 02641 05442 STO +0 60100 0 02641 PRINT FORMAT PPJRTHETAZA(J),ZBCJ),ZA(J)-ZA(J-1),ZB(J)-ZB( *050 1J-1 ),ZA(J)-Z i(J),XYXA(J) YA(J) *050 I 0"\ I I I i 05443 TSX +0 07400 4 00003 05444 STR -1 00001 0 02635 05445 STR -I 00000 0 02624 05446 STR -1 00000 0 02636 -0S5447 -STR-1 00000 0 02641 05450 CLA +0 50000 0 02624 -05451 SU-B +0 40200 0 05452 05452 IXH +3 0uO0000 0 04025 05453 STA +0 62100 005454 05454 STR -1 00000 0 00000 05455 CLA +0 50000 0 02624 05456 SUB +0 40200 0 05457 05457 TXH +3 00000 0 04336 05460 STA +0 62100 0 05461 05461 STR -1 0000000 00000 05462 CLA +0 50000 0 02624 05463 SUB +0 40200 0 04340 05464 LXA +0 53400 1 02624 05465 PAX +0 73400 2 00000 05466 CLA +0 50000 1 04025 05467 FS8 +0 30200 2 04025 0547n0 S — 0 + 60~100- 0 05577 05471 STR -1 00000 0 05577 05472 CLA +0 50000 0 02624 05473 SUB +0 40200 0 04340 05474 LXA +0 53400 1 02624 05475 PAX +0 73400 2 00000 05476 CLA +0 50000 1 04336 05477 FSB +0 30200 2 04336 05500 STO +0 60100 0 05577 05501 STR -1 00000 0 05577 05502 LXA +0 53400 1 02624 05503 LXA +0 53400 2 02624 05504 CLA +0 50000 1 04025 05505 FSB +0 30200 2 04336 05506 STO +0 60100 0 05577 05507 STR -1 00000 0 05577 05510 STR -1 00000 0 03176 05511 STR -1 00000 0 03514 05512 CLA +0 50000 0 02624 05513 SUB +0 40200 0 05514 05514 TXH +3 00000 0 03175 05515 STA +0 62100 0 05516 05516 STR -1 00000 0 00000 05517 CLA +0 50000 0 02624 05520 SUB +0 40200 0 05521 05521 TXH +3 00000 0 03513 05522 STA +0 62100 0 05523 05523 STR -1 00000 0 00000 05524 STR -1 00000 0 00000' C(J)=R *051 05525 LXA +0 53400 1 02624 05526 CLA +0 50000 0 02636 05527 STO +0 60100 1 02612 __ MM CONTINUE *052 05530 TRA +0 002000 0 05160- ------------- ---- ----- ------------------- -. _ -______ PRINT FORMAT XXtAC (1).. AC(N) *053 05531 TSX +0 07400 4 00003 05532 STR -1 00001 0 03202 05533 CLA +0 50000 0 02632 05534 SUB +0 40200 0 05535 05535 TXH +3 00000 0 00324 - 05536 ALS +0 76700 0 00022 05537 STD +0 62200 0 05540 05540 STR -1 00000 0 00323 05541 STR -1 00000 0 00000 PUNCH FORMAT DATA1t,'N,C( 1)..C(N) *054 05542 TSX +0 07400 4 00004 05543 STR -1 00001 0 02614 05544 STR -1 00000 0 02632 05545 CLA +0 50000 0 02632 05546 SUB +0 40200 0 05547 05547 TXH +3 00000 0 02612 05550 ALS +0 76700 0 00022 05551 STO +0 62200005552 05552 STR -1 00000 0 02611 05553 STR -1 00000 0 00000 WHENEVER LIC.NE.O. '055 05554 CLA +0 50000 0 02627 05555 SUB +0 40200 0 04337 05556 TZE +0 10000 0 05574 EXECUTE SMOTH.(CZB,N) *056 05557 TSX +0 07400 4 00007 05560 TXH +3 00000 0 02612 05561 TXH +3 00000 0 04336 05562 TXH +3 00000 0 02632 - - — ^_. - - - _ _.. ^ _ ^ ^ _ ^ -- - - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ---- PRINT FORMAT XX, ZB(i1).. ZB(N) *057 05563 TSX +0 07400 4 00003 05564 STR -1 00001 0 03202 05565 CLA +0 50000 0 02632 05566 SUB +0 40200 0 05567 05567 TXH +3 00000 0 04336-.055-70 AL-+7610-00022 05571 -STrO-~O —6220 ---OS-5TZ — 5-TRR —000 — 0 04335 05573 STR -1 00000 0 00000 I -q - ----- - -- - END OF CONDITIONAL TRANSFER TO START 05574 TRA +0 02000 0 02640 INTEGER NI,JK VECTOR VALUES DIM=3,1 2,200 - ^I= n *0U5 *059 *060 *061 -- - - - - - - - - - - - - - —;- - - - - - - - -7- - - - - - - - - - - - - I 02617 +0 00000 0 00310.. fI, I,%-.,A. A.. ele 02620 +0 00000 0 00002 02621 +0 00000 0 00001 02622 +0 00000 0 00003 el^..-^ X v: I e1 dt - ----- - - - - - - -X, X VtLlUK VALUtb bUN=$1-,ZtIU.U*S 02300 +0 03300 5 46060 02301 +3 10573 0 22601 VECTOR VALUES DATA1=$15/(16F5.1)*$ 02613 +2 60533 0 13454 02614 +3 10561 7 40106 VECTOR VALUES DAIA=$16F5. 1*$ 02615 -1 46060 6 06060 02616 +0 10626 0 53301 VECTOR VALUES XX=$1HO/,ilH,14F8.',F7.1)*$ 03177 +3 30134 5 46060 03200 +1 03301 7 32607 03201 +3 06073 0 1042 VECTOR VALUES UU=$1H4,S4,lHJ,S7,IHR',S9, HO,S8,2HZAtS8,2HZB,S7 1,5HZA-ZA,S5t5HZB-ZB,S5~5HZA-ZB,S7,IHU,S9,IHV,S9,1HXS9,1HY/1H 2+,522, 1H-*$ 02642 +0 27301 3 04054 02643 +0 13020 7 36202 02644 +1 17301 3 0706 02646 +0 13065 7 36211 02647 +3 06473 6 2173 02650 +2 27362 0 773C 02652 -3 12273 6 20573 02653 -3 30530 7 12240 02654 -0 07121 7 362C 02656 +0 23071 2 27362 02657 -3 12173 6 21073 02660 -3 36210 7 3023 02662 +0 77301 3 05173 02663 -3 30130 4 17362 02664 +0 13004 7 362C VECTOR VALUES PP=S1H, I 5, llFi 0.4 - -------------- 02633 +3 30154 6 06060 02634 -3 30101 2 60100 02635 +0 13060 7 331C DIMENSION A1000l,DIM),C(200),XA(200),YA(200),ZA(200),ZB(200),.AC(200) VECTOR VALUES JUMP=$1HI1$- -. 02625 +0 13001 5 46060 END OF PROGRAM 05575 TSX +0 07400 4 00011 *064-.r,iU6 ------------------ *065 26 03202 +0 13000 6 17401 *066 *066 '066 61 02645 -3 30130 6 77362 D1 02651 +0 5-3071 2 14071 )5 02655 +0 77305 3 07121 30 02661 -2 21173 0 13000 )4 '067..... *068 *068 / *069 -0*0 0 $COMPILE MA 04/17/62 00457S MAO 112 MAR _962 VERSION) PROGRAM LISTING......... ------- EXTERNAL FUNCTION (AB,C)_ - ENTRY TO SMOTH. EXECUTE ZERO.(B(1)...BIC)) THROUGH Q,FOR I=2,1,1.G.C-1 WHENEVER A(I-l).E.O.OR.A(I).E.O.OR.A(I*i).E.O, B(I)=0.25*A1I-1)+0.5*A(I)+0.25*A(I+1) Q CONTINUE BII)=O.75*A 1)+0.25*A(2) B(C)=0.25*A(C-1)+0.75*A(C) FUNCTION RETURN INTEGER I,C END OF FUNCTION -AD PROGRAM,TYPE 12 MAR 19-2 ALL NUMBERS ARE OCTAL) MAD PROGRAM,TYPE-12 MAR 1962 (ALL NUMBERS ARE OCTAL) TRANSFER TO 0 *001 *002 -*003 *004 *005 *006 -009 *010 *012 NO. OF LOCATIONS 00204 TRA VECTOR SIZE 00001 TRA VECTOR STARTS 00000 ENTRY PT. 00013 ERASABLE STARTS 77777 >! 0o PROGRAM IS AN EXTERNAL SMOTH ob00014 VARIABLE STORAGE I__. 00002 FUNCTION DICTIONARY ZERO 00000 ABSOLUTE CONSTANTS 00004 +000000000000 00011 +200600000000 STATEMENT DICTIONARY 00003 TXL -300116000115 FUNC1ION. THE FOLLOWING ARE ENTRIES 0 00003 00005 +000000000001 00012 +233000000000 00006 +000000000002 00007 +177400000000 00010 +200400000000 $DA1A 04/17/62 004575 MAP ERROR.EXIT. PRI NT ATNI 54141 LOCS. OOOOC* 00000* 20372* 21017* CAN tE SYSTEM 00000* SPRINT 00000 -(MAIN) 10000 SMOTH 15601.PUNCH 20433* ZERO- 20506*.MTX 21212* _ (PROG) 21245 SAFELY USED IN EXPANDING PROG. (OCTAL) SKIP6.ERR SQRT (SUBT) 0000o* 16005* 20542* 75414 SCARUS.IOH COS (ERAS) 00000* 16061* 2062U* 77767 DPUNCH OOOOO*.READ 20267* SIN 20620*