UCRL- 513 97
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A CODE FOR VIEWING M A K O CONDUCTORS FROM ANY ANGLE
T. N. Haratani
R , W. Moir
June 15, 1973
?.j ~ ' : L ) I I
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. . . . . . .I_ I" . _l_ - ..................... ~- .... ... ... ............
NOTlCt
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UCRL- 51397
A CODE FOR VIEWING MAFCO CONDUCTORS FROM ANY ANGL€
T. N. Haratani R. W. Moir
MS. date: June 15, 1973
A CODE FOR VIEWING MAFCO CONDUCTORS FROM ANY ANGLE
Abstract ry-
A code designated MPVER rotates to visualize conductors and-serves as a check f o r MAFCO input. @he equations de- A6FCO conductors so that they can be viewed
from any angle.7The code makes it easier scribing the rotating process a r e given. J ??
Introduction
A magnetic field code (MAFCO)' handles a variety of conductors in three dimensions. visualizing these conductors, we have written the MFVER program (Appendix) to plot the projection of conductors used
by MAFCO. To design the MPVER program we had
to transform the MAFCO input describing the conductor coordinates into a rotated coordinate system. This input consisted of parameters defining loops, arcs , helices, straight lines, and a se r i e s of straight line segments. Since helices
a r e seldom used we did not include them in the program.
Because of the difficulty of
Figure 1 shows an example of loops and a r c s in a primed coordinate system. Loops and a r c s a r e specified by xo, and zo, the coordinates in the unprimed coordinate system at the center of
YO'
curvature. Figure 1 also shows the radius
A and the Eulerian angles Q, 8, and 4. The angle 4 ranges from 41 to 42 for a r c s and from 0" to 360" for circles.
z Y '
#
X
Fig. 1. Coordinate system showing the Eulerian angles.
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The Rotation Process
A point on the a r c in the pr ime co-
In ordinates is x' = A , y' = 0, z' = 0.
the unprimed coordinates the point is located by the vector z.
In the double primed coordinates (Fig. 2 ) the point is
where the transformation mat r ix A - l is the standard rotation matrix. 2
Finally, we want to look at the pro-
jection of the point onto the x" - y" plane.
i Z I'
t
Y "
X I
Fig. 2. Coordinate system showing the viewing angles.
F o r straight lines and straight line segments we specify the end points
in the unprimed coordinates and use the t r ans format ion
The matr ix A - l (a,P, 4 ) is
z
where
j = cos4 cosa - cosp sina sin4 k = sin4 cosa - cosB sina sin4 I = sir$ sina
m = cos4 s i m + cos0 cos0 sin4 n = -sin4 sina + cos6 cosa cos4 o = -si$ cosa p = sir@ sin4 q = sir@ cos4
r = cosp.
The matr ix
A-'(CJqJv) is
where
a = cosv cosr - cosr) sin< sinv b = -sinv COSP - cosq s inr cosv c = sinq sing d = cosv s inr + cos17 COSP sinv e = -sinv s in< + cosq cos{ cosv f = -sinr) cosC g = sinr) sinv h = sinq cosv i = cosr).
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F o r a r c s and loops we perform the matr ix multiplications indicated by
Eqs. 1 through 5.
The x" and yl' components are plotted as the projection of the conductor
3' = a(jA + x,) + b(mA + yo)
+ c(pA + z o )
y" = d(jA + x,) + e(mA + Yo)
+ f(pA + zo) . (9)
F o r straight lines and straight line s egm ent s
a b c
g ,h i,
Y
and
X I ' = ax + by + cz
y" = dx + ey + fz . (11)
The form of Eq. (13) allows u s to plot straight lines and straight line segments by specifying the (x, y, z ) values of the end points. TO plot loops and a rc s we must f i rs t break the a r c into segments and plot straight lines (cords). is specified by the angle I$ which we arbi t rar i ly break into equal angular segments of 2" between $1 and 4 2 . The loops a r e broken into equal segments of
6 " . Then we use Eq. (11) to plot these straight line segment approximations to a r c s and loops.
The a r c
The instructions for input data cards To illustrate the a r e shown in Table 1.
use of the code three views of a simple conduetor a r e shown in Fig. 3 . The figure i s based on input data given i n
Table 2. Figure 4 shows more com- plicated conductors used in the design of
a direct energy conversion device. (10)
X X
Z
Zeta = O", E = 0", q = 0". Zeta = 90°, E = go", q = 0". Zeta = 120°, E = 120", q = 30".
Fig. 3. ,Three views of the Yin-Yang coil.
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Table 1 . Input and output for MPVER (MAFCO plot on Versatec).
INPUT
Card one, format (4i5) NLOOPP, NARCPL, NLINEP, NGCEPL, where each variable selects the conductors one wants plotted. Fo r example, if NLOOPP = 1 then every loop will be plotted and if NLOOPP = 2, every other loop wil l be plotted.
Card two, format (i5) NVIEWS = number of different views
Card three, format (3F10.1) TZETA (i), TETA (i), TNU (i), i = 1, NVIEWS. Zeta, eta, and nu determine the orientation of the conductors for each view.
3 Card four through the las t input card a r e MAFCO data cards. F o r each set of conductors there is a maximum of 200 loops, 500 arcs , 50 helices, 400 straight lines, and 2400 straight line segments.
OUTPUT
The output file (TOX) can be plotted on the Versatec printer/plotter via the following teletype writer message:
D C N T L R / ~ 1 TTY responds TYPE DD80 FILE NAME, X OFFSET Y OFFSET, OR L
TOX
TTY responds ALL DONE - If a DD80 plot is desired, copy the fi le TOX to another ten character file start ing with the le t te rs DX, i.e., DXTOXTOXTO. Teletype the following instructions: Give DXTOXTOXTO 999999 / 1 .2 TTY responds IK END
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Table 2. Sample input.
1 1 i 1 3
0.0 0 013 0 . 0 90 . 90 . 0.0
120 . 120 e 3P 1 0 8 0 3 0 1 1 0 Y I N YANG-5 6.15 LOBE ANGLE
0 . 30 e n. 6 5 e 0. 83.85 - 1 O O O O U O ~ 180 e 360 e
0 . -30 e 0 . 65. 0. 9 6 - 1 5 1000000~
65 e 0. n. 30 90. 90. - 1 0 0 0 0 0 0 .
-65 e 0 . 0. 30. 90 90. 1 0 0 0 0 0 0 .
30 e 0, ‘1. 65. 90. 83 .85 ~ 1 0 0 0 0 0 0 ~
1 8 0 . 360
0 . I 8 0 . 0. 1 8 0 . 0 . 180.
0 . 1 8 0 e
1 8 0 e 360 e
- 3 0 e 0 . p * 6 5 a 90 . 9 6 * 1 5 1 0 0 0 0 0 0 ~
0. 65 e r!. 30 0. go. -10 oo o o o . 0 . -65 , n * 30 . 0. 90. 1 0 0 0 0 0 0 .
180 . 360 e
-80 e 0.0 0.0 80 . 0.0 1.0 0.0 -40 0 0.0 0 e 6 80.0 0.0 0.0 0.0 0.0 0.G 0.0 80.0
Fig. 4. Conductors for a direct energy conversion device.
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References
1. W. A. Perkins and J. C. Brown, J. App. Phys. 35, 3337 (1964). 2. H. Goldstein, Classical Mechanics, (Addison-Wesley Publishing Co., Inc., Reading,
Mass., 19591, p. 107. 3 . W. A. Perkins and J. C. Brown, MAFCO-A Magnetic Field Code for Handling
General Current Elements in Three Dimensions, Lawrence Livermore Laboratory, Rept. UCRL-7744 (1966).
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Appendix - MPVER Code
80KU06 1 * I O l h 4 P Y N FLOT MPLOT 2 * CCNTROLLEE 361100 M V E R 3 * XEQ M V C R
5 * DUYP ( C E C * O C T ) 6 + FCQTRAN 7 P 90 G 9 A '4 8 OFT I H I Z E 9 CALL K E E P 8 0 (3RTOY)
4 + L I s r a
+I FL 0 T ( H S P I N PCf T 9 OU T P U T I
1 G CALL ASS TGN ( 3 7 1 5 I I 1 1 2 CLICHE STOPAGE 1 3 PARAHETES(LO=SO* O C C = 7 " C q VH=SDCCv TEN=IOq CD=CCJO* C O = l O l i 1 4 P Md 1 V C = 2401) ) 1 5 CCMNCN T A q T 9 * TCI T O , TEI TFT TGI THI T I , J A Y , JAZ 16 CCHFGN b ( L C ) q T H E T P ( L J ) q DELTA(L0) . A A ( L O ) * X R ( L O 1 , Z ( C O 1 r 1 7 C XH( i ICC)* Y M ( O C C 1 , 7 H ( O C C ) t AM(OCC)r AL1DCC)q BE(DCC)r 10 C X P ( V M ) * Y P ( V H ) q Z P ( V H ) * TZETA(TEN)* TETA(TEN)q TNU(TEN1 19 END CL ICHE 20 USE STORAGE 2 1 2 2 PARdHETLR (F I = 3 . 1 4 1 5 9 2 7 * OUT = 37 I N = 2 1 RAD=.01745329) 23 DIMENSION P I ( D C C ) , P2(C)CC) t B I G ( 4 ) r B I G A ( 3 ) . B I G R ( T E N ) v 2 4 0 x i ( C D I * Y i ( C 3 ) * Z l (CDI * x 2 (COI 9 Y2 (CO) T 22 ( C D ) 25 0 G X ( N t ' l V C l * GY ( H H I V C ) 9 GZ(HHIVC1*NGN(CO) *GI (CO) 9
26 0 H A ( L P ) * H O ( L ? ) * H P I ( L O ) * H P Z ( L 0 ) . H I ( L O ) r HXYtLO) 27 DATA ( D E L F H I = 1.3 I 2 8 D E L P H I = DELPHI RAD 2 9 N = 0 30 C 3 1 31-r IN, ~ 8 5 ~ NLOOFP, N A R C P L ~ NLINEPL, NCCEPL, NWIEWS. 3 2 R ( T Z E T A C I ) p T F T A ( 1 ) 9 T N U ( I ) , I = l q N V I E W S ) 3 3 R I T It09 9197 NPROBS 3 4 R I T IN* 9197 NLOOPI NARC, NHELIXT NLINE, NGCE 35 c 3 6 JOUT FORMAT ( 1 x 1 5HZETP=, F7.19 3Xq 4HETA=* F7.1~ 3 x 1 3HNU=* F7.1 )
3 7 885 FORMAT ( 4 1 5 / I 5 / ( 3 F I O . l ) ) 3 8 886 FCRHAT ( 3F10.1) 3 9 8 8 7 FCRMAT (4FlO.i~ I 5 1 40 8 8 8 FORMAT ( 6 F l O . l ) 4 1 889 FORMAT(OFlO.I /ZFIO.1) 4 2 S l 9 FCSMAT ( 5 1 5 1 43 c 4 4 c REA0 I N THE HAFCO DATA CARDS. 45 c 4 6 IF (1 hLGOF I LOOPS7 ARCS, LOOPS 47 c 48 C 49 C *** READ I N THE LOOPS *** 5 0 C 5 1 C 5 2 LCOPS CGNIINUE 5 3 R I T I N * 8 8 8 . ( X M ( I ) r Y M ( T 1 r Z Y ( I ) r A H ( I ) , AL ( 1 1 , BE (I).I=IqNLOOP) 5 b DC L O I = 1. NLOOP 55 AL(I) = AL(1) RAD 56 LO BE(1) = 3 E ( I ) R A D 5 7 c 5 8 N = N + I 5 9 I F I R S T = 1 60 LAST = NLOOF
* + + * ~ * ~ * * * * * * ~ * ~ * * * * ~ * * ~ * * * * * * * ~** *+**+*+**++*** * * * *+*~**~*** *
*****t*+****++*l**~*
++*****++*+r+***+***
-7 -
6 1 J A Y = LAST 6 2 J A Z = J A Y + NLOOP
64 C 6 5 C
6 3 c a L L BIGGF(IFISST~ L A S T , BIG, N)
6 6 ARCS IF f NARC ) ARK, HELIX. A Q K 6 7 C 68 C 69 C 7 0 C 7 1 C 7 2 ARK 73 7 4 75 7 6 C 77 7 8 7 9 80 8 1 82 8 3 8 4 85 8 6 8 7 8 8 89 9 0 9 1 9 2 93 94 9 5 9 6 9 7 AR 9 8 99
1 0 0
************ *** ** ** * READ I N THE ARCS IC li* ** *I. z **c z * ** 4 1 .?
J L = 0
AL(KP) = AL(KP) RAD B E I K P ) = B E I K P ) * R A D P l t K P ) = P I t K P ) RAO P E t K P ) = P Z t K P ) + RAD JL = JL t I PHIW = P I t K P )
DO AR KP = JZT K Z
TA = 1.0 T 8 = 0 0 0 T C = 0,O TD = 0 . 0 TE = 1.0 T F = 0 0 0 TG = 0 0 0 TH = 0.0 T I = 1.0 CALL ROTATE I PHIHI YPq JL 1 JL = JL t I PHIW = P Z ( K P ) CALL ROTATE ( PHIWT KPI J L 1 0 0 A R R J G = l r JL XP(JG) = ABSF(XP(JG1) YP(JG) = ABSF(YP(JG))
I O 1 ARR Z P t J G ) = ABSF(ZP(JG1) 1 0 2 BEGA(1) = AHAXAF(XP,I*JL,IqH) 1 0 3 B I G A t 2 1 = I I M A X A F ( Y P r l * J L I l , M ) 1 0 4 B I G A ( 3 ) = AHAXAF ( Z P ~ I , J L + l , M ) IO5 N = N t I 106 B I G I N ) = A M A X A F ( 9 I G A 1 1 , 3 r l r M 1 1 0 7 C 1 0 8 H E L I X I F ( k H E L I X ) HELX, L I N E S T HELX 1 9 9 c 1 1 0 C **+ THE HELICES C A R O S ARF H E 2 E L Y REA0 I N SO THAT THE MAFCC DATA CARD 111 C *** DECK CAN STAY INTACT. NO HELICES WILL BE PLOTTED. 1 1 2 c 1 1 3 HELX CONTINUE 1 1 4 C 115 C 116 C *e* READ I N THE H E L I C E S ++* 117 C 118 C 1 1 9 1 2 0 c
*+* + * +c *I c ** ***+ ****+********+I ***+ *
Q I T I N r 8 8 8 , ( H A t I ) r H O tT ) ,HPI (1) rHP2 ( I I , H I ( I ) v H X Y ( I 1 * I= I ,NHELXX)
-8-
121 L I N E S I F ( h t l h t ) L I N E , L I r L I N E 122 c 1 2 3 C 1 1 4 C * * * R F A C I N TbfE S T Q A I G H T L I M E S +** 155 c 1 2 5 C 1 2 7 L I N E K I ' IN, B B d * ( X 1 ( I ) r Y l f I I r Z l l I ) . X 2 1 I ) r ' f 2 t I ) r Z 2 t I ) r I = I q N L I N E ) 1 2 9 c 1 2 9 k r . h + i 1 3 : J Y ' I = NLIF\ l f 131 J i Z = J Y Y 4 N C I N E 133 DC C C L J = 1 9 N L I N E 1 3 3 J b Y = J Y Y t J 1 3 4 JP.' = 3 2 2 + J 1 3 5 X F : J 1 A O S F ( X 2 ( J ) - X I ( J ) 1 1 3 t> X P l J A Y 3 = ABSF V ? ( J ) - Y l . ( , l ) )
F * b * * e t * +*** * * * +** * *
ri*r i * a J c d z c i + * * *****
1 3 7 LSL X P ~ J A Z ) = a9sF Z Z ( J ) - Z I ( J ) 1 1 3 3 Y I G l h ) = f l M A X A F f XFr l r N L I N E r 1. H 1 139 c 140 C I I F ( NGCE 1 GCET P L O T T I GCE 1 4 1 C 1 4 2 C 143 C t?FAC I N THE G E N E R A L C U 2 R E N T E L E n E N T S 1 4 4 c ****** * * O * * l C S * *I** c
1 4 5 c 146 GCE NGX = NGC€ f 47 L M f \ X = 0 I49 DO LGC. i& = I * NGCE 143 L : L V Q P d 2 i 5 3 Q E T I h + 8 8 /' 9 G X (L 1 9 GY (I 1. GZ L 1 GI ( h G ) r N G N ( L G 1 1.51 L V l h i + a P 5 2 CYl '*k = L * NGNtLG) 1 1 5 3 RXI" I N 4 3 8 6 - G X ( L 1 q G Y ( L 1 r GZ(L)r L = L H I N r L Y A X 1 1 5 4 LGC C C N T I h U E 1 5 5 C 1 5 6 N : t u + 1 157 1 ~ 2 L X = L 1 5 8 D3 LGCE J = IT Y G C E 1 5 9 L =: LHAX + 1 l o g L H h X L + N G N ( J ) - 1 161. C A L L A Y I K " / I ( G X ~ L T L H A Y ~ I ~ A H N I ~ A M X ~ ) I E2 Z ' L L A M I N M X t G Y r L r L H A Y r l r A H N 2 r A M X Z ) 163 C A L L A Y l N M X ( G Z ~ C ~ L H A X I ~ ~ A Y N ~ ~ A M X ~ )
* * * i * * + ~ I * * ~ Y l Z * * * * Z
164 A X I = A b S F ( A N X l - A V N I ) 1 6 5 A X 2 5 h E S F ( AWXZ-OMN2 1 1 6 6 4 x 3 = A B S F ( A H X 3 - A H N 3 1 1 6 7 I F ( A X 1 .GE. A X 2 1 WEE 1 6 3 If ( A X 1 .GE. A X 3 1 r CROC 1 6 9 X P ( J ) = 4 x 1 1 7 0 GO T O L G C E 1 7 1 WEE IF ( A X 2 .GEm i l X 3 1 r G R O C 1 7 2 X P I J ) = A X 2 1 7 3 GO T O L G C E 174 GPOC X P ( J ) = A X 3 1 7 5 LGCE C C F l T I N U t 1 7 6 B I t [ I J ) = A H A X A F ( X P r l . h G C E i l r H 1 177 c 178 C 1 7 9 C *9cc+*****+~lr*l****+**I**I
180 C F ? E P A R E T O DO SOME D L O T T I N G
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i a i c 182 c 183 PLOTT 184 C 185 166
I 8 8 1 8 9 190 191 192 193 194 BI 195 C 196 197 198 199 200 c 201 c 202 c 2 0 3 C 204 C 205 C 2 06 207 C 208 209 C 210 2 11 2 12 213 C 2 1 4 215 2 16 2 17 2 18 219 220 221 222 2 23 2 24 2 25 2 26 2 27 228 2 29 230. 2 31 2 3 2 C 233 23C C 235 c 236 C 237 C 238 PLOTL 2 3 9 C 2 40
187 c
********I*********** ** *****
CONTINUE
CPLL CRTKO ( EHBNIIII 1 CALL OOERS (0)
BIGGER = A H A X A F ( BIG+IINIIIY I XMIN = -BIGGER YMIN = X H I N X H A X = BIGGER Y H A X = XHAX HOT 3, eI. (BrG(I) ,I=~,N) FORHAT (4E12.33
SFX = ( XHAX - XHIN I / XHX SFY = ( Y M A X - Y H I N / YHX LECX = X M X - XHN LEGY = YHX - YHN
+*********++************ SET UP FOR THE G R I D S . c * ~ c * * + * r c r * I * * ~ * * * * * I+*
00 TOP K = 11 NVIEWS
PRINT JCUTI TZETA( K I 9 T E T A t K ) I TNlJ t IO
CALL FRAME CALL SETCRT ( X H I N I Y H I N 9 1 I CALL HAPG ( XHINIXHAXIYHIN~YHAX 1
ZETA = T Z E T A t K ) R A O ETA = T E T A ( K ) R A D UNU = TNU(K1 RAO SZE = S I N F ( ZETA I CZE = C O S f (ZETA) SET = S I N F ( ETA )
CET = COSF ( ETA I SNU=SINF( UNU I CNU=COSF( UNU 1 T A= C NU* C ZE-CE T I S ZE *SNU T 8= - SNU* CZE-C ET* S Z E *C NU TC= SET* SZE TO=CNU* S ZE+CET*C ZE *SNU T E= - S NU +S ZE +CET* C ZE *C NU TF=-SET*CZE TC= SET+ SNU TH=SET*CNU T I = C E I
I F ( NLOOP 1 PLOTLT PLTI PLOTL
****+*********** PLOT THE LOOPS. +***+****+******
CONTINUE
00 P L L J K = 19 NLOOP, NLOOPP
-10-
2 41 DO PL JL = 1, 60 2 42 X.J = J L
244 C
246 C
2C8 C 2(t9 F L CCNTINUE 250 C 251 PLL CRLL TSACE ( X P + Y P 1 6 0 r l q l 1 252 C 253 PLT I F ’ ( N A R C 1 PLOTA, PLINE, PLOTA 254 C *+*************+ 255 C PLOT THE ARCS. 256 C *********c***++* 257 c 2 5 8 C *** 00 SOME CALCULATING FOR CALCOHP PLOTTING. 2 5 9 C
2 43 PHIW = 2.P * P I X J / 59. - 2.0 P I / 59.
2 4 5 C *** COMPUTE ROTATED X AND Y F O R PLOTTING. CALL THEM XP AND YP.
2 47 CALL EOTATE(PHIW, JK, JL )
260 C *** J F O R A GIVEN ARC, CALL I T ARC NUMBER JYI I MUST CALCULATE JL POINTS. 2 6 1 C *** ALONG THAT ARC, FROn P H I 1 T O PHI2 . OELPHI IS THE INCREHENT F O R PHI . 262 C *** T H E CARTESIAN PLOINTS ARE X P l J L ) A N 0 YP(JL1. STORED CONSECUTIVELY 263 C 264 PLOTA CCINTINUE 265 C
2 67 JC: = J 268 J I r Y = J + I 269 PLA J L = E) 2 7 0 PHIW = P l ( J K 1 271 C
2 7 3 C 274 PLC J L = JL t 1 275 C 2 76 CALL ROTATE(PHIH1 JK, J L ) 277 c 278 PHIW = FHIW t D E L P H I 2 79 FI = P 2 ( J K ) - PHIW 2 80 If ( FI ) PLO*PLC,PLC 281 PLO HOEL = OELPHI 095
2 66 DO P L I J = JZ, K Z t N A R c P L + l
272 C *** CCIMPUTE ROlATEO X AND Y FOR PLOTTING. CALL THEM XP AND YP.
282 C 2 83 I F (HOEL + F I 1 PLFI PLF, PLE 2 8 4 PLE P H I U = P 2 ( J K ) 2 95 GO T C PLC 286 C 287 FLF CALL TRACE ( X P I Y P , J L * l , l I 288 C 2 89 I F ( J K - J A Y ) P L H I P L I I P L H 290 PLH J K = J K + l 2 91 GO TO PLA 2 9 2 P L I CONTINUE 2 93 294 103 FCRMPT (lX~7El5.31
HOT 3,100, t X P i ( 1 ) , Y ! t ( I ) , Z M ( I l t A M ( I 1 , X P t I l , Y P ( I l . Z P ( I ) * I = l r J L )
2 9 5 HOT 3,iai 296 101 f O R M A T ( l H 1 ) 2 9 7 C
2 9 9 C 3 0 0 C
298 P L I N E I F ( K L I N E ) PLOTS. PGCI FLOTS ********+******* PLOT THE LINES.
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301 C . c * + * * + * * * * + * + * +
302 PLOTS CONTINUE 3 0 3 DO P L I N I = 1, NLINE, N L I N E P t I 3 0 4 J = I t I 3 0 5 X P ( 1 ) = TA + X I ( I ) + T O * Y I ( I ) + T C Z I ( 1 ) 3 0 6 X P ( 2 ) = T A X 2 ( I ) t T R Y 2 ( 1 ) t T C Z 2 ( I ) 3 0 7 Y P ( 1 ) = TO X I ( 1 ) t TF Y I ( I ) t TF * Z I ( 1 ) 3 0 8 Y P ( 2 ) = T O X 2 ( I ) t TF * Y 2 ( I ) + TF 2 2 ( 1 1 3 0 9 CALL TRACE ( XP1Yp12v l . l 1 3 1 0 KP(I) = i n XI(J) t TR * YI(J) + T C ZI(J) 3 1 1 X P I 2 ) = TA X 2 ( J ) + TR Y 2 ( J ) t T C Z 2 1 J ) 3 1 2 Y P ( 1 ) = TD * X I ( J ) t TE Y l t J ) + TF Z I ( J ) 313 Y P ( 2 ) = TO X 2 ( J ) + TF Y 2 ( J ) + TF Z 2 t J I 3 1 4 P L I N CALL TRACE ( XP,YPv2,1,1 1 3 1 5 C 316 C 3 1 7 C PLOT THE GENERAL CEqS 3 1 8 C + * * * * ~ * * * * ~ * * * * ~ * * * + * 3 1 9 C 320 PGC I F ( NCCE 1 PLOTGv TOP, PLOTG 3 2 1 C 322 PLOTG KG= 0
**I*+ ***+***+ ++c e+**
3 23 DC PGB J = 1, NCCE 9 NCCEPL 3 24 DO PGA I = 1, N G N I J ) 3 2 5 K G = KGt 1 3 2 6 X P ( 1 ) = T A G X ( K G ) + TB + G Y ( K G ) t TC GZ(KC) 327 PGA Y P ( 1 ) = TO G X ( K C ) t TE * G Y ( K G ) t T F * GZtKG) 3 2 8 NNG = NGN(J) 3 2 9 PGB CALL TRACE ( XP,YP,NNG.I,I 1 330 c 3 3 1 TOP CONTINUE 3 3 2 C 333 CALL PLCTE 3 3 4 c 3 3 5 CALL E X I T 3 3 6 E NO
3 3 8 OPT I H I Z E 3 3 9 USE STORAGE 3 40 C P H I = COSF ( PHIW 1 3 h l SPHT = S I N F ( PHIW I 3 4 2 SAL = S I N F ( A L ( J U ) ) 3 43 C A L = COSF ( A L t J K ) 1 3 4 4 SBE = SINf ( BEtJK) 1 3 45 CBE = COSF 4 B E I J I O ) 3 46 T J = C P H I CAL - CEE SAL SPHf 3 4 7 T f l = C P H I * SAL t CEE * CAL SPHI 3 4 8 TP = SBE S P H I 3 4 9 TS = TA T J t T B T H + TC * TP 3 50 TU = TD * TJ + TE * TW t TF Tf' 3 5 1 TY = TG TJ t TH T!l t T I TP 3 52 X P t J L ) = TS*AH(JK) t Td*XH(JK) + TB+YH(JK) t TC*ZM(JK) 3 53 YP(JL) = TV+AM[JK) t TTO*XH(JK) t TE+YM[JK) t TF+ZM(JK) 3 54 Z P ( J L ) = T Y ~ A ~ ~ J K ~ t T C * X H ~ J K ~ t T H + Y M ~ J K ~ t T I ~ Z H ~ J K ~ 355 RET URN 3 56 END
3 3 7 SUBROUTINE ROTATE(PHIW+ J K q J L )
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3 5 7 * FCRT R AN
3 59 OFT IH IZE 3 60 US€ STORAGE 3 61 D I M E N S I G N EIG(4) 3 6 2 c 3E3 c T H I S SUBROUTINE HELPS MAKE SURE THE PICTURE OOES NOT GO OFF SCALE. 3 6 4 C 3 E5 J A X = 0
3 6 7 J A X = J A X t 1 3 68 J A Y = JAY + I 3 69 J A Z = JAZ + 1 3 7 3 XP(JAX1 = PBSF (XN(J) + A H ( J ) 1 3 7 1 XP(JAY) = A6SF ( Y H ( J 1 + A H t J ) 1 3 7 2 LASTA XPtJAZ) = ABSF(Zf l (J )+AH(J) )
3 5 8 SUaROUT INE 6IGCE ( If ISST q LAST BIG* N)
3 66 DO LASTA J = I F I 2 S T r LaST
3 7 3 B I G ( N ) = A H A X A F ( XPq1,JAZql.H 1 3 74 HOT 39IDq(XP(K) r K = l r J A Z ) 3 7 5 1 0 FCRHAT ( S X q l O E 1 1 . 2 ) 3 76 RETURN 3 7 7 E NO
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Distribution
LLL lnternal Distribution Roger E. Batzel T. K. Fowler R. F. Post
J. L. Brady R. H. Bulmer R. P. Freis T. N. Haratani M. A. Harrison
B. C. Howard
S. L. Rompel F. H. Coensgen C. C. Damm J. H. Foote S. Fernbach T. J. Fessenden
C. W. Hartman E. B. Hooper W. E. Nexsen C. A. Larsen R. W. Moir W. L. B a r r A. R. Harvey A. K. Chargin C. E. Taylor
C. D. Henning G. A. Carlson B. McNamara
J. D. Lee L. C. Pittenger TZD File 30
25 External Distribution
R. W. Bussard U.S. Atomic Energy
Commission Washington, D. C.
J. File Princetdn University Princeton, New Jersey
H. Laquer Los Alamos Scientific
Los Alamos, New Mexico Laboratory
M. Lube11 Oak Ridge National Laboratory Oak Ridge, Tennessee
L. M. Lidsky Massachusetts Institute of
Technology Cam b r i dg e, M as s ac h u s et t s
TID-4 500 Distribution, UC-32
25
Mathematics and Computers 207
MSG/lc/edas
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e- .-
