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```      SUBROUTINE  VISES (Z1,ZE,Z2,X1,X2,NX,E1,E2,NE,L,M,PL)

C     [ELLIPTICAL SEQUENCE]
C     (Z1,Z2)  RANGE OF ZE
C     (X1,X2)  RANGE OF XI
C     (E1,E2)  RANGE OF ETA
C     NX       NUMBER OF XI VALUES
C     NE       NUMBER OF ETA VALUES
C     L= 1  WESTERN VIEW,  L=-1  EASTERN VIEW
C     M= 1  SOUTHERN VIEW, M=-1  NORTHERN VIEW
C     PL       PEN MOVEMENT SUBROUTINE, NORMALLY PLTCA
C     [17-MAY-75]

EXTERNAL    PL
DIMENSION   ZE(1),U(501),V(501)

IX(J,I)=(I-1)*NX+J
KI(K)=MAX0(MIN0(K+N,MK),1)
SC(Z)=ZS*(Z-Z1)+0.2

N=L*M
MM=1
MK=501
EL=FLOAT(L)
EM=FLOAT(M)
DX=(X2-X1)/FLOAT(NX-1)
DE=(E2-E1)/FLOAT(NE-1)
ZS=0.58/(Z2-Z1)

I0=(NE+1-M*(NE-3))/2
J0=((NX+1)-L*(NX-1))/2
10 K=((MK+1)*(1-N))/2
I=MAX0(MIN0(I0,NE+1),0)
J=J0
E=E1+DE*FLOAT(I-1)
X=X1+DX*FLOAT(J-1)
20 IF ((I.LT.1).OR.(I.GT.NE)) GO TO 22
K=KI(K)
U(K)=0.166*(COSH(X)*COS(E)+3.0)
V(K)=SC(ZE(IX(J,I)))+0.075*SINH(X)*SIN(E)
22 I=I-M
E=E-EM*DE
IF ((I.LT.1).OR.(I.GT.NE)) GO TO 30
K=KI(K)
U(K)=0.166*(COSH(X)*COS(E)+3.0)
V(K)=SC(ZE(IX(J,I)))+0.075*SINH(X)*SIN(E)
J=J+L
X=X+EL*DX
IF ((J.GE.1).AND.(J.LE.NX)) GO TO 20
30 IF (N.GT.0)  CALL VISHO (U,V,K,MM,PL)
IF (N.LT.0)  CALL VISHO (U(K),V(K),MK-K+1,MM,PL)
MM=-MM
I0=I0+M
IF ((I0.GE.0).AND.(I0.LE.NE+1)) GO TO 10
J0=J0+L
IF ((J0.GE.1).AND.(J0.LE.NX))   GO TO 10
RETURN
END
```
```      SUBROUTINE  VISHH (X0,T0,B0,N0,X,Y,N,I,PL)

C     [HALF HORIZON]
C     SOME OF THE HIDDEN LINE SUBROUTINES EMPLOY MORE THAN ONE HORIZON,
C     WHICH MEANS THAT THE ARRAYS CONTAINING THESE HORIZONS MUST APPEAR
C     AS EXPLICIT ARGUMENTS IN THE UPDATING SUBROUTINES. NEVERTHELESS,
C     THREE OF THE ARGUMENTS OF VISBO ARE NOTHING BUT WORKING ARRAYS
C     WHICH CAN STILL BE REMOVED FROM THE CALLING PROGRAMS IF THEY ARE
C     PLACED IN AN INTERMEDIATE SUBROUTINE SUCH AS THIS ONE.
C     X0(N0)  ARRAY OF ARGUMENTS FOR THE HORIZON
C     T0(N0)  ARRAY OF VALUES OF THE UPPER HORIZON
C     B0(N0)  ARRAY OF VALUES OF THE LOWER HORIZON
C     X(N)    ARRAY OF ARGUMENTS
C     Y(N)    ARRAY OF FUNCTION VALUES
C     I       PEN DIRECTION (1=FORWARD, -1=BACKWARD)
C     PL      PEN MOVEMENT SUBROUTINE
C     [10-MAY-75]

EXTERNAL    PL
LOGICAL     P(701)
DIMENSION   X(1),Y(1),X0(1),T0(1),B0(1)
DIMENSION   X1(701),T1(701),B1(701)
DATA        M,P/701,701*T/

CALL VISBO (X1,T1,B1,M,X0,T0,B0,N0,X,Y,P,N,I,PL)
RETURN
END

C     ------------------------------------------------------------------

SUBROUTINE  VISHO (X,Y,N,I,PL)

C     [HORIZONS]
C     SUBROUTINE WHICH UPDATES THE HORIZONS FOR THE HIDDEN LINE
C     SUBROUTINES.  THE ACTUAL WORK IS DONE BY VISBO, BUT VISHO
C     CONTAINS THE WORK ARRAYS NEEDED IN THE SIMPLEST APPLICATIONS,
C     AVOIDING THE NECESSITY TO DEFINE THEM SEPARATELY FOR EACH
C     INDIVIDUAL PROGRAM.
C     X(N)   ARRAY OF ARGUMENTS
C     Y(N)   ARRAY OF FUNCTION VALUES
C     I      DIRECTION OF PEN MOVEMENT
C     PL     PEN MOVEMENT SUBROUTINE
C     [10-MAY-75]

EXTERNAL    PL
LOGICAL     P(701)
DIMENSION   X(1),Y(1)
DIMENSION   X0(701),T0(701),B0(701)
DIMENSION   X1(701),T1(701),B1(701)
COMMON/VIS/ N0
DATA        M,P/701,701*T/

CALL VISBO (X1,T1,B1,M,X0,T0,B0,N0,X,Y,P,N,I,PL)
RETURN
END
```
```      SUBROUTINE  VISIS (Z1,ZE,Z2,J1,J2,MX,I1,I2,MY,O,PL)

C     [INCLINED SEQUENCE]
C     ZE(MX,MY) ARRAY OF FUNCTION VALUES
C     (Z1,Z2)   SPAN OF Z VALUES
C     J1,J2     RANGE OF X (HORIZONTAL COORDINATE)
C     I1,I2     RANGE OF Y (DEPTH COORDINATE)
C     O(3,3)    ORTHOGONAL MATRIX DEFINING INCLINATION
C     PL        PEN MOVEMENT SUBROUTINE, USUALLY PLTCA
C     [30-MAY-75]

EXTERNAL    PL
DIMENSION   O(3,3),ZE(1),U(501),V(501)
DATA        MK/501/

PR(I)=0.667*(O(1,I)*EU+O(2,I)*VE+O(3,I)*UU)+0.5

L=-IFIX(SIGN(1.0,O(2,1)))
M= IFIX(SIGN(1.0,O(1,1)))
NL=ISIGN(1,L)
NM=ISIGN(1,M)
N=NL*NM
IL=I1-IABS(M)
IU=I2+IABS(M)
MM=M*MX
NN=1
TE=0.5*FLOAT(NL+1)
ZS=1.0/(Z2-Z1)
DUJ=1.0/FLOAT(MX-1)
EUJ=DUJ*FLOAT(L)
DVI=1.0/FLOAT(MY-1)
EVI=DVI*FLOAT(M)
I0=(I2+I1-NM*(I2-I1))/2+M
J0=(J2+J1-NL*(J2-J1))/2
K0=((MK+1)*(1-N))/2
10 K=K0
I=MAX0(MIN0(I0,IU),IL)
J=J0
IX=J+(I-1)*MX
EU=DUJ*FLOAT(J-1)-0.5
VE=DVI*FLOAT(I-1)-0.5
20 IF ((I.LT.I1).OR.(I.GT.I2)) GO TO 22
K=MAX0(MIN0(K+N,MK),1)
UU=ZS*(ZE(IX)-Z1)
U(K)=PR(1)
V(K)=PR(2)
22 I=I-M
IX=IX-MM
VE=VE-EVI
IF ((I.LT.I1).OR.(I.GT.I2)) GO TO 30
K=MAX0(MIN0(K+N,MK),1)
UU=ZS*(ZE(IX)-Z1)
U(K)=PR(1)
V(K)=PR(2)
J=J+L
IX=IX+L
EU=EU+EUJ
IF ((J.GE.J1).AND.(J.LE.J2)) GO TO 20
```
```   30 KK=(K+1-N*(K-1))/2
CALL VISHO (U(KK),V(KK),(MK+1-N*(MK-2*K+1))/2,NN,PL)
NN=-NN
I0=I0+M
IF ((I0.GE.IL).AND.(I0.LE.IU)) GO TO 10
J0=J0+L
IF ((J0.GE.J1).AND.(J0.LE.J2)) GO TO 10
RETURN
END

C     ------------------------------------------------------------------

FUNCTION    VISLI (Z,X,Y,I)

C     [LINEAR INTERPOLATION]
C     PERFORM THE BACKWARD LINEAR INTERPOLATIONS REQUIRED BY THE HORIZON
C     ROUTINES. VISLI RECEIVES SUCH INTENSE USAGE THAT IT DELIBERATELY
C     ESCHEWS A CHECK FOR A ZERO DENOMINATOR, WHICH STILL OCCASIONALLY
C     CREATES OVERFLOWS.
C     Z     POINT AT WHICH INTERPOLATION IS MADE
C     X     ARRAY IN WHICH Z IS INTERPOLATED
C     Y     ARRAY FROM WHICH TO TAKE THE INTERPOLATED VALUE
C     I     AN INDEX FOR WHICH X(I-1).LE.Z.LE.X(I)
C     [05-MAY-74]

DIMENSION   X(1),Y(1)

X1=X(I-1)
X2=X(I)
Y1=Y(I-1)
Y2=Y(I)
VISLI=Y1+(Y2-Y1)*((Z-X1)/(X2-X1))
RETURN
END
```
```      SUBROUTINE  VISNH

C     [NULL HORIZON]
C     SETS UP THE NULL INITIAL HORIZON WHICH MOST OF THE HIDDEN LINE
C     SUBROUTINES REQUIRE.
C     [22-NOV-74]

COMMON/VIS/ N0

N0=0
RETURN
END

C     ------------------------------------------------------------------

SUBROUTINE  VISNP (PH,TH,JP,IT,NP,NT,O)

C     [NEAREST POINT]
C     DETERMINE THE COORDINATES OF THE LINE OF SIGHT JOINING THE
C     OBSERVER TO THE CENTER OF THE SPHERICAL COORDINATES.
C     (PH,TH)  SURFACE COORDINATES OF NEAREST POINT
C     (JP,IT)  INDICES OF NEAREST POINT
C     (NP,NT)  RANGE OF PHI, THETA INDICES
C     O(3,3)   ORTHOGONAL MATRIX DEFINING ROTATION
C     [16-JUN-74]

DIMENSION   O(3,3)

O31=O(3,1)
O32=O(3,2)
PH=ATAN2(O32,O31)
IF (PH.LT.0.0) PH=6.28318+PH
RH=SQRT(O31*O31+O32*O32)
TH=ATAN2(RH,O(3,3))
JP=1+IFIX(0.5+(FLOAT(NP)*PH)/6.28318)
IT=MIN0(MAX0(IFIX(1.5+(TH*FLOAT(NT-1))/3.14159),1),NT)
RETURN
END
```
```      SUBROUTINE  VISPS (Z1,ZE,Z2,R1,R2,NR,P1,P2,NP,L,M,PL)

C     [POLAR SEQUENCE]
C     L= 1  WESTERN VIEW,  L=-1  EASTERN VIEW
C     M= 1  SOUTHERN VIEW, M=-1  NORTHERN VIEW
C     [17-MAY-75]

EXTERNAL    PL
DIMENSION   ZE(1),U(501),V(501)

IX(J,I)=(I-1)*NR+J
SC(Z)=0.167+ZS*(Z-Z1)

N=L*M
MM=1
MK=501
EL=FLOAT(L)
EM=FLOAT(M)
ZS=0.667/(Z2-Z1)
DP=(P2-P1)/FLOAT(NP-1)
DR=(R2-R1)/FLOAT(NR-1)

I0=(NP+1-M*(NP-3))/2
J0=((NR+1)-L*(NR-1))/2
K0=((MK+1)*(1-N))/2
10 K=K0
I=MAX0(MIN0(I0,NP+1),0)
J=J0
P=P1+DP*FLOAT(I-1)
R=R1+DR*FLOAT(J-1)
20 IF ((I.GT.NP).OR.(I.LT.1)) GO TO 22
K=MAX0(MIN0(K+N,MK),1)
U(K)=0.5*(1.0+R*COS(P))
V(K)=SC(ZE(IX(J,I)))+0.167*R*SIN(P)
22 I=I-M
P=P-EM*DP
IF ((I.GT.NP).OR.(I.LT.1)) GO TO 30
K=MAX0(MIN0(K+N,MK),1)
U(K)=0.5*(1.0+R*COS(P))
V(K)=SC(ZE(IX(J,I)))+0.167*R*SIN(P)
J=J+L
R=R+EL*DR
IF ((J.LE.NR).AND.(J.GE.1)) GO TO 20
30 IF (N.GT.0) CALL VISHO (U,V,K,MM,PL)
IF (N.LT.0) CALL VISHO (U(K),V(K),MK-K+1,MM,PL)
MM=-MM
I0=I0+M
IF ((I0.GE.0).AND.(I0.LE.NP+1)) GO TO 10
J0=J0+L
IF ((J0.GE.1).AND.(J0.LE.NR)) GO TO 10
RETURN
END
```
```      SUBROUTINE  VISRB (X,Y,J,M,X1,Y1,N1,X2,Y2,N2,S)

C     [RESTRICTED BOUND]
C     THE BOUND IS RESTRICTED TO THE INTERVAL WHERE THE FIRST
C     FUNCTION IS DEFINED.
C     X(M),Y(M)     ARRAYS FOR THE BOUND OF TWO FUNCTIONS
C     J,M           ACTUAL DIMENSION, MAXIMUM DIMENSION OF X,Y
C     X1(N1),Y1(N1) FIRST  FUNCTION
C     X2(N2),Y2(N2) SECOND FUNCTION
C     S             TYPE OF BOUND (S=1.0,UPPER; S=-1.0,LOWER)
C     [15-MAY-74]

LOGICAL     EQ,VISSL
DIMENSION   X(1),Y(1),X1(1),Y1(1),X2(1),Y2(1)

EQ(X,Y)=ABS(Y-X).LE.1.0E-5

L=.TRUE.
J=0
J1=1
J2=1
Z1=X1(J1)
Z2=X2(J2)
IF (N1.LE.1)   RETURN
IF (N2.LE.1)   GO TO 60
IF (EQ(Z1,Z2)) GO TO 32
IF (Z1-Z2)     10,32,20

10 J=MIN0(J+1,M)
X(J)=Z1
Y(J)=Y1(J1)
J1=J1+1
Z1=X1(J1)
IF (EQ(Z1,Z2)) GO TO 32
IF (Z1-Z2)     10,32,32

20 J2=J2+1
Z2=X2(J2)
IF (EQ(Z1,Z2)) GO TO 32
IF (Z1-Z2)     32,32,20

30 IF (J1.GT.N1) RETURN
IF (J2.GT.N2) GO TO 60
Z1=X1(J1)
Z2=X2(J2)
32 Z=AMIN1(Z1,Z2)
W1=VISLI(Z,X1,Y1,MAX0(J1,2))
W2=VISLI(Z,X2,Y2,MAX0(J2,2))
IF (EQ(Z,Z1)) J1=J1+1
IF (EQ(Z,Z2)) J2=J2+1

W=S*AMAX1(S*W1,S*W2)
D=W1-W2
IF (L.OR.(J.LE.1)) GO TO 42
IF ((EQ(D,0.0)).OR.(EQ(E,0.0))) GO TO 41
IF (SIGN(1.0,D).EQ.SIGN(1.0,E)) GO TO 41
J=MIN0(J+1,M)
X(J)=U-E*((Z-U)/(D-E))
Y(J)=WW+(X(J)-U)*((W1-WW)/(Z-U))
```
```   41 IF (VISSL(Z,W,X,Y,J)) GO TO 43
42 J=MIN0(J+1,M)
43 X(J)=Z
Y(J)=W
L=.FALSE.
E=D
U=Z
WW=W1
GO TO 30

60 IF (J1.GT.N1) RETURN
J=MIN0(J+1,M)
X(J)=X1(J1)
Y(J)=Y1(J1)
J1=J1+1
GO TO 60

END

C     ------------------------------------------------------------------

SUBROUTINE  VISRS (Z1,ZE,Z2,NX,MX,NY,MY,TH,PL)

C     [ROTATED SEQUENCE]
C     ZE(J,I) ARRAY OF FUNCTION VALUES
C     (Z1,Z2) SPAN OF Z VALUES
C     NX,NY   RANGES OF J AND I
C     MX,MY   MAXIMA ATTAINABLE BY J AND I
C     TH      ANGLE OF ROTATION (DEGREES, CLOCKWISE).
C     L       DIRECTION OF VIEW (1=WEST, -1=EAST)
C     M       DIRECTION OF VIEW (1=SOUTH, -1=NORTH)
C     PL      PEN MOVEMENT SUBROUTINE
C     THE HORIZONTAL SCALE IS NOT ALWAYS CONSTANT, BUT IS ADJUSTED
C     SO THAT THE DRAWING WILL OCCUPY THE FULL BREADTH OF THE PAGE.
C     [19-DEC-74]

EXTERNAL    PL
DIMENSION   ZE(1),U(501),V(501)
DATA        M,MK,VF/1,501,0.333/

IX(J,I)=(I-1)*MX+J
SC(Z)=ZS*(Z-Z1)

IF (TH.LT.0.0) L=-1
IF (TH.GE.0.0) L= 1
N=L*M
MM=1
SI=SIND(TH)
CO=COSD(TH)
EL=FLOAT(L)
EM=FLOAT(M)
ZS=(1.0-VF)/(Z2-Z1)
SF=1.0/(ABS(CO)+ABS(SI))
U0=0.25*(EL+1.0)*(1.0-SF*(CO-SI))
V0=0.15*(EL-1.0)*SF*SI
```
```      DUI=-(SF*SI)/FLOAT(MY-1)
DUJ= (SF*CO)/FLOAT(MX-1)
DVI= (VF*SF*CO)/FLOAT(MY-1)
DVJ= (VF*SF*SI)/FLOAT(MX-1)

I0=(NY+1-M*(NY-3))/2
J0=(NX+1-L*(NX-1))/2
K0=((MK+1)*(1-N))/2
10 K=K0
I=MAX0(MIN0(I0,NY+1),0)
J=J0
EU=U0+DUI*FLOAT(I-1)+DUJ*FLOAT(J-1)
VE=V0+DVI*FLOAT(I-1)+DVJ*FLOAT(J-1)
20 IF ((I.LT.1).OR.(I.GT.NY)) GO TO 22
K=MAX0(MIN0(K+N,MK),1)
U(K)=EU
V(K)=VE+SC(ZE(IX(J,I)))
22 I=I-M
EU=EU-EM*DUI
VE=VE-EM*DVI
IF ((I.LT.1).OR.(I.GT.NY)) GO TO 30
K=MAX0(MIN0(K+N,MK),1)
U(K)=EU
V(K)=VE+SC(ZE(IX(J,I)))
J=J+L
EU=EU+EL*DUJ
VE=VE+EL*DVJ
IF ((J.GE.1).AND.(J.LE.NX)) GO TO 20
30 IF (L.GT.0) CALL VISHO (U,V,K,MM,PL)
IF (L.LT.0) CALL VISHO (U(K),V(K),MK-K+1,MM,PL)
MM=-MM
I0=I0+M
IF ((I0.GE.0).AND.(I0.LE.NY+1)) GO TO 10
J0=J0+L
IF ((J0.GE.1).AND.(J0.LE.NX))   GO TO 10
RETURN
END
```
```      LOGICAL FUNCTION  VISSL (EX,WY,X,Y,I)

C     [STRAIGHT LINE]
C     [15-MAY-74]

DIMENSION   X(1),Y(1)

X1=X(I-1)
X2=X(I)
Y1=Y(I-1)
Y2=Y(I)
D=(WY-Y1)*(X2-X1)-(EX-X1)*(Y2-Y1)
VISSL=ABS(D).LT.(1.0E-10)
RETURN
END

C     ------------------------------------------------------------------

SUBROUTINE  VISSP (RHO,PHI,R,T,P,O)

C     [SPHERICAL PROJECTION]
C     DETERMINE THE PLANAR POLAR COORDINATES IN THE PLOTTER PAGE
C     OF A POINT PROJECTED FROM THE FUNCTIONAL SURFACE, WHICH IS
C     DEFINED IN SPHERICAL POLAR COORDINATES.
C     (RHO,PHI)  PLANE POLAR COORDINATES
C     (R,T,P)    SPHERICAL SURFACE COORDINATES
C     O(3,3)     ORTHOGONAL MATRIX EXPRESSING THE FIGURE'S ROTATION
C     [20-MAY-74]

DIMENSION   O(3,3)

X=R*SIN(T)*COS(P)
Y=R*SIN(T)*SIN(P)
Z=R*COS(T)
U=O(1,1)*X+O(1,2)*Y+O(1,3)*Z
V=O(2,1)*X+O(2,2)*Y+O(2,3)*Z
RHO=SQRT(U*U+V*V)
PHI=ATAN2(V,U)/6.28318
RETURN
END
```
```      SUBROUTINE  VISSS (FU,J1,J2,NP,I1,I2,NT,L,M,Q,B,S,O,PR,PL)

C     [SPHERICAL SEQUENCE]
C     FU(NP,NT) ARRAY OF FUNCTION VALUES
C     (J1,J2)   INTERVAL OF PHI INDICES TO BE GRAPHED
C     (I1,I2)   INTERVAL OF THETA INDICES TO BE GRAPHED
C     L= 1  WESTERN VIEW,  L=-1  EASTERN VIEW
C     M= 1  SOUTHERN VIEW, M=-1  NORTHERN VIEW
C     Q         ACCORDING TO THE ORIENTATION OF EACH INFINITESIMAL
C               RECTANGLE TO THE LINE OF SIGHT AND SEARCH DIRECTION ITS
C               EDGES WILL FORM PART OF THE HORIZON OR NOT
C     B=        (ATAN2 CUT LINE DOES NOT FALL IN QUADRANT BEING GRAPHED)
C     S         S=1.0, GRAPH FU POSITIVE; S=-1.0, GRAPH FU NEGATIVE
C     O(3,3)    ORTHOGONAL ROTATION MATRIX
C     PR        PROJECTION SUBROUTINE
C     PL        PEN MOVEMENT SUBROUTINE
C     [15-MAY-75]

EXTERNAL    PL
LOGICAL     B,PE(701)
DIMENSION   FU(1),O(3,3)
DIMENSION   AZ(701),RA(701),OR(701)
DATA        MK/701/

TAN(X)=SIN(X)/COS(X)
IX(J,I)=(I-1)*NP+MOD(NP+J-1,NP)+1
ZP(X1,Y1,X2,Y2)=X1-Y1*((X2-X1)/(Y2-Y1))
WH(T,P)=Q*SIGN(1.0,1.57079-T)*(TAN(T)-TN*COS(P-PH))

NL=ISIGN(1,L)
NM=ISIGN(1,M)
N=NL*NM
IL=I1-IABS(M)
IU=I2+IABS(M)
NN=1
EL=FLOAT(L)
EM=FLOAT(M)
DP=6.28/FLOAT(NP)
DT=3.14/FLOAT(NT)
CALL VISNP (PH,TH,JP,IT,NP,NT,O)
TN=TAN(TH)

I0=((I1+I2)+NM*(I1-I2))/2+M
J0=((J1+J2)+NL*(J1-J2))/2
K0=((MK+1)*(1-N))/2
10 K=K0
I=MAX0(MIN0(I0,IU),IL)
J=J0
T=TH+DT*FLOAT(I-IT)
P=PH+DP*FLOAT(J-JP)
20 IF ((I.GT.I2).OR.(I.LT.I1)) GO TO 22
K=MAX0(MIN0(K+N,MK),1)
FV=FU(IX(J,I))
CALL PR (RA(K),AZ(K),ABS(FV),T,P,O)
PE(K)=S*FV.GT.0.0
OR(K)=WH(T,P)
```
```   22 I=I-M
T=T-EM*DT
IF ((I.GT.I2).OR.(I.LT.I1)) GO TO 30
K=MAX0(MIN0(K+N,MK),1)
FV=FU(IX(J,I))
CALL PR (RA(K),AZ(K),ABS(FV),T,P,O)
PE(K)=S*FV.GT.0.0
OR(K)=WH(T,P)
J=J+L
P=P+EL*DP
IF ((J.LE.J2).AND.(J.GE.J1)) GO TO 20

30 IF (N.GT.0) GO TO 32
M1=MK-K+1
DO 31 MM=1,M1
AZ(MM)=AZ(K+MM-1)
RA(MM)=RA(K+MM-1)
PE(MM)=PE(K+MM-1)
31 OR(MM)=OR(K+MM-1)
K=M1
32 IF (K.LE.1) GO TO 50
IF (B) GO TO 36
DO 35 MM=1,K
35 IF (AZ(MM).LT.0.0) AZ(MM)=AZ(MM)+1.0
36 IF (AZ(1).LE.AZ(K)) GO TO 38
DO 37 MM=1,K
T1=AZ(MM)
T2=RA(MM)
T3=PE(MM)
T4=OR(MM)
AZ(MM)=AZ(K-MM+1)
RA(MM)=RA(K-MM+1)
PE(MM)=OR(K-MM+1)
OR(MM)=OR(K-MM+1)
AZ(K-MM+1)=T1
RA(K-MM+1)=T2
PE(K-MM+1)=T3
37 OR(K-MM+1)=T4
38 K1=0
40 K1=K1+1
IF (K1.GE.K) GO TO 50
IF (OR(K1).GT.0.0) GO TO 40
K2=K1
IF (K1.LE.1) GO TO 41
K1=K1-1
AZ(K1)=ZP(AZ(K1),OR(K1),AZ(K1+1),OR(K1+1))
RA(K1)=ZP(RA(K1),OR(K1),RA(K1+1),OR(K1+1))
41 IF (K2.GT.K) GO TO 43
IF (OR(K2).GT.0.0) GO TO 42
K2=K2+1
GO TO 41
```
```   42 IF (K2.GT.K) GO TO 43
AZ(K2)=ZP(AZ(K2),OR(K2),AZ(K2-1),OR(K2-1))
RA(K2)=ZP(RA(K2),OR(K2),RA(K2-1),OR(K2-1))
K2=K2+1
43 IF (K2-K1.LT.2) GO TO 44
IF (AZ(K1).GE.AZ(K1+1)) AZ(K1)=AZ(K1+1)-0.0025
IF (AZ(K2-1).LE.AZ(K2-2)) AZ(K2-1)=AZ(K2-2)+0.0025
44 IF (K2-K1.GT.1) CALL VISCH (AZ(K1),RA(K1),PE(K1),K2-K1,NN,PL)
K1=K2
GO TO 40

50 NN=-NN
I0=I0+M
IF ((I0.GE.I1-1).AND.(I0.LE.I2+1)) GO TO 10
J0=J0+L
IF ((J0.GE.J1).AND.(J0.LE.J2)) GO TO 10
RETURN
END
```
```      SUBROUTINE  VISTR (Z1,S1,S2,S3,Z2,NX,MX,NY,MY,US,VS,VD,L,IS,PL)

C     [TRIPLE SURFACE]
C     US,VS   TOTAL SHEARS IN U AND V DIRECTIONS
C     VD      VERTICAL DISPLACEMENT BETWEEN FUNCION SEGMENTS
C     L       DIRECTION OF VIEW (1=WEST, -1=EAST)
C     IS      SEPARATION OPTION (1=YES,  -1=NO)
C     PL      PEN MOVEMENT SUBROUTINE
C     [16-MAY-74]

EXTERNAL    PL
DIMENSION   S1(1),S2(1),S3(1)
DIMENSION   G1(275),G2(275),G3(275),H1(275),H2(275),H3(275)
DIMENSION   U1(275),U2(275),U3(275),F1(275),F2(275),F3(275)
DIMENSION   X1(275),X2(275),X3(275)
DIMENSION   B1(275),T1(275),B2(275),T2(275),B3(275),T3(275)
DIMENSION   U(275),V1(275),V2(275),V3(275)
DATA        M,MK/1,275/

IX(J,I)=(I-1)*MX+J
SC(Z)=ZS*(Z-Z1)

N1=0
N2=0
N3=0
N=L*M
DD=2.0*VD
EF=1.0-2.0*VD
EL=FLOAT(L)
EM=FLOAT(M)
TE=0.5*(EL+1.0)
ZS=(1.0-VS)/(Z2-Z1)
DUI=-(EL*US)/FLOAT(MY-1)
DUJ=(1.0-US)/FLOAT(MX-1)
DVI=VS/FLOAT(MY-1)

I0=(NY+1-M*(NY-3))/2
J0=(NX+1-L*(NX-1))/2
K0=((MK+1)*(1-N))/2
10 K=K0
I=MAX0(MIN0(I0,NY+1),0)
J=J0
EU=TE*US+DUI*FLOAT(I-1)+DUJ*FLOAT(J-1)
VE=      DVI*FLOAT(I-1)
20 IF ((I.LT.1).OR.(I.GT.NY)) GO TO 22
K=MAX0(MIN0(K+N,MK),1)
U(K)=EU
V1(K)=VE+SC(S1(IX(J,I)))
V2(K)=VE+SC(S2(IX(J,I)))
V3(K)=VE+SC(S3(IX(J,I)))
22 I=I-M
EU=EU-DUI
VE=VE-EM*DVI
IF ((I.LT.1).OR.(I.GT.NY)) GO TO 30
K=MAX0(MIN0(K+N,MK),1)
U(K)=EU
```
```      V1(K)=VE+SC(S1(IX(J,I)))
V2(K)=VE+SC(S2(IX(J,I)))
V3(K)=VE+SC(S3(IX(J,I)))
J=J+L
EU=EU+EL*DUJ
IF ((J.GE.1).AND.(J.LE.NX)) GO TO 20

30 IF (L.GT.0) GO TO 32
NK=MK-K+1
DO 31 KK=1,NK
II=K+KK-1
U(KK)=U(II)
V1(KK)=V1(II)
V2(KK)=V2(II)
V3(KK)=V3(II)
31 II=II+1
K=NK

32 CALL VISRB (G1,H1,NG1,MK,U,V1,K,U,V2,K,1.0)
CALL VISRB (U3,F3,NU3,MK,G1,H1,NG1,U,V3,K,1.0)
CALL VISRB (G1,H1,NG1,MK,U,V2,K,U,V3,K,-1.0)
CALL VISRB (G2,H2,NG2,MK,U,V3,K,U,V1,K,-1.0)
CALL VISRB (G3,H3,NG3,MK,U,V1,K,U,V2,K,-1.0)
CALL VISRB (U1,F1,NU1,MK,G1,H1,NG1,G2,H2,NG2,1.0)
CALL VISRB (U2,F2,NU2,MK,U1,F1,NU1,G3,H3,NG3,1.0)
CALL VISRB (U1,F1,NU1,MK,G3,H3,NG3,U,V3,K,-1.0)

IF (IS.LT.0) GO TO 40
DO 36 KK=1,NU1
36 F1(KK)=EF*F1(KK)
DO 37 KK=1,NU2
37 F2(KK)=EF*F2(KK)+VD
DO 38 KK=1,NU3
38 F3(KK)=EF*F3(KK)+DD

40 CALL VISRB (G1,H1,NG1,MK,U1,F1,NU1,X2,B2,N2,-1.0)
CALL VISHH (X1,B1,T1,N1,G1,H1,NG1, 1,PL)
CALL VISRB (G1,H1,NG1,MK,U2,F2,NU2,X1,T1,N1, 1.0)
CALL VISRB (G2,H2,NG2,MK,G1,H1,NG1,X3,B3,N3,-1.0)
CALL VISHH (X2,B2,T2,N2,G2,H2,NG2,-1,PL)
CALL VISRB (G1,H1,NG1,MK,U3,F3,NU3,X2,T2,N2, 1.0)
CALL VISHH (X3,B3,T3,N3,G1,H1,NG1, 1,PL)

I0=I0+M
IF ((I0.GE.0).AND.(I0.LE.NY+1)) GO TO 10
J0=J0+L
IF ((J0.GE.1).AND.(J0.LE.NX))   GO TO 10
RETURN
END
```
```      SUBROUTINE  VISTS (Z1,ZE,Z2,N,M,PL)

C     [TRIANGULAR SEQUENCE]
C     ZE(M,M)  ARRAY OF VALUES
C     Z1,Z2    RANGE OF VALUES
C     N        ACTUAL  LENGTH OF COLUMN
C     M        MAXIMUM LENGTH OF COLUMN
C     PL       PEN MOVEMENT SUBROUTINE, PERHAPS PLTCA
C     [11-MAY-75]

EXTERNAL    PL
DIMENSION   ZE(1),U(501),V(501)

IX(J,I)=(I-1)*M+J
AM(J,I)=ZS*(ZE(IX(J,I))-Z1)

MK=501
HZ=0.35
ZS=(2.0*HZ)/(Z2-Z1)
DU=1.0/FLOAT(N-1)
DV=0.3/FLOAT(N-1)
HU=0.5*DU
VE=0.0
L=N-1
DO 30 I=1,L
K=0
EU=HU*FLOAT(I-1)
DO 10 J=I,N
K=MIN0(K+1,MK)
U(K)=EU
V(K)=VE+AM(J,I)
10 EU=EU+DU
CALL VISHO (U,V,K,1,PL)
K=0
EU=HU*FLOAT(I-1)
DO 20 J=I,L
K=MIN0(K+1,MK)
U(K)=EU
V(K)=VE+AM(J,I)
K=MIN0(K+1,MK)
U(K)=EU+HU
V(K)=VE+DV+AM(J+1,I+1)
20 EU=EU+DU
K=MIN0(K+1,MK)
U(K)=EU
V(K)=VE+AM(N,I)
CALL VISHO (U,V,K,-1,PL)
30 VE=VE+DV
RETURN
END

```