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SUBROUTINE KURV1S (N,X,Y,SLOP1,SLOPN,XP,YP,TEMP,S,SIGMA,ISLPSW)
C
C
C +-----------------------------------------------------------------+
C | |
C | Copyright (C) 1986 by UCAR |
C | University Corporation for Atmospheric Research |
C | All Rights Reserved |
C | |
C | NCARGRAPHICS Version 1.00 |
C | |
C +-----------------------------------------------------------------+
C
C
C
C DIMENSION OF X(N),Y(N),XP(N),YP(N),TEMP(N)
C ARGUMENTS
C
C LATEST REVISION FEBRUARY 5, 1974
C
C PURPOSE KURV1S DETERMINES THE PARAMETERS NECESSARY TO
C COMPUTE A SPLINE UNDER TENSION PASSING THROUGH
C A SEQUENCE OF PAIRS
C (X(1),Y(1)),...,(X(N),Y(N)) IN THE PLANE.
C THE SLOPES AT THE TWO ENDS OF THE CURVE MAY BE
C SPECIFIED OR OMITTED. FOR ACTUAL COMPUTATION
C OF POINTS ON THE CURVE IT IS NECESSARY TO CALL
C THE SUBROUTINE KURV2S.
C
C USAGE CALL KURV1S(N,X,Y,SLP1,SLPN,XP,YP,TEMP,S,SIGMA)
C
C ARGUMENTS
C
C ON INPUT N
C IS THE NUMBER OF POINTS TO BE INTERPOLATED
C (N .GE. 2).
C
C X
C IS AN ARRAY CONTAINING THE N X-COORDINATES
C OF THE POINTS.
C
C Y
C IS AN ARRAY CONTAINING THE N Y-COORDINATES
C OF THE POINTS.
C
C SLOP1 AND SLOPN
C CONTAIN THE DESIRED VALUES FOR THE SLOPE OF
C THE CURVE AT (X(1),Y(1)) AND (X(N),Y(N)),
C RESPECTIVELY. THESE QUANTITIES ARE IN
C DEGREES AND MEASURED COUNTER-CLOCKWISE
C FROM THE POSITIVE X-AXIS. IF ISLPSW IS NON-
C ZERO, ONE OR BOTH OF SLP1 AND SLPN MAY BE
C DETERMINED INTERNALLY BY KURV1S.
C
C XP AND YP
C ARE ARRAYS OF LENGTH AT LEAST N.
C
C TEMP
C IS AN ARRAY OF LENGTH AT LEAST N WHICH IS
C USED FOR SCRATCH STORAGE.
C
C SIGMA
C CONTAINS THE TENSION FACTOR. THIS IS
C NON-ZERO AND INDICATES THE CURVINESS DESIRED.
C IF ABS(SIGMA) IS VERY LARGE (E.G., 50.) THE
C RESULTING CURVE IS VERY NEARLY A POLYGONAL
C LINE. A STANDARD VALUE FOR SIGMA IS ABOUT 2.
C
C ISLPSW
C IS AN INTEGER INDICATING WHICH END SLOPES
C HAVE BEEN USER PROVIDED AND WHICH MUST BE
C COMPUTED BY KURV1S. FOR ISLPSW
C = 0 INDICATES BOTH SLOPES ARE PROVIDED,
C = 1 ONLY SLOP1 IS PROVIDED,
C = 2 ONLY SLOPN IS PROVIDED,
C = 3 NEITHER SLOP1 NOR SLOPN IS PROVIDED.
C = 4 NEITHER SLOP1 NOR SLOPN IS PROVIDED,
C BUT SLOP1=SLOPN. IN THIS CASE X(1)=
C X(N), Y(1)=Y(N) AND N.GE.3.
C ON OUTPUT XP AND YP
C CONTAIN INFORMATION ABOUT THE CURVATURE OF
C THE CURVE AT THE GIVEN NODES.
C
C S
C CONTAINS THE POLYGONAL ARCLENGTH OF THE
C CURVE.
C
C N, X, Y, SLP1, SLPN, SIGMA AND ISLPSW ARE
C UNCHANGED.
C
C ENTRY POINTS KURV1S
C
C SPECIAL CONDITIONS NONE
C
C COMMON BLOCKS NONE
C
C I/O NONE
C
C PRECISION SINGLE
C
C REQUIRED ULIB NONE
C ROUTINES
C
C SPECIALIST RUSSELL K. REW, NCAR, BOULDER, COLORADO 80302
C
C LANGUAGE FORTRAN
C
C HISTORY ORIGINALLY WRITTEN BY A. K. CLINE, MARCH 1972.
C
C
C
C
INTEGER N
REAL X(N) ,Y(N) ,XP(N) ,YP(N) ,
1 TEMP(N) ,S ,SIGMA
SAVE
C
DATA PI /3.1415926535897932/
C
NN = N
JSLPSW = ISLPSW
SLP1 = SLOP1
SLPN = SLOPN
DEGRAD = PI/180.
NM1 = NN-1
NP1 = NN+1
DELX1 = X(2)-X(1)
DELY1 = Y(2)-Y(1)
DELS1 = SQRT(DELX1*DELX1+DELY1*DELY1)
DX1 = DELX1/DELS1
DY1 = DELY1/DELS1
C
C DETERMINE SLOPES IF NECESSARY
C
IF (JSLPSW .NE. 0) GO TO 70
10 SLPP1 = SLP1*DEGRAD
SLPPN = SLPN*DEGRAD
C
C SET UP RIGHT HAND SIDES OF TRIDIAGONAL LINEAR SYSTEM FOR XP
C AND YP
C
XP(1) = DX1-COS(SLPP1)
YP(1) = DY1-SIN(SLPP1)
TEMP(1) = DELS1
SS = DELS1
IF (NN .EQ. 2) GO TO 30
DO 20 I=2,NM1
DELX2 = X(I+1)-X(I)
DELY2 = Y(I+1)-Y(I)
DELS2 = SQRT(DELX2*DELX2+DELY2*DELY2)
DX2 = DELX2/DELS2
DY2 = DELY2/DELS2
XP(I) = DX2-DX1
YP(I) = DY2-DY1
TEMP(I) = DELS2
DELX1 = DELX2
DELY1 = DELY2
DELS1 = DELS2
DX1 = DX2
DY1 = DY2
C
C ACCUMULATE POLYGONAL ARCLENGTH
C
SS = SS+DELS1
20 CONTINUE
30 XP(NN) = COS(SLPPN)-DX1
YP(NN) = SIN(SLPPN)-DY1
C
C DENORMALIZE TENSION FACTOR
C
SIGMAP = ABS(SIGMA)*FLOAT(NN-1)/SS
C
C PERFORM FORWARD ELIMINATION ON TRIDIAGONAL SYSTEM
C
S = SS
DELS = SIGMAP*TEMP(1)
EXPS = EXP(DELS)
SINHS = .5*(EXPS-1./EXPS)
SINHIN = 1./(TEMP(1)*SINHS)
DIAG1 = SINHIN*(DELS*.5*(EXPS+1./EXPS)-SINHS)
DIAGIN = 1./DIAG1
XP(1) = DIAGIN*XP(1)
YP(1) = DIAGIN*YP(1)
SPDIAG = SINHIN*(SINHS-DELS)
TEMP(1) = DIAGIN*SPDIAG
IF (NN .EQ. 2) GO TO 50
DO 40 I=2,NM1
DELS = SIGMAP*TEMP(I)
EXPS = EXP(DELS)
SINHS = .5*(EXPS-1./EXPS)
SINHIN = 1./(TEMP(I)*SINHS)
DIAG2 = SINHIN*(DELS*(.5*(EXPS+1./EXPS))-SINHS)
DIAGIN = 1./(DIAG1+DIAG2-SPDIAG*TEMP(I-1))
XP(I) = DIAGIN*(XP(I)-SPDIAG*XP(I-1))
YP(I) = DIAGIN*(YP(I)-SPDIAG*YP(I-1))
SPDIAG = SINHIN*(SINHS-DELS)
TEMP(I) = DIAGIN*SPDIAG
DIAG1 = DIAG2
40 CONTINUE
50 DIAGIN = 1./(DIAG1-SPDIAG*TEMP(NM1))
XP(NN) = DIAGIN*(XP(NN)-SPDIAG*XP(NM1))
YP(NN) = DIAGIN*(YP(NN)-SPDIAG*YP(NM1))
C
C PERFORM BACK SUBSTITUTION
C
DO 60 I=2,NN
IBAK = NP1-I
XP(IBAK) = XP(IBAK)-TEMP(IBAK)*XP(IBAK+1)
YP(IBAK) = YP(IBAK)-TEMP(IBAK)*YP(IBAK+1)
60 CONTINUE
RETURN
70 IF (NN .EQ. 2) GO TO 100
C
C IF NO SLOPES ARE GIVEN, USE SECOND ORDER INTERPOLATION ON
C INPUT DATA FOR SLOPES AT ENDPOINTS
C
IF (JSLPSW .EQ. 4) GO TO 90
IF (JSLPSW .EQ. 2) GO TO 80
DELNM1 = SQRT((X(NN-2)-X(NM1))**2+(Y(NN-2)-Y(NM1))**2)
DELN = SQRT((X(NM1)-X(NN))**2+(Y(NM1)-Y(NN))**2)
DELNN = DELNM1+DELN
C1 = (DELNN+DELN)/DELNN/DELN
C2 = -DELNN/DELN/DELNM1
C3 = DELN/DELNN/DELNM1
SX = C3*X(NN-2)+C2*X(NM1)+C1*X(NN)
SY = C3*Y(NN-2)+C2*Y(NM1)+C1*Y(NN)
C
SLPN = ATAN2(SY,SX)/DEGRAD
80 IF (JSLPSW .EQ. 1) GO TO 10
DELS2 = SQRT((X(3)-X(2))**2+(Y(3)-Y(2))**2)
DELS12 = DELS1+DELS2
C1 = -(DELS12+DELS1)/DELS12/DELS1
C2 = DELS12/DELS1/DELS2
C3 = -DELS1/DELS12/DELS2
SX = C1*X(1)+C2*X(2)+C3*X(3)
SY = C1*Y(1)+C2*Y(2)+C3*Y(3)
C
SLP1 = ATAN2(SY,SX)/DEGRAD
GO TO 10
90 DELN = SQRT((X(NM1)-X(NN))**2+(Y(NM1)-Y(NN))**2)
DELNN = DELS1+DELN
C1 = -DELS1/DELN/DELNN
C2 = (DELS1-DELN)/DELS1/DELN
C3 = DELN/DELNN/DELS1
SX = C1*X(NM1)+C2*X(1)+C3*X(2)
SY = C1*Y(NM1)+C2*Y(1)+C3*Y(2)
IF (SX.EQ.0. .AND. SY.EQ.0.) SX = 1.
SLP1 = ATAN2(SY,SX)/DEGRAD
SLPN = SLP1
GO TO 10
C
C IF ONLY TWO POINTS AND NO SLOPES ARE GIVEN, USE STRAIGHT
C LINE SEGMENT FOR CURVE
C
100 IF (JSLPSW .NE. 3) GO TO 110
XP(1) = 0.
XP(2) = 0.
YP(1) = 0.
YP(2) = 0.
C
SLP1 = ATAN2(Y(2)-Y(1),X(2)-X(1))/DEGRAD
SLPN = SLP1
RETURN
C
110 IF (JSLPSW .EQ. 2)
1 SLP1 = ATAN2(Y(2)-Y(1)-SLPN*(X(2)-X(1)),
2 X(2)-X(1)-SLPN*(Y(2)-Y(1)))/DEGRAD
C
IF (JSLPSW .EQ. 1)
1 SLPN = ATAN2(Y(2)-Y(1)-SLP1*(X(2)-X(1)),
2 X(2)-X(1)-SLP1*(Y(2)-Y(1)))/DEGRAD
GO TO 10
END
SUBROUTINE KURV2S (T,XS,YS,N,X,Y,XP,YP,S,SIGMA,NSLPSW,SLP)
C
C
C
C DIMENSION OF X(N),Y(N),XP(N),YP(N)
C ARGUMENTS
C
C LATEST REVISION OCTOBER 22, 1973
C
C PURPOSE KURV2S PERFORMS THE MAPPING OF POINTS IN THE
C INTERVAL (0.,1.) ONTO A CURVE IN THE PLANE.
C THE SUBROUTINE KURV1S SHOULD BE CALLED EARLIER
C TO DETERMINE CERTAIN NECESSARY PARAMETERS.
C THE RESULTING CURVE HAS A PARAMETRIC
C REPRESENTATION BOTH OF WHOSE COMPONENTS ARE
C SPLINES UNDER TENSION AND FUNCTIONS OF THE
C POLYGONAL ARCLENGTH PARAMETER.
C
C ACCESS CARDS *FORTRAN,S=ULIB,N=KURV
C *COSY
C
C USAGE CALL KURV2S (T,XS,YS,N,X,Y,XP,YP,S,SIGMA)
C
C ARGUMENTS
C
C ON INPUT T
C CONTAINS A REAL VALUE OF ABSOLUTE VALUE LESS
C THAN OR EQUAL TO 1. TO BE MAPPED TO A POINT
C ON THE CURVE. THE SIGN OF T IS IGNORED AND
C THE INTERVAL (0.,1.) IS MAPPED ONTO THE
C ENTIRE CURVE. IF T IS NEGATIVE, THIS
C INDICATES THAT THE SUBROUTINE HAS BEEN CALLED
C PREVIOUSLY (WITH ALL OTHER INPUT VARIABLES
C UNALTERED) AND THAT THIS VALUE OF T EXCEEDS
C THE PREVIOUS VALUE IN ABSOLUTE VALUE. WITH
C SUCH INFORMATION THE SUBROUTINE IS ABLE TO
C MAP THE POINT MUCH MORE RAPIDLY. THUS IF THE
C USER SEEKS TO MAP A SEQUENCE OF POINTS ONTO
C THE SAME CURVE, EFFICIENCY IS GAINED BY
C ORDERING THE VALUES INCREASING IN MAGNITUDE
C AND SETTING THE SIGNS OF ALL BUT THE FIRST
C NEGATIVE.
C
C N
C CONTAINS THE NUMBER OF POINTS WHICH WERE
C INTERPOLATED TO DETERMINE THE CURVE.
C
C X AND Y
C ARRAYS CONTAINING THE X- AND Y-COORDINATES
C OF THE INTERPOLATED POINTS.
C
C XP AND YP
C ARE THE ARRAYS OUTPUT FROM KURV1 CONTAINING
C CURVATURE INFORMATION.
C
C S
C CONTAINS THE POLYGONAL ARCLENGTH OF THE
C CURVE.
C
C SIGMA
C CONTAINS THE TENSION FACTOR (ITS SIGN IS
C IGNORED).
C
C NSLPSW
C IS AN INTEGER SWITCH WHICH TURNS ON OR OFF
C THE CALCULATION OF SLP
C NSLPSW
C = 0 INDICATES THAT SLP WILL NOT BE
C CALCULATED
C = 1 SLP WILL BE CALCULATED
C
C THE PARAMETERS N, X, Y, XP, YP, S AND SIGMA
C SHOULD BE INPUT UNALTERED FROM THE OUTPUT OF
C KURV1S.
C
C ON OUTPUT XS AND YS
C CONTAIN THE X- AND Y-COORDINATES OF THE IMAGE
C POINT ON THE CURVE.
C
C SLP
C CONTAINS THE SLOPE OF THE CURVE IN DEGREES AT
C THIS POINT.
C
C T, N, X, Y, XP, YP, S AND SIGMA ARE UNALTERED.
C
C ENTRY POINTS KURV2S
C
C SPECIAL CONDITIONS NONE
C
C COMMON BLOCKS NONE
C
C I/O NONE
C
C PRECISION SINGLE
C
C REQUIRED ULIB NONE
C ROUTINES
C
C SPECIALIST RUSSELL K. REW, NCAR, BOULDER, COLORADO 80302
C
C LANGUAGE FORTRAN
C
C HISTORY ORIGINALLY WRITTEN BY A. K. CLINE, MARCH 1972.
C
C
C
C
INTEGER N
REAL T ,XS ,YS ,X(N) ,
1 Y(N) ,XP(N) ,YP(N) ,S ,
2 SIGMA ,SLP
SAVE
C
DATA PI /3.1415926535897932/
C
C
C DENORMALIZE SIGMA
C
SIGMAP = ABS(SIGMA)*FLOAT(N-1)/S
C
C STRETCH UNIT INTERVAL INTO ARCLENGTH DISTANCE
C
TN = ABS(T*S)
C
C FOR NEGATIVE T START SEARCH WHERE PREVIOUSLY TERMINATED,
C OTHERWISE START FROM BEGINNING
C
IF (T .LT. 0.) GO TO 10
DEGRAD = PI/180.
I1 = 2
XS = X(1)
YS = Y(1)
SUM = 0.
IF (T .LT. 0.) RETURN
C
C DETERMINE INTO WHICH SEGMENT TN IS MAPPED
C
10 DO 30 I=I1,N
DELX = X(I)-X(I-1)
DELY = Y(I)-Y(I-1)
DELS = SQRT(DELX*DELX+DELY*DELY)
IF (SUM+DELS-TN) 20,40,40
20 SUM = SUM+DELS
30 CONTINUE
C
C IF ABS(T) IS GREATER THAN 1., RETURN TERMINAL POINT ON
C CURVE
C
XS = X(N)
YS = Y(N)
RETURN
C
C SET UP AND PERFORM INTERPOLATION
C
40 DEL1 = TN-SUM
DEL2 = DELS-DEL1
EXPS1 = EXP(SIGMAP*DEL1)
SINHD1 = .5*(EXPS1-1./EXPS1)
EXPS2 = EXP(SIGMAP*DEL2)
SINHD2 = .5*(EXPS2-1./EXPS2)
EXPS = EXPS1*EXPS2
SINHS = .5*(EXPS-1./EXPS)
XS = (XP(I)*SINHD1+XP(I-1)*SINHD2)/SINHS+
1 ((X(I)-XP(I))*DEL1+(X(I-1)-XP(I-1))*DEL2)/DELS
YS = (YP(I)*SINHD1+YP(I-1)*SINHD2)/SINHS+
1 ((Y(I)-YP(I))*DEL1+(Y(I-1)-YP(I-1))*DEL2)/DELS
I1 = I
IF (NSLPSW .EQ. 0) RETURN
COSHD1 = .5*(EXPS1+1./EXPS1)*SIGMAP
COSHD2 = .5*(EXPS2+1./EXPS2)*SIGMAP
XT = (XP(I)*COSHD1-XP(I-1)*COSHD2)/SINHS+
1 ((X(I)-XP(I))-(X(I-1)-XP(I-1)))/DELS
YT = (YP(I)*COSHD1-YP(I-1)*COSHD2)/SINHS+
1 ((Y(I)-YP(I))-(Y(I-1)-YP(I-1)))/DELS
SLP = ATAN2(YT,XT)/DEGRAD
RETURN
END
|
