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|
C***********************************************************************
C Module: mousexy.f
C
C Copyright (C) 2012 Harold Youngren, Mark Drela
C
C This program is free software; you can redistribute it and/or modify
C it under the terms of the GNU General Public License as published by
C the Free Software Foundation; either version 2 of the License, or
C (at your option) any later version.
C
C This program is distributed in the hope that it will be useful,
C but WITHOUT ANY WARRANTY; without even the implied warranty of
C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
C GNU General Public License for more details.
C
C You should have received a copy of the GNU General Public License
C along with this program; if not, write to the Free Software
C Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
C
C Report problems to: guppy@maine.com
C or drela@mit.edu
C***********************************************************************
program mousexy
c---------------------------------------------------------------
c Interactive mouse and continuous cursor input test program.
c
c Lets user specify points in a spline, then allows the user to
c drag spline points around to change the curve.
c---------------------------------------------------------------
c
parameter (ipx=100)
c
character*1 cin
c
common /Rpoints/
& ch,
& x1(ipx), y1(ipx), s1(ipx), xp1(ipx), yp1(ipx),
& x2(ipx), y2(ipx), s2(ipx), xp2(ipx), yp2(ipx)
common /Ipoints/
& iparam, iplt, n1, n2
logical lok
c
ch = 0.13
n1 = 0
n2 = 0
iplt = 0
C--- iparam controls interpolation abscissa (0 for x, 1 for s)
iparam = 1
c
1000 format(a)
C
C---Initialize the plot package before we get into plotting...
CALL PLINITIALIZE
C---put up plot window and refresh
call pltall('Enter points',
& '(terminate with q or double point)',' ')
c
ccc call NEWFACTOR(6.0)
c
5 write(*,1050)
1050 format(/' Enter points for spline (q or ret to end)',' ',' ')
C--- Get initial set of points from user
call NEWCOLORNAME('green')
call NEWPEN(1)
C
xlast = -999.
ylast = -999.
ii = 0
do j = 1, 100
call GETCURSORXY(xx,yy,ikey)
cin = char(ikey)
if(cin.EQ.'q' .OR. cin.EQ.'Q') go to 20
C--- check for doubled point to end input
if( (xx-xlast).EQ.0.0 .AND.
& (yy-ylast).EQ.0.0 ) go to 20
ii = ii + 1
x1(ii) = xx
y1(ii) = yy
if(ii.EQ.1) then
call plot(xx,yy,3)
CALL PLSYMB(999.,999.,0.4*CH,2,0.0,0)
else
call plot(xlast,ylast,3)
call plot(xx,yy,2)
CALL PLSYMB(999.,999.,0.4*CH,2,0.0,0)
endif
call PLFLUSH
xlast = xx
ylast = yy
end do
C
20 n1 = ii
c
C--- Sort points by x coordinate to get monotonic array
call sort(n1,x1,y1)
C
call plend
C
C--- initialize modified point arrays
100 do j = 1, n1
x2(j) = x1(j)
y2(j) = y1(j)
end do
n2 = n1
200 call pltall('Select point to modify',
& 'Options are "a" for add, "d" to delete',
& '"x" or "s" for abscissa, "i" to reset')
c
write(*,*)
write(*,*) 'Move spline points...'
C
call GETCURSORXY(xx,yy,ikey)
cc call NEWCOLORNAME('green')
cc call plot(xx,yy,3)
cc CALL PLSYMB(999.,999.,0.4*CH,2,0.0,0)
cin = char(ikey)
write(*,*) 'ikey cin ',ikey,cin
if(cin.EQ.'q' .OR. cin.EQ.'Q') go to 400
C--- reset modified point arrays
if(cin.EQ.'i' .OR. cin.EQ.'I') then
write(*,*) 're-initializing points...'
go to 100
endif
C--- switch interpolation to x
if(cin.EQ.'x' .OR. cin.EQ.'X') then
write(*,*) 'interpolating in x...'
iparam = 0
go to 200
endif
C--- switch interpolation to s
if(cin.EQ.'s' .OR. cin.EQ.'S') then
write(*,*) 'interpolating in s...'
iparam = 1
go to 200
endif
C--- sort points by x coordinate to get monotonic array
if(cin.EQ.'r' .OR. cin.EQ.'R') then
write(*,*) 'sorting points in x...'
call sort(n1,x1,y1)
call sort(n2,x2,y2)
go to 200
endif
C
C--- find closest point to cursor
jp = 0
dsqmin = 999.
do j = 1, n2
dsq = (xx-x2(j))**2 + (yy-y2(j))**2
if(dsq.LT.dsqmin) then
dsqmin = dsq
jp = j
endif
end do
C
C--- add point to arrays at cursor position
if(cin.EQ.'a' .OR. cin.EQ.'A') then
write(*,*) 'adding point at cursor...'
if(iparam.EQ.1) then
C--- find position in s
call scalc(x2,y2,s2,n2)
call splind(x2,xp2,s2,n2,-999.,-999.)
call splind(y2,yp2,s2,n2,-999.,-999.)
call NEARPT(xx,yy,SNEAR,X2,XP2,Y2,YP2,S2,N2)
ja = 0
do j = 2, n2
if(SNEAR.GT.s2(j-1) .AND. SNEAR.LT.s2(j)) ja = j
end do
else
C--- find position in x
ja = 0
do j=2,n2
if(xx.GT.x2(j-1) .AND. xx.LT.x2(j)) ja = j
end do
if(xx.LT.x2(1)) ja =1
if(xx.GT.x2(n2)) ja = n2+1
endif
C--- shift array and add point
if(ja.NE.0) then
do j=n2,ja,-1
x2(j+1) = x2(j)
y2(j+1) = y2(j)
end do
x2(ja) = xx
y2(ja) = yy
n2 = n2+1
endif
go to 200
endif
C
C--- delete point at cursor position
if(cin.EQ.'d' .OR. cin.EQ.'D') then
write(*,*) 'deleting point at cursor...'
if(jp.EQ.n2) then
n2 = n2-1
else
do j=jp+1,n2
x2(j-1) = x2(j)
y2(j-1) = y2(j)
end do
n2 = n2-1
endif
go to 200
endif
c
if((index('abcdefghijklmnopqrstuvwxyz',cin).NE.0) .OR.
& (index('ABCDEFGHIJKLMNOPQRSTUVWXYZ',cin).NE.0) .OR.
& (index('0123456789',cin).NE.0)) go to 200
c
write(*,*) 'Cursor at x,y ',xx,yy
write(*,*) 'Point ',jp,' selected at x,y ',x1(jp),y1(jp)
C--- now read cursor and move point
300 call pltall('Move point...',' ',' ')
call GETCURSORXYC(xx,yy,ibtn)
write(*,*) xx,yy,ibtn
if(ibtn.eq.0) go to 200
x2(jp) = xx
y2(jp) = yy
go to 300
c
400 continue
ccc pause
stop
end
subroutine pltall(msg1,msg2,msg3)
C--- Graphics refresh routine for curve modification
C Resplines original (x1,y1,n1) and modified (x2,y2,n2) curves
C and plots the splines with symbols at the curve points
C
C Curves are splined vs "s" or vs "x", determined by iparam = 1 or 0
C
character*(*) msg1, msg2, msg3
parameter (ipx=100)
c
common /Rpoints/
& ch,
& x1(ipx), y1(ipx), s1(ipx), xp1(ipx), yp1(ipx),
& x2(ipx), y2(ipx), s2(ipx), xp2(ipx), yp2(ipx)
common /Ipoints/
& iparam, iplt, n1, n2
C
C--- (Re)Open window for plotting (clears old window)
call PLOPEN(0.8,0,1)
XMSG = 0.5
YMSG = 1.0
CALL PLCHAR(XMSG,YMSG,1.2*CH,'TEST FOR MOUSE READ',0.0,-1)
if(msg1.NE.' ') then
YMSG = YMSG - 1.3*CH
CALL PLCHAR(XMSG,YMSG,CH,msg1,0.0,-1)
endif
if(msg2.NE.' ') then
YMSG = YMSG - 1.3*CH
CALL PLCHAR(XMSG,YMSG,CH,msg2,0.0,-1)
endif
if(msg3.NE.' ') then
YMSG = YMSG - 1.3*CH
CALL PLCHAR(XMSG,YMSG,CH,msg3,0.0,-1)
endif
C
C--- re-origin
ccc call PLOT(5.5, 4.25, -3)
C--- curve #1 (original)
if(n1.GT.1) then
C--- spline input curve and plot
if(iparam.EQ.1) then
call scalc(x1,y1,s1,n1)
call splind(x1,xp1,s1,n1,-999.,-999.)
call splind(y1,yp1,s1,n1,-999.,-999.)
else
call splind(y1,yp1,x1,n1,-999.,-999.)
endif
C
call NEWCOLORNAME('blue')
call plot(x1(1),y1(1),3)
CALL PLSYMB(999.,999.,0.4*CH,1,0.0,0)
ninter = 10
dfn = 1.0/float(ninter)
do j = 1, n1-1
ds = s1(j+1) - s1(j)
dx = x1(j+1) - x1(j)
do n = 1, ninter
if(iparam.EQ.1) then
ss = s1(j) + ds*float(n)*dfn
xx = seval(ss,x1,xp1,s1,n1)
yy = seval(ss,y1,yp1,s1,n1)
else
xx = x1(j) + dx*float(n)*dfn
yy = seval(xx,y1,yp1,x1,n1)
endif
call plot(xx,yy,2)
end do
CALL PLSYMB(999.,999.,0.4*CH,1,0.0,0)
end do
endif
C--- curve #2 (modified)
if(n2.GT.1) then
C--- spline modified curve and plot
if(iparam.EQ.1) then
call scalc(x2,y2,s2,n2)
call splind(x2,xp2,s2,n2,-999.,-999.)
call splind(y2,yp2,s2,n2,-999.,-999.)
else
call splind(y2,yp2,x2,n2,-999.,-999.)
endif
C
call NEWCOLORNAME('red')
call plot(x2(1),y2(1),3)
CALL PLSYMB(999.,999.,0.4*CH,1,0.0,0)
ninter = 10
dfn = 1.0/float(ninter)
do j = 1, n2-1
ds = s2(j+1) - s2(j)
dx = x2(j+1) - x2(j)
do n = 1, ninter
if(iparam.EQ.1) then
ss = s2(j) + ds*float(n)*dfn
xx = seval(ss,x2,xp2,s2,n2)
yy = seval(ss,y2,yp2,s2,n2)
else
xx = x2(j) + dx*float(n)*dfn
yy = seval(xx,y2,yp2,x2,n2)
endif
call plot(xx,yy,2)
end do
CALL PLSYMB(999.,999.,0.4*CH,1,0.0,0)
end do
endif
call PLFLUSH
return
end
C***********************************************************************
C Module: spline.f
C
C Copyright (C) 2000 Mark Drela
C
C This program is free software; you can redistribute it and/or modify
C it under the terms of the GNU General Public License as published by
C the Free Software Foundation; either version 2 of the License, or
C (at your option) any later version.
C
C This program is distributed in the hope that it will be useful,
C but WITHOUT ANY WARRANTY; without even the implied warranty of
C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
C GNU General Public License for more details.
C
C You should have received a copy of the GNU General Public License
C along with this program; if not, write to the Free Software
C Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
C***********************************************************************
SUBROUTINE SPLINE(X,XS,S,N)
DIMENSION X(N),XS(N),S(N)
PARAMETER (NMAX=1000)
DIMENSION A(NMAX),B(NMAX),C(NMAX)
C-------------------------------------------------------
C Calculates spline coefficients for X(S). |
C Zero 2nd derivative end conditions are used. |
C To evaluate the spline at some value of S, |
C use SEVAL and/or DEVAL. |
C |
C S independent variable array (input) |
C X dependent variable array (input) |
C XS dX/dS array (calculated) |
C N number of points (input) |
C |
C-------------------------------------------------------
IF(N.GT.NMAX) STOP 'SPLINE: array overflow, increase NMAX'
C
DO 1 I=2, N-1
DSM = S(I) - S(I-1)
DSP = S(I+1) - S(I)
B(I) = DSP
A(I) = 2.0*(DSM+DSP)
C(I) = DSM
XS(I) = 3.0*((X(I+1)-X(I))*DSM/DSP + (X(I)-X(I-1))*DSP/DSM)
1 CONTINUE
C
C---- set zero second derivative end conditions
A(1) = 2.0
C(1) = 1.0
XS(1) = 3.0*(X(2)-X(1)) / (S(2)-S(1))
B(N) = 1.0
A(N) = 2.0
XS(N) = 3.0*(X(N)-X(N-1)) / (S(N)-S(N-1))
C
C---- solve for derivative array XS
CALL TRISOL(A,B,C,XS,N)
C
RETURN
END ! SPLINE
SUBROUTINE SPLIND(X,XS,S,N,XS1,XS2)
DIMENSION X(N),XS(N),S(N)
PARAMETER (NMAX=1000)
DIMENSION A(NMAX),B(NMAX),C(NMAX)
C-------------------------------------------------------
C Calculates spline coefficients for X(S). |
C Specified 1st derivative and/or usual zero 2nd |
C derivative end conditions are used. |
C To evaluate the spline at some value of S, |
C use SEVAL and/or DEVAL. |
C |
C S independent variable array (input) |
C X dependent variable array (input) |
C XS dX/dS array (calculated) |
C N number of points (input) |
C XS1,XS2 endpoint derivatives (input) |
C If = 999.0, then usual zero second |
C derivative end condition(s) are used |
C If = -999.0, then zero third |
C derivative end condition(s) are used |
C |
C-------------------------------------------------------
IF(N.GT.NMAX) STOP 'SPLIND: array overflow, increase NMAX'
C
DO 1 I=2, N-1
DSM = S(I) - S(I-1)
DSP = S(I+1) - S(I)
B(I) = DSP
A(I) = 2.0*(DSM+DSP)
C(I) = DSM
XS(I) = 3.0*((X(I+1)-X(I))*DSM/DSP + (X(I)-X(I-1))*DSP/DSM)
1 CONTINUE
C
IF(XS1.EQ.999.0) THEN
C----- set zero second derivative end condition
A(1) = 2.0
C(1) = 1.0
XS(1) = 3.0*(X(2)-X(1)) / (S(2)-S(1))
ELSE IF(XS1.EQ.-999.0) THEN
C----- set zero third derivative end condition
A(1) = 1.0
C(1) = 1.0
XS(1) = 2.0*(X(2)-X(1)) / (S(2)-S(1))
ELSE
C----- set specified first derivative end condition
A(1) = 1.0
C(1) = 0.
XS(1) = XS1
ENDIF
C
IF(XS2.EQ.999.0) THEN
B(N) = 1.0
A(N) = 2.0
XS(N) = 3.0*(X(N)-X(N-1)) / (S(N)-S(N-1))
ELSE IF(XS2.EQ.-999.0) THEN
B(N) = 1.0
A(N) = 1.0
XS(N) = 2.0*(X(N)-X(N-1)) / (S(N)-S(N-1))
ELSE
A(N) = 1.0
B(N) = 0.
XS(N) = XS2
ENDIF
C
IF(N.EQ.2 .AND. XS1.EQ.-999.0 .AND. XS2.EQ.-999.0) THEN
B(N) = 1.0
A(N) = 2.0
XS(N) = 3.0*(X(N)-X(N-1)) / (S(N)-S(N-1))
ENDIF
C
C---- solve for derivative array XS
CALL TRISOL(A,B,C,XS,N)
C
RETURN
END ! SPLIND
SUBROUTINE SPLINA(X,XS,S,N)
IMPLICIT REAL (A-H,O-Z)
DIMENSION X(N),XS(N),S(N)
LOGICAL LEND
C-------------------------------------------------------
C Calculates spline coefficients for X(S). |
C A simple averaging of adjacent segment slopes |
C is used to achieve non-oscillatory curve |
C End conditions are set by end segment slope |
C To evaluate the spline at some value of S, |
C use SEVAL and/or DEVAL. |
C |
C S independent variable array (input) |
C X dependent variable array (input) |
C XS dX/dS array (calculated) |
C N number of points (input) |
C |
C-------------------------------------------------------
C
LEND = .TRUE.
DO 1 I=1, N-1
DS = S(I+1)-S(I)
IF (DS.EQ.0.) THEN
XS(I) = XS1
LEND = .TRUE.
ELSE
DX = X(I+1)-X(I)
XS2 = DX / DS
IF (LEND) THEN
XS(I) = XS2
LEND = .FALSE.
ELSE
XS(I) = 0.5*(XS1 + XS2)
ENDIF
ENDIF
XS1 = XS2
1 CONTINUE
XS(N) = XS1
C
RETURN
END ! SPLINA
SUBROUTINE TRISOL(A,B,C,D,KK)
DIMENSION A(KK),B(KK),C(KK),D(KK)
C-----------------------------------------
C Solves KK long, tri-diagonal system |
C |
C A C D |
C B A C D |
C B A . . |
C . . C . |
C B A D |
C |
C The righthand side D is replaced by |
C the solution. A, C are destroyed. |
C-----------------------------------------
C
DO 1 K=2, KK
KM = K-1
C(KM) = C(KM) / A(KM)
D(KM) = D(KM) / A(KM)
A(K) = A(K) - B(K)*C(KM)
D(K) = D(K) - B(K)*D(KM)
1 CONTINUE
C
D(KK) = D(KK)/A(KK)
C
DO 2 K=KK-1, 1, -1
D(K) = D(K) - C(K)*D(K+1)
2 CONTINUE
C
RETURN
END ! TRISOL
FUNCTION SEVAL(SS,X,XS,S,N)
DIMENSION X(N), XS(N), S(N)
C--------------------------------------------------
C Calculates X(SS) |
C XS array must have been calculated by SPLINE |
C--------------------------------------------------
ILOW = 1
I = N
C
10 IF(I-ILOW .LE. 1) GO TO 11
C
IMID = (I+ILOW)/2
IF(SS .LT. S(IMID)) THEN
I = IMID
ELSE
ILOW = IMID
ENDIF
GO TO 10
C
11 DS = S(I) - S(I-1)
T = (SS - S(I-1)) / DS
CX1 = DS*XS(I-1) - X(I) + X(I-1)
CX2 = DS*XS(I) - X(I) + X(I-1)
SEVAL = T*X(I) + (1.0-T)*X(I-1) + (T-T*T)*((1.0-T)*CX1 - T*CX2)
RETURN
END ! SEVAL
FUNCTION DEVAL(SS,X,XS,S,N)
DIMENSION X(N), XS(N), S(N)
C--------------------------------------------------
C Calculates dX/dS(SS) |
C XS array must have been calculated by SPLINE |
C--------------------------------------------------
ILOW = 1
I = N
C
10 IF(I-ILOW .LE. 1) GO TO 11
C
IMID = (I+ILOW)/2
IF(SS .LT. S(IMID)) THEN
I = IMID
ELSE
ILOW = IMID
ENDIF
GO TO 10
C
11 DS = S(I) - S(I-1)
T = (SS - S(I-1)) / DS
CX1 = DS*XS(I-1) - X(I) + X(I-1)
CX2 = DS*XS(I) - X(I) + X(I-1)
DEVAL = X(I) - X(I-1) + (1.-4.0*T+3.0*T*T)*CX1 + T*(3.0*T-2.)*CX2
DEVAL = DEVAL/DS
RETURN
END ! DEVAL
FUNCTION D2VAL(SS,X,XS,S,N)
DIMENSION X(N), XS(N), S(N)
C--------------------------------------------------
C Calculates d2X/dS2(SS) |
C XS array must have been calculated by SPLINE |
C--------------------------------------------------
ILOW = 1
I = N
C
10 IF(I-ILOW .LE. 1) GO TO 11
C
IMID = (I+ILOW)/2
IF(SS .LT. S(IMID)) THEN
I = IMID
ELSE
ILOW = IMID
ENDIF
GO TO 10
C
11 DS = S(I) - S(I-1)
T = (SS - S(I-1)) / DS
CX1 = DS*XS(I-1) - X(I) + X(I-1)
CX2 = DS*XS(I) - X(I) + X(I-1)
D2VAL = (6.*T-4.)*CX1 + (6.*T-2.0)*CX2
D2VAL = D2VAL/DS**2
RETURN
END ! D2VAL
FUNCTION CURV(SS,X,XS,Y,YS,S,N)
DIMENSION X(N), XS(N), Y(N), YS(N), S(N)
C-----------------------------------------------
C Calculates curvature of splined 2-D curve |
C at S = SS |
C |
C S arc length array of curve |
C X, Y coordinate arrays of curve |
C XS,YS derivative arrays |
C (calculated earlier by SPLINE) |
C-----------------------------------------------
C
ILOW = 1
I = N
C
10 IF(I-ILOW .LE. 1) GO TO 11
C
IMID = (I+ILOW)/2
IF(SS .LT. S(IMID)) THEN
I = IMID
ELSE
ILOW = IMID
ENDIF
GO TO 10
C
11 DS = S(I) - S(I-1)
T = (SS - S(I-1)) / DS
C
CX1 = DS*XS(I-1) - X(I) + X(I-1)
CX2 = DS*XS(I) - X(I) + X(I-1)
XD = X(I) - X(I-1) + (1.0-4.0*T+3.0*T*T)*CX1 + T*(3.0*T-2.0)*CX2
XDD = (6.0*T-4.0)*CX1 + (6.0*T-2.0)*CX2
C
CY1 = DS*YS(I-1) - Y(I) + Y(I-1)
CY2 = DS*YS(I) - Y(I) + Y(I-1)
YD = Y(I) - Y(I-1) + (1.0-4.0*T+3.0*T*T)*CY1 + T*(3.0*T-2.0)*CY2
YDD = (6.0*T-4.0)*CY1 + (6.0*T-2.0)*CY2
C
SD = SQRT(XD*XD + YD*YD)
SD = MAX(SD,0.001*DS)
C
CURV = (XD*YDD - YD*XDD) / SD**3
C
RETURN
END ! CURV
FUNCTION CURVS(SS,X,XS,Y,YS,S,N)
DIMENSION X(N), XS(N), Y(N), YS(N), S(N)
C-----------------------------------------------
C Calculates curvature derivative of |
C splined 2-D curve at S = SS |
C |
C S arc length array of curve |
C X, Y coordinate arrays of curve |
C XS,YS derivative arrays |
C (calculated earlier by SPLINE) |
C-----------------------------------------------
C
ILOW = 1
I = N
C
10 IF(I-ILOW .LE. 1) GO TO 11
C
IMID = (I+ILOW)/2
IF(SS .LT. S(IMID)) THEN
I = IMID
ELSE
ILOW = IMID
ENDIF
GO TO 10
C
11 DS = S(I) - S(I-1)
T = (SS - S(I-1)) / DS
C
CX1 = DS*XS(I-1) - X(I) + X(I-1)
CX2 = DS*XS(I) - X(I) + X(I-1)
XD = X(I) - X(I-1) + (1.0-4.0*T+3.0*T*T)*CX1 + T*(3.0*T-2.0)*CX2
XDD = (6.0*T-4.0)*CX1 + (6.0*T-2.0)*CX2
XDDD = 6.0*CX1 + 6.0*CX2
C
CY1 = DS*YS(I-1) - Y(I) + Y(I-1)
CY2 = DS*YS(I) - Y(I) + Y(I-1)
YD = Y(I) - Y(I-1) + (1.0-4.0*T+3.0*T*T)*CY1 + T*(3.0*T-2.0)*CY2
YDD = (6.0*T-4.0)*CY1 + (6.0*T-2.0)*CY2
YDDD = 6.0*CY1 + 6.0*CY2
C
SD = SQRT(XD*XD + YD*YD)
SD = MAX(SD,0.001*DS)
C
BOT = SD**3
DBOTDT = 3.0*SD*(XD*XDD + YD*YDD)
C
TOP = XD*YDD - YD*XDD
DTOPDT = XD*YDDD - YD*XDDD
C
CURVS = (DTOPDT*BOT - DBOTDT*TOP) / BOT**2
C
RETURN
END ! CURVS
SUBROUTINE SINVRT(SI,XI,X,XS,S,N)
DIMENSION X(N), XS(N), S(N)
C-------------------------------------------------------
C Calculates the "inverse" spline function S(X). |
C Since S(X) can be multi-valued or not defined, |
C this is not a "black-box" routine. The calling |
C program must pass via SI a sufficiently good |
C initial guess for S(XI). |
C |
C XI specified X value (input) |
C SI calculated S(XI) value (input,output) |
C X,XS,S usual spline arrays (input) |
C |
C-------------------------------------------------------
C
SISAV = SI
C
DO 10 ITER=1, 10
RES = SEVAL(SI,X,XS,S,N) - XI
RESP = DEVAL(SI,X,XS,S,N)
DS = -RES/RESP
SI = SI + DS
IF(ABS(DS/(S(N)-S(1))) .LT. 1.0E-5) RETURN
10 CONTINUE
WRITE(*,*)
& 'SINVRT: spline inversion failed. Input value returned.'
SI = SISAV
C
RETURN
END ! SINVRT
SUBROUTINE SCALC(X,Y,S,N)
DIMENSION X(N), Y(N), S(N)
C----------------------------------------
C Calculates the arc length array S |
C for a 2-D array of points (X,Y). |
C----------------------------------------
C
S(1) = 0.
DO 10 I=2, N
S(I) = S(I-1) + SQRT((X(I)-X(I-1))**2 + (Y(I)-Y(I-1))**2)
10 CONTINUE
C
RETURN
END ! SCALC
SUBROUTINE SPLNXY(X,XS,Y,YS,S,N)
DIMENSION X(N), XS(N), Y(N), YS(N), S(N)
C-----------------------------------------
C Splines 2-D shape X(S), Y(S), along |
C with true arc length parameter S. |
C-----------------------------------------
PARAMETER (KMAX=32)
DIMENSION XT(0:KMAX), YT(0:KMAX)
C
KK = KMAX
NPASS = 10
C
C---- set first estimate of arc length parameter
CALL SCALC(X,Y,S,N)
C
C---- spline X(S) and Y(S)
CALL SEGSPL(X,XS,S,N)
CALL SEGSPL(Y,YS,S,N)
C
C---- re-integrate true arc length
DO 100 IPASS=1, NPASS
C
SERR = 0.
C
DS = S(2) - S(1)
DO I = 2, N
DX = X(I) - X(I-1)
DY = Y(I) - Y(I-1)
C
CX1 = DS*XS(I-1) - DX
CX2 = DS*XS(I ) - DX
CY1 = DS*YS(I-1) - DY
CY2 = DS*YS(I ) - DY
C
XT(0) = 0.
YT(0) = 0.
DO K=1, KK-1
T = FLOAT(K) / FLOAT(KK)
XT(K) = T*DX + (T-T*T)*((1.0-T)*CX1 - T*CX2)
YT(K) = T*DY + (T-T*T)*((1.0-T)*CY1 - T*CY2)
ENDDO
XT(KK) = DX
YT(KK) = DY
C
SINT1 = 0.
DO K=1, KK
SINT1 = SINT1
& + SQRT((XT(K)-XT(K-1))**2 + (YT(K)-YT(K-1))**2)
ENDDO
C
SINT2 = 0.
DO K=2, KK, 2
SINT2 = SINT2
& + SQRT((XT(K)-XT(K-2))**2 + (YT(K)-YT(K-2))**2)
ENDDO
C
SINT = (4.0*SINT1 - SINT2) / 3.0
C
IF(ABS(SINT-DS) .GT. ABS(SERR)) SERR = SINT - DS
C
IF(I.LT.N) DS = S(I+1) - S(I)
C
S(I) = S(I-1) + SQRT(SINT)
ENDDO
C
SERR = SERR / (S(N) - S(1))
WRITE(*,*) IPASS, SERR
C
C------ re-spline X(S) and Y(S)
CALL SEGSPL(X,XS,S,N)
CALL SEGSPL(Y,YS,S,N)
C
IF(ABS(SERR) .LT. 1.0E-7) RETURN
C
100 CONTINUE
C
RETURN
END ! SPLNXY
SUBROUTINE SEGSPL(X,XS,S,N)
C-----------------------------------------------
C Splines X(S) array just like SPLINE, |
C but allows derivative discontinuities |
C at segment joints. Segment joints are |
C defined by identical successive S values. |
C-----------------------------------------------
DIMENSION X(N), XS(N), S(N)
C
IF(S(1).EQ.S(2) ) STOP 'SEGSPL: First input point duplicated'
IF(S(N).EQ.S(N-1)) STOP 'SEGSPL: Last input point duplicated'
C
ISEG0 = 1
DO 10 ISEG=2, N-2
IF(S(ISEG).EQ.S(ISEG+1)) THEN
NSEG = ISEG - ISEG0 + 1
CALL SPLIND(X(ISEG0),XS(ISEG0),S(ISEG0),NSEG,-999.0,-999.0)
ISEG0 = ISEG+1
ENDIF
10 CONTINUE
C
NSEG = N - ISEG0 + 1
CALL SPLIND(X(ISEG0),XS(ISEG0),S(ISEG0),NSEG,-999.0,-999.0)
C
RETURN
END ! SEGSPL
SUBROUTINE SEGSPLD(X,XS,S,N,XS1,XS2)
C-----------------------------------------------
C Splines X(S) array just like SPLIND, |
C but allows derivative discontinuities |
C at segment joints. Segment joints are |
C defined by identical successive S values. |
C-----------------------------------------------
DIMENSION X(N), XS(N), S(N)
C
IF(S(1).EQ.S(2) ) STOP 'SEGSPL: First input point duplicated'
IF(S(N).EQ.S(N-1)) STOP 'SEGSPL: Last input point duplicated'
C
ISEG0 = 1
DO 10 ISEG=2, N-2
IF(S(ISEG).EQ.S(ISEG+1)) THEN
NSEG = ISEG - ISEG0 + 1
CALL SPLIND(X(ISEG0),XS(ISEG0),S(ISEG0),NSEG,XS1,XS2)
ISEG0 = ISEG+1
ENDIF
10 CONTINUE
C
NSEG = N - ISEG0 + 1
CALL SPLIND(X(ISEG0),XS(ISEG0),S(ISEG0),NSEG,XS1,XS2)
C
RETURN
END ! SEGSPL
SUBROUTINE NEARPT(XPNT,YPNT,SNEAR,X,XP,Y,YP,S,N)
IMPLICIT REAL (A-H,M,O-Z)
DIMENSION X(N),XP(N),Y(N),YP(N),S(N)
C========================================================
C Finds arc length position S=SNEAR of a point
C on a 2-D splined curve X(S),Y(S) nearest the
C specified point XPNT,YPNT.
C
C Assumes the value passed in via SNEAR is a good
C initial guess.
C========================================================
C
C---- convergence tolerance
EPS = 1.0E-4 * (S(N) - S(1))
C
C---- Newton iteration loop
DO 215 IPASS=1, 10
CALL SEVALL(SNEAR,X,XP,S,N,XXI,XPI,X2I)
CALL SEVALL(SNEAR,Y,YP,S,N,YYI,YPI,Y2I)
C
C------ residual is dot product with curve tangent vector
RES = (XXI-XPNT)*XPI + (YYI-YPNT)*YPI
C
RES_S = (XPI )*XPI + (YPI )*YPI
& + (XXI-XPNT)*X2I + (YYI-YPNT)*Y2I
C
DSN = -RES/RES_S
SNEAR = SNEAR + DSN
IF(ABS(DSN) .LT. EPS) GO TO 216
C
215 CONTINUE
WRITE(*,*) 'NEARPT: Convergence failed. Continuing...'
216 CONTINUE
C
RETURN
END ! NEARPT
SUBROUTINE SEVALL(SS,X,XS,S,N,
& XX, XXS, XXSS )
IMPLICIT REAL (A-H,M,O-Z)
DIMENSION X(N),XS(N),S(N)
C--------------------------------------------------
C Calculates all spline derivatives. |
C (Combines SEVAL, DEVAL, D2VAL) |
C XS array must have been calculated by SPLINE |
C--------------------------------------------------
ILOW = 1
I = N
C
10 IF(I-ILOW .LE. 1) GO TO 11
C
IMID = (I+ILOW)/2
IF(SS .LT. S(IMID)) THEN
I = IMID
ELSE
ILOW = IMID
ENDIF
GO TO 10
C
11 DS = S(I) - S(I-1)
T = (SS - S(I-1)) / DS
C
F0 = X(I-1)
F1 = DS*XS(I-1)
F2 = -DS*(2.0*XS(I-1) + XS(I)) + 3.0*(X(I) - X(I-1))
F3 = DS*( XS(I-1) + XS(I)) - 2.0*(X(I) - X(I-1))
C
XX = F0 + T*(F1 + T*( F2 + T* F3))
XXS = F1 + T*(2.0*F2 + T*3.0*F3)
XXSS = 2.0*F2 + T*6.0*F3
C
XXS = XXS/DS
XXSS = XXSS/DS**2
C
RETURN
END ! SEVALL
SUBROUTINE SORT(KK,S,W)
C--- Sorts input arrays S(KK),W(KK) by abscissa S
C Eliminates duplicate S points from arrays, updates KK
DIMENSION S(KK), W(KK)
LOGICAL DONE
C
C---- sort arrays
DO IPASS=1, 1234
DONE = .TRUE.
DO 101 N=1, KK-1
NP = N+1
IF(S(NP).GE.S(N)) GO TO 101
TEMP = S(NP)
S(NP) = S(N)
S(N) = TEMP
TEMP = W(NP)
W(NP) = W(N)
W(N) = TEMP
DONE = .FALSE.
101 CONTINUE
IF(DONE) GO TO 11
END DO
WRITE(*,*) 'Sort failed'
C
C---- search for duplicate pairs and eliminate each one
11 KKS = KK
DO 20 K=1, KKS
IF(K.GE.KK) RETURN
IF(S(K).NE.S(K+1)) GO TO 20
C------- eliminate pair
KK = KK-2
DO KT=K, KK
S(KT) = S(KT+2)
W(KT) = W(KT+2)
END DO
20 CONTINUE
C
RETURN
END
|
