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C
C The following code was excerpted from: dsmdf2.f
C
SUBROUTINE DSMDF2(HFLAG,NVC,NPOLG,MAXWK,VCL,HVL,PVL,IANG,IVRT,
$ XIVRT,WIDSQ,EDGVAL,VRTVAL,AREA,WK)
IMPLICIT LOGICAL (A-Z)
LOGICAL HFLAG
INTEGER MAXWK,NPOLG,NVC
INTEGER HVL(NPOLG),IVRT(*),PVL(4,*),XIVRT(NPOLG+1)
DOUBLE PRECISION AREA(NPOLG),EDGVAL(*),IANG(*)
DOUBLE PRECISION VCL(2,NVC),VRTVAL(NVC),WIDSQ(NPOLG),WK(MAXWK)
C
C Written and copyright by:
C Barry Joe, Dept. of Computing Science, Univ. of Alberta
C Edmonton, Alberta, Canada T6G 2H1
C Phone: (403) 492-5757 Email: barry@cs.ualberta.ca
C
C Purpose: Set up data structure for heuristic mesh distribution
C function from data structure for convex polygon decomposition
C if HFLAG is .TRUE., else set up only IVRT and XIVRT.
C Also compute areas of convex polygons.
C
C Input parameters:
C HFLAG - .TRUE. if data structure is to be constructed,
C .FALSE. if only IVRT, XIVRT, AREA are to be computed
C NVC - number of vertex coordinates in VCL array
C NPOLG - number of polygonal subregions in HVL array
C MAXWK - maximum size available for WK array; should be
C 2 times maximum number of vertices in any polygon
C VCL(1:2,1:NVC) - vertex coordinate list
C HVL(1:NPOLG) - head vertex list
C PVL(1:4,1:*),IANG(1:*) - polygon vertex list, interior angles
C
C Output parameters:
C IVRT(1:*) - indices of polygon vertices in VCL, ordered by
C polygon; same size as PVL
C XIVRT(1:NPOLG+1) - pointer to first vertex of each polygon
C in IVRT; vertices of polygon K are IVRT(I) for I from
C XIVRT(K) to XIVRT(K+1)-1
C WIDSQ(1:NPOLG) - square of width of convex polygons
C EDGVAL(1:*) - value associated with each edge of decomp.;
C same size as PVL
C VRTVAL(1:NVC) - value associated with each vertex of decomp.
C [Note: Above 5 arrays are for heuristic mdf data structure.]
C AREA(1:NPOLG) - area of convex polygons
C
C Working parameters:
C WK(1:MAXWK) - double precision work array
C
C Abnormal return:
C IERR is set to 7 or 201
C
C Routines called:
C AREAPG, WIDTH2
C
INTEGER IERR
DOUBLE PRECISION PI,TOL
COMMON /GERROR/ IERR
COMMON /GCONST/ PI,TOL
SAVE /GERROR/,/GCONST/
C
INTEGER EDGV,LOC,POLG,SUCC
PARAMETER (LOC = 1, POLG = 2, SUCC = 3, EDGV = 4)
C
INTEGER I,IL,J,JL,K,L,M,NVRT,XC,YC
DOUBLE PRECISION AREAPG,PIMTOL,S
C
C Compute area and square of width of polygons.
C
PIMTOL = PI - TOL
DO 30 K = 1,NPOLG
NVRT = 0
I = HVL(K)
10 CONTINUE
IF (IANG(I) .LT. PIMTOL) NVRT = NVRT + 1
I = PVL(SUCC,I)
IF (I .NE. HVL(K)) GO TO 10
IF (NVRT + NVRT .GT. MAXWK) THEN
IERR = 7
RETURN
ENDIF
XC = 0
20 CONTINUE
IF (IANG(I) .LT. PIMTOL) THEN
J = PVL(LOC,I)
XC = XC + 1
WK(XC) = VCL(1,J)
WK(XC+NVRT) = VCL(2,J)
ENDIF
I = PVL(SUCC,I)
IF (I .NE. HVL(K)) GO TO 20
XC = 1
YC = XC + NVRT
AREA(K) = AREAPG(NVRT,WK(XC),WK(YC))*0.5D0
IF (HFLAG) THEN
CALL WIDTH2(NVRT,WK(XC),WK(YC),I,J,WIDSQ(K))
IF (IERR .NE. 0) RETURN
ENDIF
30 CONTINUE
C
C Set up IVRT, XIVRT, EDGVAL, VRTVAL arrays.
C
L = 1
DO 50 K = 1,NPOLG
XIVRT(K) = L
I = HVL(K)
IL = PVL(LOC,I)
40 CONTINUE
IVRT(L) = IL
J = PVL(SUCC,I)
JL = PVL(LOC,J)
IF (HFLAG) THEN
S = MIN((VCL(1,JL)-VCL(1,IL))**2 + (VCL(2,JL)-VCL(2,IL))
$ **2, WIDSQ(K))
M = PVL(EDGV,I)
IF (M .GT. 0) S = MIN(S,WIDSQ(PVL(POLG,M)))
EDGVAL(L) = S
ENDIF
L = L + 1
I = J
IL = JL
IF (I .NE. HVL(K)) GO TO 40
50 CONTINUE
XIVRT(NPOLG+1) = L
IF (.NOT. HFLAG) RETURN
DO 60 I = 1,NVC
VRTVAL(I) = 0.0D0
60 CONTINUE
DO 80 K = 1,NPOLG
J = XIVRT(K+1) - 1
L = J
DO 70 I = XIVRT(K),L
IL = IVRT(I)
IF (VRTVAL(IL) .EQ. 0.0D0) THEN
VRTVAL(IL) = MIN(EDGVAL(I),EDGVAL(J))
ELSE
VRTVAL(IL) = MIN(VRTVAL(IL),EDGVAL(I),EDGVAL(J))
ENDIF
J = I
70 CONTINUE
80 CONTINUE
END
C
C The following code was excerpted from: eqdis2.f
C
SUBROUTINE EQDIS2(HFLAG,UMDF,KAPPA,ANGSPC,ANGTOL,DMIN,NMIN,NTRID,
$ NVC,NPOLG,NVERT,MAXVC,MAXHV,MAXPV,MAXIW,MAXWK,VCL,REGNUM,HVL,
$ PVL,IANG,AREA,PSI,H,IWK,WK)
IMPLICIT LOGICAL (A-Z)
LOGICAL HFLAG
INTEGER MAXHV,MAXIW,MAXPV,MAXVC,MAXWK,NMIN,NPOLG,NTRID,NVC,NVERT
INTEGER HVL(MAXHV),IWK(MAXIW),PVL(4,MAXPV),REGNUM(MAXHV)
DOUBLE PRECISION ANGSPC,ANGTOL,DMIN,KAPPA,UMDF
DOUBLE PRECISION AREA(MAXHV),H(MAXHV),IANG(MAXPV),PSI(MAXHV)
DOUBLE PRECISION VCL(2,MAXVC),WK(MAXWK)
EXTERNAL UMDF
C
C Written and copyright by:
C Barry Joe, Dept. of Computing Science, Univ. of Alberta
C Edmonton, Alberta, Canada T6G 2H1
C Phone: (403) 492-5757 Email: barry@cs.ualberta.ca
C
C Purpose: Further subdivide convex polygons so that an approx.
C equidistributing triangular mesh can be constructed with
C respect to heuristic or user-supplied mesh distribution
C function, and determine triangle size for each polygon of
C decomposition.
C
C Input parameters:
C HFLAG - .TRUE. if heuristic mdf, .FALSE. if user-supplied mdf
C UMDF(X,Y) - d.p user-supplied mdf with d.p arguments
C KAPPA - mesh smoothness parameter in interval [0.0,1.0]
C ANGSPC - angle spacing parameter in radians used to determine
C extra points as possible endpoints of separators
C ANGTOL - angle tolerance parameter in radians used in
C accepting separators
C DMIN - parameter used to determine if variation of mdf in
C polygon is 'sufficiently high'
C NMIN - parameter used to determine if 'sufficiently large'
C number of triangles in polygon
C NTRID - desired number of triangles in mesh
C NVC - number of vertex coordinates or positions used in VCL
C array
C NPOLG - number of polygonal subregions or positions used in
C HVL array
C NVERT - number of polygon vertices or positions used in PVL
C array
C MAXVC - maximum size available for VCL array, should be >=
C number of vertex coordinates required for decomposition
C (approx NVC + 2*NS where NS is expected number of new
C separators)
C MAXHV - maximum size available for HVL, REGNUM, AREA, PSI, H
C arrays; should be >= number of polygons required for
C decomposition (approx NPOLG + NS)
C MAXPV - maximum size available for PVL, IANG arrays; should be
C >= number of polygon vertices required for decomposition
C (approx NVERT + 5*NS)
C MAXIW - maximum size available for IWK array; should be >=
C MAX(2*NP, NVERT + NPOLG + 3*NVRT + INT(2*PI/ANGSPC))
C where NVRT is maximum number of vertices in a convex
C polygon of the (input) decomposition, NP is expected
C value of NPOLG on output
C MAXWK - maximum size available for WK array; should be >=
C NVC + NVERT + 2*NPOLG + 3*(NVRT + INT(2*PI/ANGSPC))
C VCL(1:2,1:NVC) - vertex coordinate list
C REGNUM(1:NPOLG) - region numbers
C HVL(1:NPOLG) - head vertex list
C PVL(1:4,1:NVERT),IANG(1:NVERT) - polygon vertex list and
C interior angles; see routine DSPGDC for more details
C [Note: The data structures should be as output from routine
C CVDEC2.]
C
C Updated parameters:
C NVC,NPOLG,NVERT,VCL,REGNUM,HVL,PVL,IANG
C
C Output parameters:
C AREA(1:NPOLG) - area of convex polygons in decomposition
C PSI(1:NPOLG) - smoothed mean mdf values in the convex polygons
C H(1:NPOLG) - triangle size for convex polygons
C
C Working parameters:
C IWK(1:MAXIW) - integer work array
C WK(1:MAXWK) - double precsion work array
C
C Abnormal return:
C IERR is set to 3, 4, 5, 6, 7, 200, 201, or 222
C
C Routines called:
C DSMDF2, MFDEC2, TRISIZ
C
INTEGER IERR
COMMON /GERROR/ IERR
SAVE /GERROR/
C
INTEGER EDGVAL,IVRT,M,N,VRTVAL,WIDSQ,XIVRT
C
IVRT = 1
XIVRT = IVRT + NVERT
M = XIVRT + NPOLG
IF (M .GT. MAXIW) THEN
IERR = 6
RETURN
ENDIF
WIDSQ = 1
IF (HFLAG) THEN
EDGVAL = WIDSQ + NPOLG
VRTVAL = EDGVAL + NVERT
N = NPOLG + NVERT + NVC
IF (N .GT. MAXWK) THEN
IERR = 7
RETURN
ENDIF
ELSE
EDGVAL = 1
VRTVAL = 1
N = 0
ENDIF
CALL DSMDF2(HFLAG,NVC,NPOLG,MAXWK-N,VCL,HVL,PVL,IANG,IWK(IVRT),
$ IWK(XIVRT),WK(WIDSQ),WK(EDGVAL),WK(VRTVAL),AREA,WK(N+1))
IF (IERR .NE. 0) RETURN
CALL MFDEC2(HFLAG,UMDF,KAPPA,ANGSPC,ANGTOL,DMIN,NMIN,NTRID,NVC,
$ NPOLG,NVERT,MAXVC,MAXHV,MAXPV,MAXIW-M,MAXWK-N,VCL,REGNUM,HVL,
$ PVL,IANG,IWK(IVRT),IWK(XIVRT),WK(WIDSQ),WK(EDGVAL),WK(VRTVAL),
$ AREA,PSI,IWK(M+1),WK(N+1))
IF (IERR .NE. 0) RETURN
IF (2*NPOLG .GT. MAXIW) THEN
IERR = 6
RETURN
ENDIF
CALL TRISIZ(NTRID,NPOLG,HVL,PVL,AREA,PSI,H,IWK,IWK(NPOLG+1))
END
C
C The following code was excerpted from: intpg.f
C
SUBROUTINE INTPG(NVRT,XC,YC,CTRX,CTRY,ARPOLY,HFLAG,UMDF,WSQ,NEV,
$ IFV,LISTEV,IVRT,EDGVAL,VRTVAL,VCL,MDFINT,MEAN,STDV,MDFTR)
IMPLICIT LOGICAL (A-Z)
LOGICAL HFLAG
INTEGER IFV,NEV,NVRT
INTEGER IVRT(*),LISTEV(NEV)
DOUBLE PRECISION ARPOLY,CTRX,CTRY,MDFINT,MEAN,STDV,UMDF,WSQ
DOUBLE PRECISION EDGVAL(*),MDFTR(0:NVRT-1),VCL(2,*),VRTVAL(*)
DOUBLE PRECISION XC(0:NVRT),YC(0:NVRT)
C
C Written and copyright by:
C Barry Joe, Dept. of Computing Science, Univ. of Alberta
C Edmonton, Alberta, Canada T6G 2H1
C Phone: (403) 492-5757 Email: barry@cs.ualberta.ca
C
C Purpose: Compute integral of MDF2(X,Y) [heuristic mdf] or
C UMDF(X,Y) [user-supplied mdf] in convex polygon.
C
C Input parameters:
C NVRT - number of vertices in polygon
C XC(0:NVRT),YC(0:NVRT) - coordinates of polygon vertices in
C CCW order, translated so that centroid is at origin;
C (XC(0),YC(0)) = (XC(NVRT),YC(NVRT))
C CTRX, CTRY - coordinates of centroid before translation
C ARPOLY - area of polygon
C HFLAG - .TRUE. if heuristic mdf, .FALSE. if user-supplied mdf
C UMDF(X,Y) - d.p user-supplied mdf with d.p arguments
C WSQ - square of width of original polygon of decomposition
C NEV,IFV,LISTEV(1:NEV) - output from routine PRMDF2
C IVRT(1:*),EDGVAL(1:*),VRTVAL(1:*) - arrays output from DSMDF2;
C if .NOT. HFLAG then only first array exists
C VCL(1:2,1:*) - vertex coordinate list
C
C Output parameters:
C MDFINT - integral of mdf in polygon
C MEAN - mean mdf value in polygon
C STDV - standard deviation of mdf in polygon
C MDFTR(0:NVRT-1) - mean mdf value in each triangle of polygon;
C triangles are determined by polygon vertices and centroid
C
C Routines called:
C UMDF
C
INTEGER NQPT
PARAMETER (NQPT = 3)
C
EXTERNAL UMDF
INTEGER I,J,K,KP1,L,M
DOUBLE PRECISION AREATR,D,MDFSQI,S,SUM1,SUM2,TEMP,VAL
DOUBLE PRECISION X,X0,X1,XX,Y,Y0,Y1,YY
C
DOUBLE PRECISION WT(NQPT),QC(3,NQPT)
DATA WT/0.3333333333333333D0,0.3333333333333333D0,
$ 0.3333333333333333D0/
DATA QC/0.6666666666666666D0,0.1666666666666667D0,
$ 0.1666666666666667D0,0.1666666666666667D0,
$ 0.6666666666666666D0,0.1666666666666667D0,
$ 0.1666666666666667D0,0.1666666666666667D0,
$ 0.6666666666666666D0/
SAVE WT,QC
C
C NQPT is number of quad pts for numerical integration in triangle
C WT(I) is weight of Ith quadrature point
C QC(1:3,I) are barycentric coordinates of Ith quadrature point
C
MDFINT = 0.0D0
MDFSQI = 0.0D0
DO 30 L = 0,NVRT-1
AREATR = 0.5D0*(XC(L)*YC(L+1) - XC(L+1)*YC(L))
SUM1 = 0.0D0
SUM2 = 0.0D0
DO 20 M = 1,NQPT
XX = QC(1,M)*XC(L) + QC(2,M)*XC(L+1)
YY = QC(1,M)*YC(L) + QC(2,M)*YC(L+1)
IF (HFLAG) THEN
C VAL = MDF2(XX+CTRX,YY+CTRY,WSQ,NEV,IFV,LISTEV,IVRT,
C $ EDGVAL,VRTVAL,VCL)
C Insert code for function MDF2 to reduce number of calls.
C
X = XX + CTRX
Y = YY + CTRY
S = WSQ
DO 10 I = 1,NEV
K = LISTEV(I)
IF (K .LT. 0) THEN
K = -K
D = (VCL(1,K) - X)**2 + (VCL(2,K) - Y)**2
D = MAX(0.25D0*D,VRTVAL(K))
S = MIN(S,D)
ELSE
KP1 = K + 1
IF (I .EQ. NEV .AND. IFV .GT. 0) KP1 = IFV
J = IVRT(KP1)
X0 = X - VCL(1,J)
Y0 = Y - VCL(2,J)
X1 = VCL(1,IVRT(K)) - VCL(1,J)
Y1 = VCL(2,IVRT(K)) - VCL(2,J)
IF (X0*X1 + Y0*Y1 .LE. 0.0D0) THEN
D = X0**2 + Y0**2
ELSE
X0 = X0 - X1
Y0 = Y0 - Y1
IF (X0*X1 + Y0*Y1 .GE. 0.0D0) THEN
D = X0**2 + Y0**2
ELSE
D = (X1*Y0 - Y1*X0)**2/(X1**2 + Y1**2)
ENDIF
ENDIF
D = MAX(0.25D0*D,EDGVAL(K))
S = MIN(S,D)
ENDIF
10 CONTINUE
VAL = 1.0D0/S
ELSE
VAL = UMDF(XX+CTRX,YY+CTRY)
ENDIF
TEMP = WT(M)*VAL
SUM1 = SUM1 + TEMP
SUM2 = SUM2 + TEMP*VAL
20 CONTINUE
MDFTR(L) = SUM1
MDFINT = MDFINT + SUM1*AREATR
MDFSQI = MDFSQI + SUM2*AREATR
30 CONTINUE
MEAN = MDFINT/ARPOLY
STDV = MDFSQI/ARPOLY - MEAN**2
STDV = SQRT(MAX(STDV,0.0D0))
END
C
C The following code was excerpted from: mfdec2.f
C
SUBROUTINE MFDEC2(HFLAG,UMDF,KAPPA,ANGSPC,ANGTOL,DMIN,NMIN,NTRID,
$ NVC,NPOLG,NVERT,MAXVC,MAXHV,MAXPV,MAXIW,MAXWK,VCL,REGNUM,HVL,
$ PVL,IANG,IVRT,XIVRT,WIDSQ,EDGVAL,VRTVAL,AREA,PSI,IWK,WK)
IMPLICIT LOGICAL (A-Z)
LOGICAL HFLAG
INTEGER MAXHV,MAXIW,MAXPV,MAXVC,MAXWK,NMIN,NPOLG,NTRID,NVC,NVERT
INTEGER HVL(MAXHV),IVRT(NVERT),IWK(MAXIW),PVL(4,MAXPV)
INTEGER REGNUM(MAXHV),XIVRT(NPOLG+1)
DOUBLE PRECISION ANGSPC,ANGTOL,DMIN,KAPPA,UMDF
DOUBLE PRECISION AREA(MAXHV),EDGVAL(NVERT),IANG(MAXPV),PSI(MAXHV)
DOUBLE PRECISION VCL(2,MAXVC),VRTVAL(NVC),WIDSQ(NPOLG),WK(MAXWK)
EXTERNAL UMDF
C
C Written and copyright by:
C Barry Joe, Dept. of Computing Science, Univ. of Alberta
C Edmonton, Alberta, Canada T6G 2H1
C Phone: (403) 492-5757 Email: barry@cs.ualberta.ca
C
C Purpose: Further subdivide convex polygons so that the variation
C of heuristic or user-supplied mesh distribution function in
C each polygon is limited.
C
C Input parameters:
C HFLAG - .TRUE. if heuristic mdf, .FALSE. if user-supplied mdf
C UMDF(X,Y) - d.p user-supplied mdf with d.p arguments
C KAPPA - mesh smoothness parameter in interval [0.0,1.0]
C ANGSPC - angle spacing parameter in radians used to determine
C extra points as possible endpoints of separators
C ANGTOL - angle tolerance parameter in radians used in
C accepting separators
C DMIN - parameter used to determine if variation of mdf in
C polygon is 'sufficiently high'
C NMIN - parameter used to determine if 'sufficiently large'
C number of triangles in polygon
C NTRID - desired number of triangles in mesh
C NVC - number of vertex coordinates or positions used in VCL
C array
C NPOLG - number of polygonal subregions or positions used in
C HVL array
C NVERT - number of polygon vertices or positions used in PVL
C array
C MAXVC - maximum size available for VCL array
C MAXHV - maximum size available for HVL,REGNUM,AREA,PSI arrays
C MAXPV - maximum size available for PVL, IANG arrays
C MAXIW - maximum size available for IWK array; should be about
C 3*NVRT + INT(2*PI/ANGSPC) where NVRT is maximum number of
C vertices in a convex polygon of the (input) decomposition
C MAXWK - maximum size available for WK array; should be about
C NPOLG + 3*(NVRT + INT(2*PI/ANGSPC)) + 2
C VCL(1:2,1:NVC) - vertex coordinate list
C REGNUM(1:NPOLG) - region numbers
C HVL(1:NPOLG) - head vertex list
C PVL(1:4,1:NVERT),IANG(1:NVERT) - polygon vertex list and
C interior angles
C IVRT(1:NVERT),XIVRT(1:NPOLG+1),WIDSQ(1:NPOLG),EDGVAL(1:NVERT),
C VRTVAL(1:NVC) - arrays output from routine DSMDF2;
C if .NOT. HFLAG then only first two arrays exist
C AREA(1:NPOLG) - area of convex polygons in decomposition
C
C Updated parameters:
C NVC,NPOLG,NVERT,VCL,REGNUM,HVL,PVL,IANG,AREA
C
C Output parameters:
C PSI(1:NPOLG) - mean mdf values in the convex polygons
C
C Working parameters:
C IWK(1:MAXIW) - integer work array
C WK(1:MAXWK) - double precision work array
C
C Abnormal return:
C IERR is set to 3, 4, 5, 6, 7, 200, or 222
C
C Routines called:
C AREAPG, INSED2, INSVR2, INTPG, PRMDF2, SEPMDF, SEPSHP
C
INTEGER IERR
DOUBLE PRECISION PI,TOL
COMMON /GERROR/ IERR
COMMON /GCONST/ PI,TOL
SAVE /GERROR/,/GCONST/
C
INTEGER EDGV,LOC,POLG,SUCC
PARAMETER (LOC = 1, POLG = 2, SUCC = 3, EDGV = 4)
C
INTEGER I,I1,I2,IFV,II,INC,INDPVL,J,K,L,LISTEV,M,MAXN,MDFTR,NEV
INTEGER NP,NVRT,P,V,W,XC,YC
DOUBLE PRECISION ALPHA,ANGSP2,AREAPG,AREARG,C1,C2,COSALP,CTRX
DOUBLE PRECISION CTRY,DELTA,DX,DY,INTREG,MDFINT,MEAN,NUMER,NWAREA
DOUBLE PRECISION PI2,R,SINALP,STDV,SUMX,SUMY,THETA1,THETA2,WSQ
DOUBLE PRECISION X1,X2,Y1,Y2
C
C WK(1:NPOLG) is used for mdf standard deviation in polygons.
C Compute AREARG = area of region and INTREG = estimated integral
C of MDF2(X,Y) or UMDF(X,Y).
C
NVRT = 0
DO 10 I = 1,NPOLG
NVRT = MAX(NVRT,XIVRT(I+1)-XIVRT(I))
10 CONTINUE
IF (HFLAG .AND. 2*NVRT .GT. MAXIW) THEN
IERR = 6
RETURN
ELSE IF (NPOLG + 3*NVRT + 2 .GT. MAXWK) THEN
IERR = 7
RETURN
ENDIF
LISTEV = 1
XC = NPOLG + 1
YC = XC + NVRT + 1
MDFTR = YC + NVRT + 1
AREARG = 0.0D0
INTREG = 0.0D0
NEV = -1
DO 40 I = 1,NPOLG
IF (HFLAG) THEN
WSQ = WIDSQ(I)
CALL PRMDF2(I,WSQ,IVRT,XIVRT,EDGVAL,VRTVAL,NEV,IFV,
$ IWK(LISTEV))
ENDIF
IF (NEV .EQ. 0) THEN
PSI(I) = 1.0D0/WSQ
WK(I) = 0.0D0
MDFINT = PSI(I)*AREA(I)
ELSE
NVRT = XIVRT(I+1) - XIVRT(I)
K = XIVRT(I)
SUMX = 0.0D0
SUMY = 0.0D0
DO 20 J = 0,NVRT-1
L = IVRT(K)
WK(XC+J) = VCL(1,L)
WK(YC+J) = VCL(2,L)
SUMX = SUMX + WK(XC+J)
SUMY = SUMY + WK(YC+J)
K = K + 1
20 CONTINUE
CTRX = SUMX/DBLE(NVRT)
CTRY = SUMY/DBLE(NVRT)
DO 30 J = 0,NVRT-1
WK(XC+J) = WK(XC+J) - CTRX
WK(YC+J) = WK(YC+J) - CTRY
30 CONTINUE
WK(XC+NVRT) = WK(XC)
WK(YC+NVRT) = WK(YC)
CALL INTPG(NVRT,WK(XC),WK(YC),CTRX,CTRY,AREA(I),HFLAG,UMDF,
$ WSQ,NEV,IFV,IWK(LISTEV),IVRT,EDGVAL,VRTVAL,VCL,MDFINT,
$ PSI(I),WK(I),WK(MDFTR))
ENDIF
AREARG = AREARG + AREA(I)
INTREG = INTREG + MDFINT
40 CONTINUE
C
C If HFLAG, compute mean mdf values from KAPPA, etc. Scale PSI(I)'s
C so that integral in region is 1. Determine which polygons need to
C be further subdivided (indicated by negative PSI(I) value).
C
IF (HFLAG) THEN
C1 = (1.0D0 - KAPPA)/INTREG
C2 = KAPPA/AREARG
ELSE
C1 = 1.0D0/INTREG
C2 = 0.0D0
ENDIF
DO 50 I = 1,NPOLG
PSI(I) = PSI(I)*C1 + C2
IF (C1*WK(I) .GT. PSI(I)*DMIN) THEN
IF (NTRID*PSI(I)*AREA(I) .GT. NMIN) PSI(I) = -PSI(I)
ENDIF
50 CONTINUE
C
C Further subdivide polygons for which STDV/MEAN > DMIN and
C (estimated number of triangles) > NMIN.
C
ANGSP2 = 2.0D0*ANGSPC
PI2 = 2.0D0*PI
INC = INT(PI2/ANGSPC)
NEV = 0
NP = NPOLG
XC = 1
DO 140 I = 1,NP
IF (PSI(I) .LT. 0.0D0) THEN
IF (HFLAG) THEN
WSQ = WIDSQ(I)
CALL PRMDF2(I,WSQ,IVRT,XIVRT,EDGVAL,VRTVAL,NEV,IFV,
$ IWK(LISTEV))
ENDIF
L = NPOLG + 1
K = I
60 CONTINUE
IF (K .GT. NPOLG) GO TO 130
70 CONTINUE
IF (PSI(K) .GE. 0.0D0) GO TO 120
NVRT = 0
SUMX = 0.0D0
SUMY = 0.0D0
J = HVL(K)
80 CONTINUE
NVRT = NVRT + 1
M = PVL(LOC,J)
SUMX = SUMX + VCL(1,M)
SUMY = SUMY + VCL(2,M)
J = PVL(SUCC,J)
IF (J .NE. HVL(K)) GO TO 80
CTRX = SUMX/DBLE(NVRT)
CTRY = SUMY/DBLE(NVRT)
MAXN = NVRT + INC
IF (NEV + MAXN + 1 .GT. MAXIW) THEN
IERR = 6
RETURN
ELSE IF (3*MAXN + 2 .GT. MAXWK) THEN
IERR = 7
RETURN
ENDIF
YC = XC + MAXN + 1
MDFTR = YC + MAXN + 1
INDPVL = LISTEV + NEV
NVRT = 0
M = PVL(LOC,J)
X1 = VCL(1,M) - CTRX
Y1 = VCL(2,M) - CTRY
WK(XC) = X1
WK(YC) = Y1
THETA1 = ATAN2(Y1,X1)
P = J
IWK(INDPVL) = J
90 CONTINUE
J = PVL(SUCC,J)
M = PVL(LOC,J)
X2 = VCL(1,M) - CTRX
Y2 = VCL(2,M) - CTRY
THETA2 = ATAN2(Y2,X2)
IF (THETA2 .LT. THETA1) THETA2 = THETA2 + PI2
DELTA = THETA2 - THETA1
IF (DELTA .GE. ANGSP2) THEN
M = INT(DELTA/ANGSPC)
DELTA = DELTA/DBLE(M)
DX = X2 - X1
DY = Y2 - Y1
NUMER = X1*DY - Y1*DX
ALPHA = THETA1
DO 100 II = 1,M-1
ALPHA = ALPHA + DELTA
COSALP = COS(ALPHA)
SINALP = SIN(ALPHA)
R = NUMER/(DY*COSALP - DX*SINALP)
NVRT = NVRT + 1
WK(XC+NVRT) = R*COSALP
WK(YC+NVRT) = R*SINALP
IWK(INDPVL+NVRT) = -P
100 CONTINUE
ENDIF
NVRT = NVRT + 1
WK(XC+NVRT) = X2
WK(YC+NVRT) = Y2
X1 = X2
Y1 = Y2
THETA1 = THETA2
P = J
IWK(INDPVL+NVRT) = J
IF (J .NE. HVL(K)) GO TO 90
CALL INTPG(NVRT,WK(XC),WK(YC),CTRX,CTRY,AREA(K),HFLAG,
$ UMDF,WSQ,NEV,IFV,IWK(LISTEV),IVRT,EDGVAL,VRTVAL,
$ VCL,MDFINT,MEAN,STDV,WK(MDFTR))
PSI(K) = MEAN*C1 + C2
IF (C1*STDV .GT. PSI(K)*DMIN) THEN
IF (NTRID*PSI(K)*AREA(K) .GT. NMIN) THEN
CALL SEPMDF(ANGTOL,NVRT,WK(XC),WK(YC),AREA(K),
$ MEAN,WK(MDFTR),IWK(INDPVL),IANG,I1,I2)
IF (I1 .LT. 0) THEN
IF (YC + 3*NVRT .GT. MAXWK) THEN
IERR = 7
RETURN
ENDIF
CALL SEPSHP(ANGTOL,NVRT,WK(XC),WK(YC),
$ IWK(INDPVL),IANG,I1,I2,WK(YC+NVRT+1))
IF (IERR .NE. 0) RETURN
ENDIF
IF (I1 .LT. 0) THEN
IERR = 222
RETURN
ENDIF
V = IWK(INDPVL+I1)
IF (V .LT. 0) THEN
CALL INSVR2(WK(XC+I1)+CTRX,WK(YC+I1)+CTRY,-V,
$ NVC,NVERT,MAXVC,MAXPV,VCL,PVL,IANG,V)
IF (IERR .NE. 0) RETURN
ENDIF
W = IWK(INDPVL+I2)
IF (W .LT. 0) THEN
CALL INSVR2(WK(XC+I2)+CTRX,WK(YC+I2)+CTRY,-W,
$ NVC,NVERT,MAXVC,MAXPV,VCL,PVL,IANG,W)
IF (IERR .NE. 0) RETURN
ENDIF
CALL INSED2(V,W,NPOLG,NVERT,MAXHV,MAXPV,VCL,
$ REGNUM,HVL,PVL,IANG)
IF (IERR .NE. 0) RETURN
NVRT = 0
J = HVL(K)
110 CONTINUE
M = PVL(LOC,J)
WK(XC+NVRT) = VCL(1,M)
WK(YC+NVRT) = VCL(2,M)
NVRT = NVRT + 1
J = PVL(SUCC,J)
IF (J .NE. HVL(K)) GO TO 110
NWAREA = AREAPG(NVRT,WK(XC),WK(YC))*0.5D0
AREA(NPOLG) = AREA(K) - NWAREA
AREA(K) = NWAREA
PSI(K) = -PSI(K)
PSI(NPOLG) = PSI(K)
ENDIF
ENDIF
GO TO 70
120 CONTINUE
IF (K .EQ. I) THEN
K = L
ELSE
K = K + 1
ENDIF
GO TO 60
130 CONTINUE
ENDIF
140 CONTINUE
END
C
C The following code was excerpted from: mmasep.f
C
SUBROUTINE MMASEP(ANGTOL,XC,YC,INDPVL,IANG,V,W,I1,I2)
IMPLICIT LOGICAL (A-Z)
INTEGER I1,I2,INDPVL(0:*),V(2),W(2)
DOUBLE PRECISION ANGTOL,IANG(*),XC(0:*),YC(0:*)
C
C Written and copyright by:
C Barry Joe, Dept. of Computing Science, Univ. of Alberta
C Edmonton, Alberta, Canada T6G 2H1
C Phone: (403) 492-5757 Email: barry@cs.ualberta.ca
C
C Purpose: Find best of four possible separators according to
C max-min angle criterion.
C
C Input parameters:
C ANGTOL - angle tolerance parameter (in radians) for accepting
C separator
C XC(0:NVRT),YC(0:NVRT) - coordinates of polygon vertices in
C CCW order where NVRT is number of vertices;
C (XC(0),YC(0)) = (XC(NVRT),YC(NVRT))
C INDPVL(0:NVRT) - indices in PVL of vertices; INDPVL(I) = -K if
C (XC(I),YC(I)) is extra vertex inserted on edge from
C K to PVL(SUCC,K)
C IANG(1:*) - interior angle array
C V(1:2),W(1:2) - indices in XC, YC in range 0 to NVRT-1; four
C possible separators are V(I),W(J), I,J = 1,2
C
C Output parameters:
C I1,I2 - indices in range 0 to NVRT-1 of best separator
C according to max-min angle criterion; I1 = -1
C if no satisfactory separator is found
C
C Routines called:
C ANGLE
C
DOUBLE PRECISION PI,TOL
COMMON /GCONST/ PI,TOL
SAVE /GCONST/
C
INTEGER I,J,K,L,M
DOUBLE PRECISION ALPHA,ANGLE,ANGMAX,ANGMIN,BETA,DELTA,GAMMA
C
ANGMAX = 0.0D0
DO 20 I = 1,2
L = V(I)
K = INDPVL(L)
IF (K .GT. 0) THEN
ALPHA = IANG(K)
ELSE
ALPHA = PI
ENDIF
DO 10 J = 1,2
M = W(J)
IF (L .EQ. M) GO TO 10
K = INDPVL(M)
IF (K .GT. 0) THEN
BETA = IANG(K)
ELSE
BETA = PI
ENDIF
GAMMA = ANGLE(XC(M),YC(M),XC(L),YC(L),XC(L+1),YC(L+1))
DELTA = ANGLE(XC(L),YC(L),XC(M),YC(M),XC(M+1),YC(M+1))
ANGMIN = MIN(GAMMA,ALPHA-GAMMA,DELTA,BETA-DELTA)
IF (ANGMIN .GT. ANGMAX) THEN
ANGMAX = ANGMIN
I1 = L
I2 = M
ENDIF
10 CONTINUE
20 CONTINUE
IF (ANGMAX .LT. ANGTOL) I1 = -1
END
C
C The following code was excerpted from: prmdf2.f
C
SUBROUTINE PRMDF2(IPOLY,WSQ,IVRT,XIVRT,EDGVAL,VRTVAL,NEV,IFV,
$ LISTEV)
IMPLICIT LOGICAL (A-Z)
INTEGER IFV,IPOLY,IVRT(*),LISTEV(*),NEV,XIVRT(*)
DOUBLE PRECISION EDGVAL(*),VRTVAL(*),WSQ
C
C Written and copyright by:
C Barry Joe, Dept. of Computing Science, Univ. of Alberta
C Edmonton, Alberta, Canada T6G 2H1
C Phone: (403) 492-5757 Email: barry@cs.ualberta.ca
C
C Purpose: Preprocessing step for evaluating mesh distribution
C function in polygon IPOLY - the edges and vertices for
C which distances must be computed are determined.
C
C Input parameters:
C IPOLY - index of polygon
C WSQ - square of width of polygon IPOLY
C IVRT(1:*) - indices of polygon vertices in VCL, ordered by
C polygon
C XIVRT(1:*) - pointer to first vertex of each polygon in IVRT;
C vertices of polygon IPOLY are IVRT(I) for I from
C XIVRT(IPOLY) to XIVRT(IPOLY+1)-1
C EDGVAL(1:*) - value associated with each edge of decomp.
C VRTVAL(1:*) - value associated with each vertex of decomp.
C
C Output parameters:
C NEV - number of edges and vertices for which distances must
C be evaluated
C IFV - index of first vertex XIVRT(IPOLY) if LISTEV(NEV)
C = XIVRT(IPOLY+1) - 1; 0 otherwise
C LISTEV(1:*) - array of length <= [XIVRT(IPOLY+1)-XIVRT(IPOLY)]
C *2 containing indices of edges and vertices mentioned
C above; indices of vertices are negated
C
INTEGER I,IM1,J,L
C
IFV = 0
NEV = 0
IM1 = XIVRT(IPOLY+1) - 1
L = IM1
DO 10 I = XIVRT(IPOLY),L
J = IVRT(I)
IF (VRTVAL(J) .LT. MIN(EDGVAL(I),EDGVAL(IM1))) THEN
NEV = NEV + 1
LISTEV(NEV) = -J
ENDIF
IF (EDGVAL(I) .LT. WSQ) THEN
NEV = NEV + 1
LISTEV(NEV) = I
ENDIF
IM1 = I
10 CONTINUE
IF (NEV .GT. 0) THEN
IF (LISTEV(NEV) .EQ. L) IFV = XIVRT(IPOLY)
ENDIF
END
C
C The following code was excerpted from: sepmdf.f
C
SUBROUTINE SEPMDF(ANGTOL,NVRT,XC,YC,ARPOLY,MEAN,MDFTR,INDPVL,
$ IANG,I1,I2)
IMPLICIT LOGICAL (A-Z)
INTEGER I1,I2,NVRT
INTEGER INDPVL(0:NVRT)
DOUBLE PRECISION ANGTOL,ARPOLY,MEAN
DOUBLE PRECISION IANG(*),MDFTR(0:NVRT-1),XC(0:NVRT),YC(0:NVRT)
C
C Written and copyright by:
C Barry Joe, Dept. of Computing Science, Univ. of Alberta
C Edmonton, Alberta, Canada T6G 2H1
C Phone: (403) 492-5757 Email: barry@cs.ualberta.ca
C
C Purpose: Determine separator to split convex polygon into two
C parts based on mesh distribution function.
C
C Input parameters:
C ANGTOL - angle tolerance parameter (in radians)
C NVRT - number of vertices in polygon
C XC(0:NVRT),YC(0:NVRT) - coordinates of polygon vertices in
C CCW order, translated so that centroid is at origin;
C (XC(0),YC(0)) = (XC(NVRT),YC(NVRT))
C ARPOLY - area of polygon
C MEAN - mean mdf value in polygon
C MDFTR(0:NVRT-1) - mean mdf value in each triangle of polygon;
C triangles are determined by polygon vertices and centroid
C INDPVL(0:NVRT) - indices in PVL of vertices; INDPVL(I) = -K if
C (XC(I),YC(I)) is extra vertex inserted on edge from
C K to PVL(SUCC,K)
C IANG(1:*) - interior angle array
C
C Output parameters:
C I1,I2 - indices in range 0 to NVRT-1 of best separator
C according to mdf and max-min angle criterion; I1 = -1
C if no satisfactory separator is found
C
C Routines called:
C ANGLE, MMASEP
C
DOUBLE PRECISION PI,TOL
COMMON /GCONST/ PI,TOL
SAVE /GCONST/
C
INTEGER HI,I,L,M,V(2),W(2)
DOUBLE PRECISION ANGLE,AREATR,SUM
C
C Determine triangle with highest mean mesh density; then determine
C triangles adjacent to this triangle with mesh density >= MEAN
C such that the area of these triangles is <= ARPOLY/2.
C Note that twice the triangle area is computed.
C
HI = 0
DO 10 I = 1,NVRT-1
IF (MDFTR(I) .GT. MDFTR(HI)) HI = I
10 CONTINUE
SUM = XC(HI)*YC(HI+1) - XC(HI+1)*YC(HI)
L = HI - 1
IF (L .LT. 0) L = NVRT - 1
M = HI + 1
IF (M .GE. NVRT) M = 0
20 CONTINUE
IF (MDFTR(L) .GE. MDFTR(M)) THEN
I = L
ELSE
I = M
ENDIF
IF (MDFTR(I) .LT. MEAN) GO TO 30
AREATR = XC(I)*YC(I+1) - XC(I+1)*YC(I)
SUM = SUM + AREATR
IF (SUM .GT. ARPOLY) GO TO 30
IF (I .EQ. L) THEN
L = L - 1
IF (L .LT. 0) L = NVRT - 1
ELSE
M = M + 1
IF (M .GE. NVRT) M = 0
ENDIF
GO TO 20
30 CONTINUE
L = L + 1
IF (L .GE. NVRT) L = 0
C
C Interchange role of L and M depending on angle determined by
C (XC(M),YC(M)), (0,0), and (XC(L),YC(L)).
C Possible separators are L,M; L,M+1; L+1,M; L+1,M+1.
C
IF (ANGLE(XC(M),YC(M),0.0D0,0.0D0,XC(L),YC(L)) .GT. PI) THEN
I = L
L = M
M = I
ENDIF
V(1) = L
V(2) = L - 1
IF (V(2) .LT. 0) V(2) = NVRT - 1
W(1) = M
W(2) = M + 1
IF (W(2) .GE. NVRT) W(2) = 0
CALL MMASEP(ANGTOL,XC,YC,INDPVL,IANG,V,W,I1,I2)
END
C
C The following code was excerpted from: sepshp.f
C
SUBROUTINE SEPSHP(ANGTOL,NVRT,XC,YC,INDPVL,IANG,I1,I2,WK)
IMPLICIT LOGICAL (A-Z)
INTEGER I1,I2,NVRT
INTEGER INDPVL(0:NVRT)
DOUBLE PRECISION ANGTOL,IANG(*),WK(2*NVRT),XC(0:NVRT),YC(0:NVRT)
C
C Written and copyright by:
C Barry Joe, Dept. of Computing Science, Univ. of Alberta
C Edmonton, Alberta, Canada T6G 2H1
C Phone: (403) 492-5757 Email: barry@cs.ualberta.ca
C
C Purpose: Determine separator to split convex polygon into two
C parts based on shape (diameter) of polygon.
C
C Input parameters:
C ANGTOL - angle tolerance parameter (in radians)
C NVRT - number of vertices in polygon
C XC(0:NVRT), YC(0:NVRT) - coordinates of polygon vertices in
C CCW order, translated so that centroid is at origin;
C (XC(0),YC(0)) = (XC(NVRT),YC(NVRT))
C INDPVL(0:NVRT) - indices in PVL of vertices; INDPVL(I) = -K if
C (XC(I),YC(I)) is extra vertex inserted on edge from
C K to PVL(SUCC,K)
C IANG(1:*) - interior angle array
C
C Output parameters:
C I1,I2 - indices in range 0 to NVRT-1 of best separator
C according to shape and max-min angle criterion; I1 = -1
C if no satisfactory separator is found
C
C Working parameters:
C WK(1:2*NVRT) - space for two working arrays of length NVRT
C
C Abnormal return:
C IERR is set to 200
C
C Routines called:
C DIAM2, MMASEP
C
INTEGER IERR
DOUBLE PRECISION PI,TOL
COMMON /GERROR/ IERR
COMMON /GCONST/ PI,TOL
SAVE /GERROR/,/GCONST/
C
INTEGER I,K,N,V(2),W(2)
DOUBLE PRECISION DIST,DX,DY,PIMTOL,XA,YA
C
C Determine diameter of polygon. Possible separators endpoints (two
C on each side of polygon) are nearest to perpendicular bisector of
C diameter. (XA,YA) and (XA+DX,YA+DY) are on bisector. Distance to
C bisector is proportional to two times triangle area.
C
PIMTOL = PI - TOL
N = 0
DO 10 I = 0,NVRT-1
K = INDPVL(I)
IF (K .GT. 0) THEN
IF (IANG(K) .LT. PIMTOL) THEN
N = N + 1
WK(N) = XC(I)
WK(N+NVRT) = YC(I)
ENDIF
ENDIF
10 CONTINUE
CALL DIAM2(N,WK,WK(NVRT+1),I1,I2,DIST)
IF (IERR .NE. 0) RETURN
IF (I1 .GT. I2) THEN
I = I1
I1 = I2
I2 = I
ENDIF
DX = WK(I2+NVRT) - WK(I1+NVRT)
DY = WK(I1) - WK(I2)
XA = 0.5D0*(WK(I1) + WK(I2) - DX)
YA = 0.5D0*(WK(I1+NVRT) + WK(I2+NVRT) - DY)
C
I = I1 - 1
20 CONTINUE
IF (XC(I) .EQ. WK(I1) .AND. YC(I) .EQ. WK(I1+NVRT)) THEN
I1 = I
ELSE
I = I + 1
GO TO 20
ENDIF
I = MAX(I2-1,I1+1)
30 CONTINUE
IF (XC(I) .EQ. WK(I2) .AND. YC(I) .EQ. WK(I2+NVRT)) THEN
I2 = I
ELSE
I = I + 1
GO TO 30
ENDIF
I = I1 + 1
40 CONTINUE
DIST = DX*(YC(I) - YA) - DY*(XC(I) - XA)
IF (DIST .GE. 0.0D0) THEN
V(1) = I - 1
V(2) = I
ELSE
I = I + 1
GO TO 40
ENDIF
I = I2 + 1
50 CONTINUE
IF (I .GE. NVRT) I = 0
DIST = DX*(YC(I) - YA) - DY*(XC(I) - XA)
IF (DIST .LE. 0.0D0) THEN
W(1) = I - 1
W(2) = I
IF (I .LE. 0) W(1) = NVRT - 1
ELSE
I = I + 1
GO TO 50
ENDIF
CALL MMASEP(ANGTOL,XC,YC,INDPVL,IANG,V,W,I1,I2)
END
C
C The following code was excerpted from: sfdwmf.f
C
SUBROUTINE SFDWMF(L,R,PSI,INDP,LOCH)
IMPLICIT LOGICAL (A-Z)
INTEGER L,R
INTEGER INDP(R),LOCH(*)
DOUBLE PRECISION PSI(*)
C
C Written and copyright by:
C Barry Joe, Dept. of Computing Science, Univ. of Alberta
C Edmonton, Alberta, Canada T6G 2H1
C Phone: (403) 492-5757 Email: barry@cs.ualberta.ca
C
C Purpose: Sift PSI(INDP(L)) down heap which has maximum PSI value
C at root of heap and is maintained by pointers in INDP.
C
C Input parameters:
C L - element of heap to be sifted down
C R - upper bound of heap
C PSI(1:*) - key values for heap
C INDP(1:R) - indices of PSI which are maintained in heap
C LOCH(1:*) - location of indices in heap (inverse of INDP)
C
C Updated parameters:
C INDP,LOCH
C
INTEGER I,J,K
DOUBLE PRECISION T
C
I = L
J = 2*I
K = INDP(I)
T = PSI(K)
10 CONTINUE
IF (J .GT. R) GO TO 20
IF (J .LT. R) THEN
IF (PSI(INDP(J)) .LT. PSI(INDP(J+1))) J = J + 1
ENDIF
IF (T .GE. PSI(INDP(J))) GO TO 20
INDP(I) = INDP(J)
LOCH(INDP(I)) = I
I = J
J = 2*I
GO TO 10
20 CONTINUE
INDP(I) = K
LOCH(K) = I
END
C
C The following code was excerpted from: sfupmf.f
C
SUBROUTINE SFUPMF(R,PSI,INDP,LOCH)
IMPLICIT LOGICAL (A-Z)
INTEGER R
INTEGER INDP(R),LOCH(*)
DOUBLE PRECISION PSI(*)
C
C Written and copyright by:
C Barry Joe, Dept. of Computing Science, Univ. of Alberta
C Edmonton, Alberta, Canada T6G 2H1
C Phone: (403) 492-5757 Email: barry@cs.ualberta.ca
C
C Purpose: Sift PSI(INDP(R)) up heap which has maximum PSI value
C at root of heap and is maintained by pointers in INDP.
C
C Input parameters:
C R - element of heap to be sifted up
C PSI(1:*) - key values for heap
C INDP(1:R) - indices of PSI which are maintained in heap
C LOCH(1:*) - location of indices in heap (inverse of INDP)
C
C Updated parameters:
C INDP,LOCH
C
INTEGER I,J,K
DOUBLE PRECISION T
C
I = R
J = INT(I/2)
K = INDP(I)
T = PSI(K)
10 CONTINUE
IF (I .LE. 1) GO TO 20
IF (T .LE. PSI(INDP(J))) GO TO 20
INDP(I) = INDP(J)
LOCH(INDP(I)) = I
I = J
J = INT(I/2)
GO TO 10
20 CONTINUE
INDP(I) = K
LOCH(K) = I
END
C
C The following code was excerpted from: trisiz.f
C
SUBROUTINE TRISIZ(NTRID,NPOLG,HVL,PVL,AREA,PSI,H,INDP,LOCH)
IMPLICIT LOGICAL (A-Z)
INTEGER NPOLG,NTRID
INTEGER HVL(NPOLG),INDP(NPOLG),LOCH(NPOLG),PVL(4,*)
DOUBLE PRECISION AREA(NPOLG),H(NPOLG),PSI(NPOLG)
C
C Written and copyright by:
C Barry Joe, Dept. of Computing Science, Univ. of Alberta
C Edmonton, Alberta, Canada T6G 2H1
C Phone: (403) 492-5757 Email: barry@cs.ualberta.ca
C
C Purpose: Smooth PSI (mean mesh distribution function) values using
C heap so that they differ by a factor of at most 4 in adjacent
C polygons and then compute triangle sizes for each polygon.
C
C Input parameters:
C NTRID - desired number of triangles in mesh
C NPOLG - number of polygons or positions used in HVL array
C HVL(1:NPOLG) - head vertex list
C PVL(1:4,1:*) - polygon vertex list
C AREA(1:NPOLG) - area of convex polygons in decomposition
C PSI(1:NPOLG) - mean mdf values in the convex polygons
C
C Updated parameters:
C PSI(1:NPOLG) - values are 'smoothed' on output
C
C Output parameters:
C H(1:NPOLG) - triangle size for convex polygons
C
C Working parameters:
C INDP(1:NPOLG) - indices of polygon or PSI which are maintained
C in heap according to PSI values
C LOCH(1:NPOLG) - location of polygon indices in heap
C
C Routines called:
C SFDWMF, SFUPMF
C
INTEGER EDGV,LOC,POLG,SUCC
PARAMETER (LOC = 1, POLG = 2, SUCC = 3, EDGV = 4)
C
INTEGER I,J,K,L,R
DOUBLE PRECISION FACTOR,SUM
C
FACTOR = 0.25D0
DO 10 I = 1,NPOLG
INDP(I) = I
LOCH(I) = I
10 CONTINUE
K = INT(NPOLG/2)
DO 20 L = K,1,-1
CALL SFDWMF(L,NPOLG,PSI,INDP,LOCH)
20 CONTINUE
DO 40 R = NPOLG,2,-1
J = INDP(1)
INDP(1) = INDP(R)
LOCH(INDP(1)) = 1
CALL SFDWMF(1,R-1,PSI,INDP,LOCH)
I = HVL(J)
30 CONTINUE
K = PVL(EDGV,I)
IF (K .GT. 0) THEN
K = PVL(POLG,K)
IF (PSI(K) .LT. PSI(J)*FACTOR) THEN
PSI(K) = PSI(J)*FACTOR
CALL SFUPMF(LOCH(K),PSI,INDP,LOCH)
ENDIF
ENDIF
I = PVL(SUCC,I)
IF (I .NE. HVL(J)) GO TO 30
40 CONTINUE
C
SUM = 0.0D0
DO 50 I = 1,NPOLG
SUM = SUM + PSI(I)*AREA(I)
50 CONTINUE
FACTOR = 2.0D0/DBLE(NTRID)
DO 60 I = 1,NPOLG
PSI(I) = PSI(I)/SUM
H(I) = SQRT(FACTOR/PSI(I))
60 CONTINUE
END
C
C The following code was excerpted from: umdf2.f
C
DOUBLE PRECISION FUNCTION UMDF2(X,Y)
IMPLICIT LOGICAL (A-Z)
DOUBLE PRECISION X,Y
C
C Purpose: Dummy user-supplied mesh distribution function which
C is provided if heuristic mesh distribution function is used.
C
C Input parameters:
C X,Y - coordinates of 2-D point
C
C Returned function value:
C UMDF2 - mesh distribution function value at (X,Y)
C
UMDF2 = 1.0D0
END
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