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C
C The following code was excerpted from: bedgmv.f
C
SUBROUTINE BEDGMV(NVC,NPOLG,NVERT,MAXVC,H,VCL,HVL,PVL,VSTART,VNUM)
IMPLICIT LOGICAL (A-Z)
INTEGER MAXVC,NPOLG,NVC,NVERT
INTEGER HVL(NPOLG),PVL(4,NVERT),VSTART(NVERT),VNUM(NVERT)
DOUBLE PRECISION H(NPOLG),VCL(2,MAXVC)
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: Generate mesh vertices on boundary of convex polygons
C of decomposition with spacing determined by H array.
C
C Input parameters:
C NVC - number of coordinates or positions used in VCL array
C NPOLG - number of polygons or positions used in HVL array
C NVERT - number of vertices or positions used in PVL array
C MAXVC - maximum size available for VCL array
C H(1:NPOLG) - spacing of mesh vertices for convex polygons
C VCL(1:2,1:NVC) - vertex coordinate list
C HVL(1:NPOLG) - head vertex list
C PVL(1:4,1:NVERT) - polygon vertex list
C
C Updated parameters:
C NVC,VCL
C
C Output parameters:
C VSTART(1:NVERT) - start location in VCL for mesh vertices on
C each edge in PVL if there are any, else 0
C VNUM(1:NVERT) - number of mesh vertices on interior of each
C edge in PVL; entry is negated if mesh vertices are
C listed in backward order in VCL
C
C Abnormal return:
C IERR is set to 3
C
INTEGER IERR
COMMON /GERROR/ IERR
SAVE /GERROR/
C
INTEGER EDGV,LOC,POLG,SUCC
PARAMETER (LOC = 1, POLG = 2, SUCC = 3, EDGV = 4)
C
INTEGER I,IA,J,K,L,M,U,V
DOUBLE PRECISION DX,DY,HH,LENG,X,Y
C
DO 10 I = 1,NVERT
VSTART(I) = -1
10 CONTINUE
DO 40 K = 1,NPOLG
I = HVL(K)
20 CONTINUE
J = PVL(SUCC,I)
IF (VSTART(I) .EQ. -1) THEN
U = PVL(LOC,I)
V = PVL(LOC,J)
X = VCL(1,U)
Y = VCL(2,U)
LENG = SQRT((VCL(1,V) - X)**2 + (VCL(2,V) - Y)**2)
IA = PVL(EDGV,I)
IF (IA .LE. 0) THEN
HH = H(K)
ELSE
HH = SQRT(H(K)*H(PVL(POLG,IA)))
ENDIF
L = INT(LENG/HH)
IF (LENG/HH - L .GT. DBLE(L)/DBLE(2*L+1)) L = L + 1
IF (L .LE. 1) THEN
VSTART(I) = 0
VNUM(I) = 0
ELSE
DX = (VCL(1,V) - X)/DBLE(L)
DY = (VCL(2,V) - Y)/DBLE(L)
L = L - 1
IF (NVC + L .GT. MAXVC) THEN
IERR = 3
RETURN
ENDIF
VSTART(I) = NVC + 1
VNUM(I) = L
DO 30 M = 1,L
X = X + DX
Y = Y + DY
NVC = NVC + 1
VCL(1,NVC) = X
VCL(2,NVC) = Y
30 CONTINUE
ENDIF
IF (IA .GT. 0) THEN
VSTART(IA) = VSTART(I)
VNUM(IA) = -VNUM(I)
ENDIF
ENDIF
I = J
IF (I .NE. HVL(K)) GO TO 20
40 CONTINUE
END
C
C The following code was excerpted from: cvdtri.f
C
SUBROUTINE CVDTRI(INTER,LDV,NT,VCL,TIL,TEDG,SPTR)
IMPLICIT LOGICAL (A-Z)
LOGICAL INTER
INTEGER LDV,NT
INTEGER SPTR(NT),TEDG(3,NT),TIL(3,NT)
DOUBLE PRECISION VCL(LDV,*)
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: Convert triangles in strip near boundary of polygon
C or inside polygon to Delaunay triangles.
C
C Input parameters:
C INTER - .TRUE. iff at least one interior mesh vertex
C LDV - leading dimension of VCL in calling routine
C NT - number of triangles in strip or polygon
C VCL(1:2,1:*) - vertex coordinate list
C TIL(1:3,1:NT) - triangle incidence list
C TEDG(1:3,1:NT) - TEDG(J,I) refers to edge with vertices
C TIL(J:J+1,I) and contains index of merge edge or
C > NT for edge of chains
C
C Updated parameters:
C TIL,TEDG - updated due to diagonal edge swaps
C
C Working parameter:
C SPTR(1:NT) - SPTR(I) = -1 if merge edge I is not in LOP stack,
C else >= 0 and pointer (index of SPTR) to next edge in
C stack (0 indicates bottom of stack)
C
C Abnormal return:
C IERR is set to 231
C
C Routines called:
C FNDTRI, LOP
C
INTEGER IERR
COMMON /GERROR/ IERR
SAVE /GERROR/
C
INTEGER E,IND(2),ITR(2),K,MXTR,TOP
LOGICAL SFLAG
C
SFLAG = .TRUE.
DO 10 K = 1,NT
SPTR(K) = -1
10 CONTINUE
DO 30 K = 1,NT
MXTR = K + 1
IF (K .EQ. NT) THEN
IF (.NOT. INTER) RETURN
MXTR = NT
SFLAG = .FALSE.
ENDIF
TOP = K
SPTR(K) = 0
20 CONTINUE
E = TOP
TOP = SPTR(E)
CALL FNDTRI(E,MXTR,SFLAG,TEDG,ITR,IND)
IF (IERR .NE. 0) RETURN
CALL LOP(ITR,IND,K,TOP,LDV,VCL,TIL,TEDG,SPTR)
IF (TOP .GT. 0) GO TO 20
30 CONTINUE
END
C
C The following code was excerpted from: fndtri.f
C
SUBROUTINE FNDTRI(IEDG,MXTR,SFLAG,TEDG,ITR,IND)
IMPLICIT LOGICAL (A-Z)
LOGICAL SFLAG
INTEGER IEDG,IND(2),ITR(2),MXTR,TEDG(3,MXTR)
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 two triangles containing edge with index IEDG
C in array TEDG.
C
C Input parameters:
C IEDG - index of edge to be searched in TEDG
C MXTR - maximum index of triangle to be searched in TEDG
C SFLAG - .TRUE. iff second triangle is to be searched from
C end of array
C TEDG(1:3,1:MXTR) - triangle edge indices; see routine CVDTRI
C
C Output parameters:
C ITR(1:2),IND(1:2) - indices such that IEDG =
C TEDG(IND(1),ITR(1)) = TEDG(IND(2),ITR(2))
C
C Abnormal return:
C IERR is set to 231
C
INTEGER IERR
COMMON /GERROR/ IERR
SAVE /GERROR/
C
INTEGER I,J,K
C
C Search from end of array TEDG.
C
K = 1
J = 1
I = MXTR
10 CONTINUE
IF (TEDG(J,I) .NE. IEDG) THEN
J = J + 1
IF (J .GT. 3) THEN
J = 1
I = I - 1
IF (I .LE. 0) THEN
IERR = 231
RETURN
ENDIF
ENDIF
GO TO 10
ENDIF
ITR(K) = I
IND(K) = J
IF (K .EQ. 2) RETURN
K = 2
IF (SFLAG) THEN
J = 1
I = I - 1
IF (I .LE. 0) THEN
IERR = 231
RETURN
ENDIF
GO TO 10
ENDIF
C
C Search from beginning of array TEDG for second triangle.
C
J = 1
I = 1
20 CONTINUE
IF (I .GE. ITR(1)) THEN
IERR = 231
RETURN
ENDIF
30 CONTINUE
IF (TEDG(J,I) .NE. IEDG) THEN
J = J + 1
IF (J .GT. 3) THEN
J = 1
I = I + 1
GO TO 20
ELSE
GO TO 30
ENDIF
ENDIF
ITR(2) = I
IND(2) = J
END
C
C The following code was excerpted from: inttri.f
C
SUBROUTINE INTTRI(NVRT,XC,YC,H,IBOT,COSTH,SINTH,LDV,NVC,NTRI,
$ MAXVC,MAXTI,MAXCW,VCL,TIL,NCW,CWALK)
IMPLICIT LOGICAL (A-Z)
INTEGER IBOT,LDV,MAXCW,MAXTI,MAXVC,NCW,NTRI,NVC,NVRT
INTEGER CWALK(0:MAXCW),TIL(3,MAXTI)
DOUBLE PRECISION COSTH,H,SINTH
DOUBLE PRECISION VCL(LDV,MAXVC),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: Generate triangles inside convex polygon using quasi-
C uniform grid of spacing H. It is assumed that diameter of
C polygon is parallel to y-axis.
C
C Input parameters:
C NVRT - number of vertices on the boundary of convex polygon
C XC(0:NVRT),YC(0:NVRT) - vertex coordinates in CCW order;
C (XC(0),YC(0)) = (XC(NVRT),YC(NVRT))
C H - spacing of mesh vertices in polygon
C IBOT - index of bottom vertex; diameter contains vertices
C (XC(0),YC(0)) and (XC(IBOT),YC(IBOT))
C COSTH,SINTH - COS(THETA), SIN(THETA) where THETA in [-PI,PI]
C is rotation angle to get diameter parallel to y-axis
C LDV - leading dimension of VCL in calling routine
C NVC - number of coordinates or positions used in VCL array
C NTRI - number of triangles or positions used in TIL
C MAXVC - maximum size available for VCL array
C MAXTI - maximum size available for TIL array
C MAXCW - maximum size available for CWALK array; assumed to be
C >= 6*(1 + INT((YC(0) - YC(IBOT))/H))
C VCL(1:2,1:NVC) - vertex coordinate list
C TIL(1:3,1:NTRI) - triangle incidence list
C
C Updated parameters:
C NVC,NTRI,VCL,TIL
C
C Output parameters:
C NCW - number of mesh vertices in closed walk, except NCW = 0
C for 1 vertex
C CWALK(0:NCW) - indices in VCL of mesh vertices of closed
C walk; CWALK(0) = CWALK(NCW)
C
C Abnormal return:
C IERR is set to 3, 9, or 10
C
INTEGER IERR
DOUBLE PRECISION PI,TOL
COMMON /GERROR/ IERR
COMMON /GCONST/ PI,TOL
SAVE /GERROR/,/GCONST/
C
INTEGER I,IL,IM1L,IM1R,IR,J,K,L,L0,L1,LW,M,N,P,R,R0,R1,RW
DOUBLE PRECISION A,B,CY,SY,X,XJ,XK,XL,XM1L,XM1R,XR,Y
C
IL = 0
IM1L = 0
IM1R = 0
IR = 0
LW = 0
M = 0
RW = 0
XM1L = 0.0
XM1R = 0.0
N = INT((YC(0) - YC(IBOT))/H)
Y = YC(0) - 0.5D0*(YC(0) - YC(IBOT) - DBLE(N)*H)
L = 0
R = NVRT
DO 110 I = 0,N
C
C Determine left and right x-coordinates of polygon for
C scan line with y-coordinate Y, and generate mesh vertices.
C
10 CONTINUE
IF (YC(L+1) .GT. Y) THEN
L = L + 1
GO TO 10
ENDIF
20 CONTINUE
IF (YC(R-1) .GT. Y) THEN
R = R - 1
GO TO 20
ENDIF
XL = XC(L) + (XC(L+1) - XC(L))*(Y - YC(L))/(YC(L+1) - YC(L))
XR = XC(R) + (XC(R-1) - XC(R))*(Y - YC(R))/(YC(R-1) - YC(R))
M = INT((XR - XL)/H)
X = XL + 0.5D0*(XR - XL - DBLE(M)*H)
IF (NVC + M + 1 .GT. MAXVC) THEN
IERR = 3
RETURN
ENDIF
CY = COSTH*Y
SY = SINTH*Y
IL = NVC + 1
XL = X
DO 30 J = 0,M
NVC = NVC + 1
VCL(1,NVC) = COSTH*X + SY
VCL(2,NVC) = CY - SINTH*X
X = X + H
30 CONTINUE
IR = NVC
XR = X - H
IF (N .EQ. 0) THEN
NCW = 0
CWALK(0) = NVC
RETURN
ELSE IF (I .EQ. 0) THEN
LW = 0
CWALK(LW) = IL
RW = MAXCW + 1
DO 40 J = IL,IR
RW = RW - 1
CWALK(RW) = J
40 CONTINUE
GO TO 100
ENDIF
C
C Generate triangles between scan lines Y+H and Y.
C
A = MAX(XL,XM1L)
B = MIN(XR,XM1R)
IF (XM1L .EQ. A) THEN
L0 = IM1L
X = (XM1L - XL)/H
J = INT(X + TOL)
IF (ABS(X - DBLE(J)) .LE. TOL) J = J - 1
IF (J .LT. 0) J = 0
L1 = IL + J
ELSE
L1 = IL
X = (XL - XM1L)/H
J = INT(X + TOL)
IF (ABS(X - DBLE(J)) .LE. TOL) J = J - 1
IF (J .LT. 0) J = 0
L0 = IM1L + J
ENDIF
IF (XM1R .EQ. B) THEN
R0 = IM1R
X = (XR - XM1R)/H
J = INT(X + TOL)
IF (ABS(X - DBLE(J)) .LE. TOL) J = J - 1
IF (J .LT. 0) J = 0
R1 = IR - J
ELSE
R1 = IR
X = (XM1R - XR)/H
J = INT(X + TOL)
IF (ABS(X - DBLE(J)) .LE. TOL) J = J - 1
IF (J .LT. 0) J = 0
R0 = IM1R - J
ENDIF
IF (L0 .LT. R0 .OR. L1 .LT. R1) THEN
J = L0
K = L1
XJ = XM1L + DBLE(J-IM1L)*H
XK = XL + DBLE(K-IL)*H
50 CONTINUE
IF (K .LT. R1 .AND. (XK .LE. XJ .OR. J .EQ. R0)) THEN
P = K
K = K + 1
XK = XK + H
ELSE
P = J
J = J + 1
XJ = XJ + H
ENDIF
NTRI = NTRI + 1
IF (NTRI .GT. MAXTI) THEN
IERR = 9
RETURN
ENDIF
TIL(1,NTRI) = J
TIL(2,NTRI) = P
TIL(3,NTRI) = K
IF (J .LT. R0 .OR. K .LT. R1) GO TO 50
ENDIF
C
C Generate paths of closed walk between scan lines Y+H and Y.
C
IF (XM1L .LT. XL) THEN
DO 60 J = IM1L+1,L0
LW = LW + 1
CWALK(LW) = J
60 CONTINUE
LW = LW + 1
CWALK(LW) = IL
ELSE
DO 70 J = L1,IL,-1
LW = LW + 1
CWALK(LW) = J
70 CONTINUE
ENDIF
IF (XM1R .GT. XR) THEN
DO 80 J = IM1R-1,R0,-1
RW = RW - 1
CWALK(RW) = J
80 CONTINUE
RW = RW - 1
CWALK(RW) = IR
ELSE
DO 90 J = R1,IR
RW = RW - 1
CWALK(RW) = J
90 CONTINUE
ENDIF
100 CONTINUE
Y = Y - H
IM1L = IL
IM1R = IR
XM1L = XL
XM1R = XR
110 CONTINUE
C
C Add last path of left walk and shift indices of right walk.
C
IF (M .EQ. 0) THEN
RW = RW + 1
ELSE
DO 120 J = IL+1,IR-1
LW = LW + 1
CWALK(LW) = J
120 CONTINUE
ENDIF
IF (RW .LE. LW) THEN
IERR = 10
RETURN
ENDIF
DO 130 J = RW,MAXCW
LW = LW + 1
CWALK(LW) = CWALK(J)
130 CONTINUE
NCW = LW
END
C
C The following code was excerpted from: lop.f
C
SUBROUTINE LOP(ITR,IND,MXEDG,TOP,LDV,VCL,TIL,TEDG,SPTR)
IMPLICIT LOGICAL (A-Z)
INTEGER IND(2),ITR(2),LDV,MXEDG,TOP
INTEGER SPTR(*),TEDG(3,*),TIL(3,*)
DOUBLE PRECISION VCL(LDV,*)
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: Apply local optimization procedure to two triangles
C indicated by ITR(1) and ITR(2). This may result in swapping
C diagonal edge of quadrilateral.
C
C Input parameters:
C ITR(1),ITR(2) - indices of triangles for LOP
C IND(1),IND(2) - indices indicating common edge of triangles
C MXEDG - maximum index of edge to be considered for LOP
C TOP - index of SPTR indicating top of stack
C LDV - leading dimension of VCL in calling routine
C VCL(1:2,1:*) - vertex coordinate list
C TIL(1:3,1:*) - triangle incidence list
C TEDG(1:3,1:*) - triangle edge indices; see routine CVDTRI
C SPTR(1:*) - stack pointers; see routine CVDTRI
C
C Updated parameters:
C TOP,TIL,TEDG,SPTR - updated due diagonal edge swaps
C
C Routines called:
C DIAEDG
C
INTEGER A,B,C,D,DIAEDG,I,IEDG,IN,IND1M1,IND1P1,IND2M1,IND2P1,J
C
C Common edge is BC, other two vertices are A and D.
C
IEDG = TEDG(IND(1),ITR(1))
SPTR(IEDG) = -1
IND1M1 = IND(1) - 1
IF (IND1M1 .LE. 0) IND1M1 = 3
IND1P1 = IND(1) + 1
IF (IND1P1 .GE. 4) IND1P1 = 1
IND2M1 = IND(2) - 1
IF (IND2M1 .LE. 0) IND2M1 = 3
IND2P1 = IND(2) + 1
IF (IND2P1 .GE. 4) IND2P1 = 1
B = TIL(IND(1),ITR(1))
C = TIL(IND1P1,ITR(1))
A = TIL(IND1M1,ITR(1))
D = TIL(IND2M1,ITR(2))
IN = DIAEDG(VCL(1,D),VCL(2,D),VCL(1,C),VCL(2,C),VCL(1,A),VCL(2,A),
$ VCL(1,B),VCL(2,B))
IF (IN .EQ. 1) THEN
C
C Check if four edges of quadrilateral should be put on LOP
C stack, and swap edge BC for AD.
C
I = TEDG(IND1M1,ITR(1))
DO 10 J = 1,4
IF (J .EQ. 2) THEN
I = TEDG(IND1P1,ITR(1))
ELSE IF (J .EQ. 3) THEN
I = TEDG(IND2M1,ITR(2))
ELSE IF (J .EQ. 4) THEN
I = TEDG(IND2P1,ITR(2))
ENDIF
IF (I .LE. MXEDG) THEN
IF (SPTR(I) .EQ. -1) THEN
SPTR(I) = TOP
TOP = I
ENDIF
ENDIF
10 CONTINUE
TIL(IND1P1,ITR(1)) = D
TIL(IND2P1,ITR(2)) = A
TEDG(IND(1),ITR(1)) = TEDG(IND2P1,ITR(2))
TEDG(IND(2),ITR(2)) = TEDG(IND1P1,ITR(1))
TEDG(IND1P1,ITR(1)) = IEDG
TEDG(IND2P1,ITR(2)) = IEDG
ENDIF
END
C
C The following code was excerpted from: mtredg.f
C
SUBROUTINE MTREDG(UTYPE,I1,I2,I3,IBNDRY,NT,TIL,TEDG)
IMPLICIT LOGICAL (A-Z)
LOGICAL UTYPE
INTEGER I1,I2,I3,IBNDRY,NT
INTEGER TEDG(3,*),TIL(3,*)
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 fields for triangle as needed by routine TMERGE.
C
C Input parameters:
C UTYPE - .TRUE. iff triangle contains two 'U' vertices
C I1, I2, I3 - indices of 3 triangle vertices in VCL; the first
C 2 indices also belong to the next merge edge
C IBNDRY - index of boundary edge for TEDG
C NT - number of entries in TIL, TEDG so far
C TIL(1:NT) - triangle incidence list
C TEDG(1:NT) - triangle edge indices; see routine TMERGE
C
C Updated parameters:
C NT,TIL,TEDG - one more triangle is added at end of arrays
C
NT = NT + 1
TIL(1,NT) = I1
TIL(2,NT) = I2
TIL(3,NT) = I3
TEDG(1,NT) = NT
IF (UTYPE) THEN
TEDG(2,NT) = NT - 1
TEDG(3,NT) = IBNDRY
ELSE
TEDG(2,NT) = IBNDRY
TEDG(3,NT) = NT - 1
ENDIF
END
C
C The following code was excerpted from: rotpg.f
C
SUBROUTINE ROTPG(NVRT,XC,YC,I1,I2,IBOT,COSTH,SINTH)
IMPLICIT LOGICAL (A-Z)
INTEGER I1,I2,IBOT,NVRT
DOUBLE PRECISION COSTH,SINTH,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: Rotate convex polygon so that a line segment joining two
C of its vertices is parallel to y-axis.
C
C Input parameters:
C NVRT - number of vertices on the boundary of convex polygon
C XC(0:NVRT),YC(0:NVRT) - vertex coordinates in CCW order;
C (XC(0),YC(0)) = (XC(NVRT),YC(NVRT))
C I1,I2 - index of vertices of line segment; I1, I2 > 0
C
C Output parameters:
C XC(0:NVRT),YC(0:NVRT) - rotated vertex coordinates; indices are
C also rotated so that (XC(0),YC(0)) = (XC(NVRT),YC(NVRT))
C is top vertex and (XC(IBOT),YC(IBOT)) is bottom vertex
C IBOT - index of bottom vertex
C COSTH,SINTH - COS(THETA) and SIN(THETA) where THETA in
C [-PI,PI] is rotation angle
C
DOUBLE PRECISION PI,TOL
COMMON /GCONST/ PI,TOL
SAVE /GCONST/
C
INTEGER A,B,I,ITOP,J,K,L,M,R
DOUBLE PRECISION THETA,X0,Y0
C
ITOP = I1
IBOT = I2
IF (YC(I1) .EQ. YC(I2)) THEN
IF (XC(I1) .LT. XC(I2)) THEN
THETA = -PI/2.0D0
ELSE
THETA = PI/2.0D0
ENDIF
ELSE
IF (YC(I1) .LT. YC(I2)) THEN
ITOP = I2
IBOT = I1
ENDIF
THETA = PI/2.0D0 - ATAN2(YC(ITOP)-YC(IBOT), XC(ITOP)-XC(IBOT))
ENDIF
COSTH = COS(THETA)
SINTH = SIN(THETA)
DO 10 I = 1,NVRT
X0 = XC(I)
XC(I) = COSTH*X0 - SINTH*YC(I)
YC(I) = SINTH*X0 + COSTH*YC(I)
10 CONTINUE
C
C Rotate indices.
C
IF (ITOP .EQ. NVRT) GO TO 50
A = NVRT
B = ITOP
20 CONTINUE
R = MOD(A,B)
A = B
B = R
IF (R .GT. 0) GO TO 20
M = NVRT/A - 1
DO 40 I = 1,A
X0 = XC(I)
Y0 = YC(I)
K = I
DO 30 J = 1,M
L = K + ITOP
IF (L .GT. NVRT) L = L - NVRT
XC(K) = XC(L)
YC(K) = YC(L)
K = L
30 CONTINUE
XC(K) = X0
YC(K) = Y0
40 CONTINUE
IBOT = IBOT - ITOP
IF (IBOT .LT. 0) IBOT = IBOT + NVRT
50 CONTINUE
XC(0) = XC(NVRT)
YC(0) = YC(NVRT)
END
C
C The following code was excerpted from: tmerge.f
C
SUBROUTINE TMERGE(INTER,NBL,NCR,CHBL,CHCR,LDV,VCL,TIL,TEDG)
IMPLICIT LOGICAL (A-Z)
LOGICAL INTER
INTEGER LDV,NBL,NCR
INTEGER CHBL(0:NBL),CHCR(0:NCR),TEDG(3,NBL+NCR),TIL(3,NBL+NCR)
DOUBLE PRECISION VCL(LDV,*)
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: Form triangles in strip near boundary of polygon or
C inside polygon by merging two chains of vertices.
C
C Input parameters:
C INTER - .TRUE. iff at least one interior mesh vertex
C NBL - number of vertices on boundary cycle if INTER,
C otherwise on left boundary chain
C NCR - number of vertices on closed walk if INTER,
C otherwise on right boundary chain
C CHBL(0:NBL) - indices in VCL of vertices on boundary cycle
C or left boundary chain; if INTER, CHBL(NBL) = CHBL(0)
C CHCR(0:NCR) - indices in VCL of vertices on closed walk
C or right boundary chain; if INTER, CHCR(NCR) = CHCR(0),
C otherwise CHCR(0) is not referenced
C LDV - leading dimension of VCL in calling routine
C VCL(1:2,1:*) - vertex coordinate list
C
C Output parameters:
C TIL(1:3,1:NT) - triangle incidence list, where NT =
C NBL + NCR - K where K = 0 if INTER, else K = 2
C TEDG(1:3,1:NT) - TEDG(J,I) refers to edge with vertices
C TIL(J:J+1,I) and contains index of merge edge or
C NBL+NCR+1 for edge of chains
C [Note: It is assumed there is enough space in 2 arrays.]
C
C Abnormal return:
C IERR is set to 230
C
C Routines called:
C DIAEDG, LRLINE, MTREDG
C
INTEGER IERR
COMMON /GERROR/ IERR
SAVE /GERROR/
C
INTEGER DIAEDG,I,IBNDRY,IN,J,LRI,LRIP1,LRLINE,NL,NR,NT
DOUBLE PRECISION XI,XIP1,XJ,XJP1,YI,YIP1,YJ,YJP1
C
IBNDRY = NBL + NCR + 1
NT = 0
LRI = 0
LRIP1 = 0
IF (INTER) THEN
NL = NBL
NR = NCR
I = 0
J = 0
ELSE
CALL MTREDG(.TRUE.,CHBL(1),CHCR(1),CHBL(0),IBNDRY,NT,TIL,TEDG)
TEDG(2,1) = IBNDRY
IF (NBL + NCR .LE. 3) RETURN
NL = NBL - 1
NR = NCR - 1
I = 1
J = 1
LRI = 1
LRIP1 = 1
ENDIF
C
C Main while loop for determining next triangle and edge.
C
10 CONTINUE
IF (I .GE. NL .OR. J .GE. NR) GO TO 20
XI = VCL(1,CHBL(I))
YI = VCL(2,CHBL(I))
XIP1 = VCL(1,CHBL(I+1))
YIP1 = VCL(2,CHBL(I+1))
XJ = VCL(1,CHCR(J))
YJ = VCL(2,CHCR(J))
XJP1 = VCL(1,CHCR(J+1))
YJP1 = VCL(2,CHCR(J+1))
IN = DIAEDG(XJP1,YJP1,XJ,YJ,XI,YI,XIP1,YIP1)
IF (INTER) THEN
LRI = LRLINE(XI,YI,XJ,YJ,XJP1,YJP1,0.0D0)
LRIP1 = LRLINE(XIP1,YIP1,XJ,YJ,XJP1,YJP1,0.0D0)
ENDIF
IF (IN .LE. 0 .OR. LRI .LE. 0 .AND. LRIP1 .LE. 0) THEN
CALL MTREDG(.TRUE.,CHBL(I+1),CHCR(J),CHBL(I),IBNDRY,NT,TIL,
$ TEDG)
I = I + 1
ELSE
CALL MTREDG(.FALSE.,CHBL(I),CHCR(J+1),CHCR(J),IBNDRY,NT,TIL,
$ TEDG)
J = J + 1
ENDIF
GO TO 10
C
C Add remaining triangles at end of strip or bottom of polygon.
C
20 CONTINUE
IF (I .LT. NL) THEN
IF (.NOT. INTER .AND. J .EQ. NR) NL = NL + 1
30 CONTINUE
CALL MTREDG(.TRUE.,CHBL(I+1),CHCR(J),CHBL(I),IBNDRY,NT,TIL,
$ TEDG)
I = I + 1
IF (I .LT. NL) GO TO 30
ELSE
C J < NR .OR. I = NL = J = NR = 1
IF (.NOT. INTER .AND. I .EQ. NL) NR = NR + 1
40 CONTINUE
CALL MTREDG(.FALSE.,CHBL(I),CHCR(J+1),CHCR(J),IBNDRY,NT,TIL,
$ TEDG)
IF (INTER) THEN
LRI = LRLINE(VCL(1,CHBL(I)),VCL(2,CHBL(I)),
$ VCL(1,CHCR(J+1)),VCL(2,CHCR(J+1)),VCL(1,CHCR(J)),
$ VCL(2,CHCR(J)),0.0D0)
IF (LRI .GE. 0) THEN
IERR = 230
RETURN
ENDIF
ENDIF
J = J + 1
IF (J .LT. NR) GO TO 40
ENDIF
C
IF (INTER) THEN
IF (TEDG(2,1) .EQ. 0) THEN
TEDG(2,1) = NBL + NCR
ELSE
TEDG(3,1) = NBL + NCR
ENDIF
ENDIF
END
C
C The following code was excerpted from: tripr2.f
C
SUBROUTINE TRIPR2(NVC,NPOLG,NVERT,MAXVC,MAXTI,MAXIW,MAXWK,H,VCL,
$ HVL,PVL,IANG,NTRI,TIL,VSTART,VNUM,TSTART,IWK,WK)
IMPLICIT LOGICAL (A-Z)
INTEGER MAXIW,MAXTI,MAXVC,MAXWK,NPOLG,NTRI,NVC,NVERT
INTEGER HVL(NPOLG),IWK(MAXIW),PVL(4,NVERT),TIL(3,MAXTI)
INTEGER TSTART(NPOLG),VNUM(NVERT),VSTART(NVERT)
DOUBLE PRECISION H(NPOLG),IANG(NVERT),VCL(2,MAXVC),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: Generate mesh vertices and triangles inside each convex
C polygon of decomposition according to mesh spacings in H array
C to get a triangulation of a polygonal region.
C
C Input parameters:
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 mesh vertices in triangulation of region
C MAXTI - maximum size available for TIL array, should be >=
C number of triangles in triangulation of region
C MAXIW - maximum size available for IWK array, should be >=
C 5*(NBC+NCW)+2 where NBC is maximum number of mesh edges
C on boundary of a polygon, NCW is maximum number of edges
C on boundary of interior triangulation
C MAXWK - maximum size available for WK array, should be >=
C 5*NVRT+4 where NVRT is max no. of vertices in a polygon
C H(1:NPOLG) - mesh spacings for polygons of decomposition
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
C Updated parameters:
C NVC,VCL - updated due to generation of mesh vertices
C
C Output parameters:
C NTRI - number of triangles in triangulation of region
C TIL(1:3,1:NTRI) - triangle incidence list; TIL(1:3,I) contains
C indices in VCL of 3 vertices of Ith triangle in CCW order
C VSTART(1:NVERT) - start location in VCL for mesh vertices on
C each edge in PVL if there are any, else 0
C VNUM(1:NVERT) - number of mesh vertices on interior of each
C edge in PVL; entry is negated if mesh vertices are
C listed in backward order in VCL
C TSTART(1:NPOLG) - start location in TIL of triangles in
C each polygon; TIL(1:3,I) for I=TSTRT(K),...,TSTRT(K+1)-1
C are the triangles in Kth polygon
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, 6, 7, 9, 10, 200, 202, 230, or 231
C
C Routines called:
C BEDGMV, TRPOLG
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 BNDCYC,I,J,K,NBC,NVRT,XC,YC
DOUBLE PRECISION PIMTOL
C
NTRI = 0
PIMTOL = PI - TOL
CALL BEDGMV(NVC,NPOLG,NVERT,MAXVC,H,VCL,HVL,PVL,VSTART,VNUM)
IF (IERR .NE. 0) RETURN
DO 50 K = 1,NPOLG
NVRT = 0
NBC = 0
I = HVL(K)
10 CONTINUE
IF (IANG(I) .LT. PIMTOL) NVRT = NVRT + 1
NBC = NBC + 1 + ABS(VNUM(I))
I = PVL(SUCC,I)
IF (I .NE. HVL(K)) GO TO 10
IF (NBC + 1 .GT. MAXIW) THEN
IERR = 6
RETURN
ELSE IF (2*NVRT + 2 .GT. MAXWK) THEN
IERR = 7
RETURN
ENDIF
XC = 1
YC = XC + NVRT + 1
BNDCYC = 1
20 CONTINUE
J = PVL(LOC,I)
IF (IANG(I) .LT. PIMTOL) THEN
WK(XC) = VCL(1,J)
WK(YC) = VCL(2,J)
XC = XC + 1
YC = YC + 1
ENDIF
IWK(BNDCYC) = J
BNDCYC = BNDCYC + 1
IF (VNUM(I) .GE. 0) THEN
DO 30 J = VSTART(I),VSTART(I)+VNUM(I)-1
IWK(BNDCYC) = J
BNDCYC = BNDCYC + 1
30 CONTINUE
ELSE
DO 40 J = VSTART(I)-VNUM(I)-1,VSTART(I),-1
IWK(BNDCYC) = J
BNDCYC = BNDCYC + 1
40 CONTINUE
ENDIF
I = PVL(SUCC,I)
IF (I .NE. HVL(K)) GO TO 20
WK(XC) = WK(1)
WK(YC) = WK(NVRT+2)
IWK(BNDCYC) = IWK(1)
XC = 1
YC = XC + NVRT + 1
BNDCYC = 1
TSTART(K) = NTRI + 1
CALL TRPOLG(NVRT,WK(XC),WK(YC),H(K),NBC,IWK(BNDCYC),2,NVC,NTRI,
$ MAXVC,MAXTI,MAXIW-NBC-1,MAXWK-2*NVRT-2,VCL,TIL,IWK(NBC+2),
$ WK(2*NVRT+3))
IF (IERR .NE. 0) RETURN
50 CONTINUE
END
C
C The following code was excerpted from: trpolg.f
C
SUBROUTINE TRPOLG(NVRT,XC,YC,H,NBC,BNDCYC,LDV,NVC,NTRI,MAXVC,
$ MAXTI,MAXIW,MAXWK,VCL,TIL,IWK,WK)
IMPLICIT LOGICAL (A-Z)
INTEGER LDV,MAXIW,MAXTI,MAXVC,MAXWK,NBC,NTRI,NVC,NVRT
INTEGER BNDCYC(0:NBC),TIL(3,MAXTI),IWK(MAXIW)
DOUBLE PRECISION H,VCL(LDV,MAXVC),WK(MAXWK),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: Generate Delaunay triangular mesh inside convex polygon
C using quasi-uniform grid of spacing H.
C
C Input parameters:
C NVRT - number of vertices on the boundary of convex polygon
C XC(0:NVRT),YC(0:NVRT) - vertex coordinates in CCW order;
C (XC(0),YC(0)) = (XC(NVRT),YC(NVRT)); it is assumed
C that all interior angles are < PI
C H - spacing of mesh vertices in polygon
C NBC - size of BNDCYC
C BNDCYC(0:NBC) - indices in VCL of mesh vertices of boundary
C cycle; BNDCYC(0) = BNDCYC(NBC); contains (XC(I),YC(I))
C LDV - leading dimension of VCL in calling routine
C NVC - number of coordinates or positions used in VCL array
C NTRI - number of triangles or positions used in TIL
C MAXVC - maximum size available for VCL array
C MAXTI - maximum size available for TIL array
C MAXIW - maximum size available for IWK array, should be >=
C 6*(1 + INT(DIAM/H)) + 4*(NBC + NCW) where DIAM is
C diameter of polygon, NCW is number of edges on boundary
C of interior triangulation
C MAXWK - maximum size available for WK array, should be >=
C 3*NVRT+2
C VCL(1:2,1:NVC) - vertex coordinate list
C TIL(1:3,1:NTRI) - triangle incidence list
C
C Updated parameters:
C BNDCYC(0:NBC) - elements of array may be rotated
C NVC,NTRI,VCL,TIL
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, 6, 7, 9, 10, 200, 202, 230, or 231
C
C Routines called:
C CVDTRI, DIAM2, INTTRI, ROTIAR, ROTPG, SHRNK2, TMERGE
C
INTEGER IERR
COMMON /GERROR/ IERR
SAVE /GERROR/
C
INTEGER CWALK,I,I1,I2,IBOT,IEDGE,IND,MAXCW,MBC,NCW,NSHR,NT
INTEGER SDIST,SPTR,TEDG,XS,YS
DOUBLE PRECISION COSTH,DIST,HS,SINTH,SMDIST,X0,XI,Y0,YI,YR
LOGICAL INTER
CWALK = 0.0
YR = 0.0
C
IF (NVRT + 1 .GT. MAXIW) THEN
IERR = 6
RETURN
ELSE IF (3*NVRT + 2 .GT. MAXWK) THEN
IERR = 7
RETURN
ENDIF
XS = 1
YS = XS + NVRT + 1
SDIST = YS + NVRT + 1
IEDGE = 1
HS = H/SQRT(2.0D0)
DO 10 I = 0,NVRT-1
WK(SDIST+I) = HS
10 CONTINUE
CALL SHRNK2(NVRT,XC,YC,WK(SDIST),NSHR,WK(XS),WK(YS),IWK(IEDGE))
IF (IERR .NE. 0) RETURN
INTER = (NSHR .GT. 0)
C
IF (INTER) THEN
CALL DIAM2(NSHR,WK(XS+1),WK(YS+1),I1,I2,DIST)
IF (IERR .NE. 0) RETURN
CALL ROTPG(NSHR,WK(XS),WK(YS),I1,I2,IBOT,COSTH,SINTH)
MAXCW = 6*(1 + INT((WK(YS) - WK(YS+IBOT))/H))
IF (MAXCW + 1 .GT. MAXIW) THEN
IERR = 6
RETURN
ENDIF
CWALK = 1
CALL INTTRI(NSHR,WK(XS),WK(YS),H,IBOT,COSTH,SINTH,LDV,NVC,NTRI,
$ MAXVC,MAXTI,MAXCW,VCL,TIL,NCW,IWK(CWALK))
IF (IERR .NE. 0) RETURN
C
C Determine the mesh vertex which should be moved to front of
C BNDCYC - closest to CWALK(0) and also with y-coordinate >
C that of CWALK(0) when rotated if NCW > 0.
C
X0 = VCL(1,IWK(CWALK))
Y0 = VCL(2,IWK(CWALK))
IF (NCW .GT. 0) YR = SINTH*X0 + COSTH*Y0
SMDIST = 100000.0D0*H**2
DO 20 I = 0,NBC-1
XI = VCL(1,BNDCYC(I))
YI = VCL(2,BNDCYC(I))
IF (NCW .GT. 0) THEN
IF (SINTH*XI + COSTH*YI .LE. YR) GO TO 20
ENDIF
DIST = (XI - X0)**2 + (YI - Y0)**2
IF (DIST .LT. SMDIST) THEN
SMDIST = DIST
IND = I
ENDIF
20 CONTINUE
CALL ROTIAR(NBC,BNDCYC,IND)
BNDCYC(NBC) = BNDCYC(0)
NT = NBC + NCW
TEDG = CWALK + NCW + 1
ELSE
CALL DIAM2(NVRT,XC(1),YC(1),I1,I2,DIST)
IF (IERR .NE. 0) RETURN
IND = 0
30 CONTINUE
IF (IND .GE. NBC) GO TO 40
IF (XC(I1) .EQ. VCL(1,BNDCYC(IND)) .AND. YC(I1) .EQ.
$ VCL(2,BNDCYC(IND))) GO TO 40
IND = IND + 1
GO TO 30
40 CONTINUE
CALL ROTIAR(NBC,BNDCYC,IND)
BNDCYC(NBC) = BNDCYC(0)
MBC = 1
50 CONTINUE
IF (MBC .GE. NBC) GO TO 60
IF (XC(I2) .EQ. VCL(1,BNDCYC(MBC)) .AND. YC(I2) .EQ.
$ VCL(2,BNDCYC(MBC))) GO TO 60
MBC = MBC + 1
GO TO 50
60 CONTINUE
IND = NBC
DO 70 I = MBC+1,MBC+(NBC-MBC-1)/2
IND = IND - 1
I1 = BNDCYC(I)
BNDCYC(I) = BNDCYC(IND)
BNDCYC(IND) = I1
70 CONTINUE
BNDCYC(NBC) = BNDCYC(MBC)
NT = NBC - 2
TEDG = 1
C Left boundary chain contains mesh vertices BNDCYC(0:MBC)
C and right chain contains BNDCYC(0,MBC+1:NBC); MBC < NBC.
ENDIF
C
IF (NTRI + NT .GT. MAXTI) THEN
IERR = 9
RETURN
ELSE IF (TEDG + 4*NT - 1 .GT. MAXIW) THEN
IERR = 6
RETURN
ENDIF
IF (INTER) THEN
CALL TMERGE(INTER,NBC,NCW,BNDCYC,IWK(CWALK),LDV,VCL,
$ TIL(1,NTRI+1),IWK(TEDG))
ELSE
CALL TMERGE(INTER,MBC,NBC-MBC,BNDCYC,BNDCYC(MBC),LDV,VCL,
$ TIL(1,NTRI+1),IWK(TEDG))
ENDIF
IF (IERR .NE. 0) RETURN
SPTR = TEDG + 3*NT
CALL CVDTRI(INTER,LDV,NT,VCL,TIL(1,NTRI+1),IWK(TEDG),IWK(SPTR))
NTRI = NTRI + NT
END
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