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C
C The following code was excerpted from: vispol.f
C
SUBROUTINE VISPOL(XEYE,YEYE,NVRT,XC,YC,NVIS,IVIS)
IMPLICIT LOGICAL (A-Z)
INTEGER NVIS,NVRT
INTEGER IVIS(0:NVRT)
DOUBLE PRECISION XEYE,YEYE
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 the visibility polygon VP from an eyepoint in
C the interior or blocked exterior of a simple polygon P or
C on the boundary of a simply connected polygonal region P.
C In the latter case, the interior angles at all vertices must
C be strictly between 0 and 2*PI.
C
C Input parameters:
C XEYE,YEYE - coordinates of eyepoint; must be a simple vertex
C if it lies on the boundary (i.e. occurs only once)
C NVRT - upper subscript of XC, YC (approx number of vertices)
C XC(0:NVRT),YC(0:NVRT) - If eyepoint is interior or blocked
C exterior then arrays contain coordinates in CCW or CW
C order, respectively, with (XC(0),YC(0)) = (XC(NVRT),
C YC(NVRT)); (XC(0),YC(0)) is a vertex visible from
C (XEYE,YEYE), e.g. as computed by routine ROTIPG.
C If eyepoint is a vertex of P then arrays contain
C coordinates in CCW order; (XC(0),YC(0)) is successor
C vertex of (XEYE,YEYE); (XC(NVRT),YC(NVRT)) is
C predecessor vertex of (XEYE,YEYE).
C
C Updated parameters:
C XC(0:NVIS),YC(0:NVIS) - vertices of VP in CCW order;
C if eyepoint is interior or blocked exterior then
C (XC(0),YC(0)) = (XC(NVIS),YC(NVIS)), else (XC(0),YC(0))
C and (XC(NVIS),YC(NVIS)) are the successor and
C predecessor vertices of (XEYE,YEYE) in VP
C
C Output parameters:
C NVIS - upper subscript of XC, YC on output (approx number
C of vertices of VP); NVIS <= NVRT
C IVIS(0:NVIS) - contains information about the vertices of VP
C w.r.t. the vertices of P; IVIS(I) = K if (XC(I),YC(I))
C is the vertex of index K in the input polygon; IVIS(I)
C = -K if (XC(I),YC(I)) is on the interior of the edge
C joining vertices of index K-1 and K in input polygon
C
C Note about algorithm:
C On input, XC and YC contain vertex coordinates of P. During
C the algorithm, part of XC, YC is used as a stack, which, on
C output, contains the vertex coordinates of VP. The stack
C vertices overwrite the input vertices as the input vertices
C are scanned. Elements of IVIS are set when vertices are added
C to the stack; these values may have +NV or -NV added to them
C to indicate that stack point has same angle as previous one.
C
C Reference:
C B. Joe and R. B. Simpson, BIT 27 (1987), pp. 458-473.
C
C Abnormal return:
C IERR is set to 206, 207, 208, 209, or 210
C
C Routines called:
C LRLINE, VPLEFT, VPRGHT, VPSCNA, VPSCNB, VPSCNC, VPSCND
C
INTEGER CUR,IERR,NV,OPER,TOP
DOUBLE PRECISION XE,XW,YE,YW
LOGICAL BEYE
COMMON /GERROR/ IERR
COMMON /GVPVAR/ NV,OPER,CUR,TOP,XE,YE,XW,YW,BEYE
SAVE /GERROR/,/GVPVAR/
C
C Variables in common block GVPVAR:
C NV - NVRT
C OPER - operation code 1 to 7 for LEFT, RIGHT, SCANA, SCANB,
C SCANC, SCAND, FINISH
C CUR - index of current vertex of P in XC, YC arrays
C TOP - index of top vertex of stack in XC, YC arrays
C (TOP <= CUR is always satisfied)
C XE,YE - XEYE,YEYE
C XW,YW - coordinates of point on last or second-last edge
C processed (needed for routines VPSCNB, VPSCNC, VPSCND)
C BEYE - .TRUE. iff eyepoint is on boundary
C
INTEGER I,LR,LRLINE
C
BEYE = XC(0) .NE. XC(NVRT) .OR. YC(0) .NE. YC(NVRT)
NV = NVRT
XE = XEYE
YE = YEYE
IVIS(0) = 0
CUR = 1
IF (.NOT. BEYE) GO TO 20
10 CONTINUE
LR = LRLINE(XC(NV-1),YC(NV-1),XE,YE,XC(NV),YC(NV),0.0D0)
IF (LR .EQ. 0) THEN
NV = NV - 1
GO TO 10
ENDIF
C
20 CONTINUE
LR = LRLINE(XC(CUR),YC(CUR),XE,YE,XC(0),YC(0),0.0D0)
IF (LR .EQ. 0) THEN
CUR = CUR + 1
GO TO 20
ENDIF
IF (LR .EQ. -1) THEN
OPER = 1
IF (CUR .EQ. 1) THEN
TOP = 1
IVIS(1) = CUR
ELSE IF (BEYE) THEN
TOP = 1
XC(0) = XC(CUR-1)
YC(0) = YC(CUR-1)
IVIS(0) = CUR - 1
XC(1) = XC(CUR)
YC(1) = YC(CUR)
IVIS(1) = CUR
ELSE
TOP = 2
XC(1) = XC(CUR-1)
YC(1) = YC(CUR-1)
IVIS(1) = CUR - 1 + NV
XC(2) = XC(CUR)
YC(2) = YC(CUR)
IVIS(2) = CUR
ENDIF
ELSE
OPER = 3
TOP = 0
IF (BEYE .AND. CUR. GT. 1) THEN
XC(0) = XC(CUR-1)
YC(0) = YC(CUR-1)
IVIS(0) = CUR - 1
ENDIF
ENDIF
C
C Angular displacement of stack points are in nondecreasing order,
C with at most two consecutive points having the same displacement.
C
30 CONTINUE
IF (OPER .EQ. 1) THEN
CALL VPLEFT(XC,YC,IVIS)
ELSE IF (OPER .EQ. 2) THEN
CALL VPRGHT(XC,YC,IVIS)
ELSE IF (OPER .EQ. 3) THEN
CALL VPSCNA(XC,YC,IVIS)
ELSE IF (OPER .EQ. 4) THEN
CALL VPSCNB(XC,YC,IVIS)
ELSE IF (OPER .EQ. 5) THEN
CALL VPSCNC(XC,YC,IVIS)
ELSE
CALL VPSCND(XC,YC,IVIS)
ENDIF
IF (IERR .NE. 0) THEN
NVIS = TOP
RETURN
ENDIF
IF (OPER .LE. 6) GO TO 30
C
C Add or subtract NV from those IVIS values which are used to
C indicate that stack point has same angle as previous one.
C
DO 40 I = 1,TOP
IF (IVIS(I) .GT. NV) THEN
IVIS(I) = IVIS(I) - NV
ELSE IF (IVIS(I) .LT. -NV) THEN
IVIS(I) = IVIS(I) + NV
ENDIF
40 CONTINUE
NVIS = TOP
END
C
C The following code was excerpted from: visvrt.f
C
SUBROUTINE VISVRT(ANGSPC,XEYE,YEYE,NVIS,XC,YC,IVIS,MAXN,NVSVRT,
$ THETA)
IMPLICIT LOGICAL (A-Z)
INTEGER MAXN,NVIS,NVSVRT
INTEGER IVIS(0:MAXN)
DOUBLE PRECISION ANGSPC,XEYE,YEYE
DOUBLE PRECISION THETA(0:MAXN),XC(0:MAXN),YC(0:MAXN)
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 a list of visible vertices, ordered by
C increasing "polar angle", on the boundary of the visibilty
C polygon from boundary eyepoint (XEYE,YEYE). This list
C includes the vertices of visibility polygon such that a
C line segment from (XEYE,YEYE) to vertex lies in interior
C of polygon, as well as extra points on edges which subtend
C an angle >= 2*ANGSPC at (XEYE,YEYE). These extra points are
C at an equal angular spacing of >= ANGSPC and < 2*ANGSPC. The
C successor and predecessor of eyepoint are included in list.
C
C Input parameters:
C ANGSPC - angle spacing parameter in radians which controls
C how many extra points become visible vertices
C XEYE,YEYE - coordinates of boundary eyepoint
C NVIS - (number of vertices of visibility polygon) - 2
C XC(0:NVIS),YC(0:NVIS) - the coordinates of the vertices of
C visibility polygon in CCW order; (XC(0),YC(0)) and
C (XC(NVIS),YC(NVIS)) are the successor and predecessor
C vertices of eyepoint in visibility polygon; at most 2
C consecutive vertices have same polar angle wrt eyepoint
C IVIS(0:NVIS) - contains information about the vertices of
C XC, YC arrays with respect to the original polygon from
C which visibility polygon is computed; if IVIS(I) >= 0
C then (XC(I),YC(I)) has index I in original polygon;
C if IVIS(I) < 0 then (XC(I),YC(I)) is on the edge
C ending at vertex of index -IVIS(I) in original polygon;
C indexing starts at 0 from successor of eyepoint
C MAXN - upper bound on NVSVRT; should be at least
C NVIS + INT(PHI/ANGSPC) where PHI is the interior
C angle at (XEYE,YEYE)
C
C Updated parameters:
C XC(0:NVSVRT),YC(0:NVSVRT) - coordinates of visible vertices
C which overwrite the input coordinates
C IVIS(0:NVSVRT) - contains information about the output
C vertices of XC, YC arrays as described above for input
C
C Output parameters:
C NVSVRT - (number of visible vertices) - 1
C THETA(0:NVSVRT) - polar angles of visible vertices wrt (XEYE,
C YEYE) at origin and (XC(0),YC(0)) on positive x-axis
C
C Routines called:
C ANGLE, LRLINE
C
DOUBLE PRECISION PI,TOL
COMMON /GCONST/ PI,TOL
SAVE /GCONST/
C
INTEGER CUR,I,IND,K,LR,LRLINE,N,TOP
DOUBLE PRECISION ALPHA,ANG,ANG1,ANG2,ANGDIF,ANGLE,ANGSP2
DOUBLE PRECISION COSANG,DIFF,DX,DY,NUMER,R,SINANG
C
C Shift input vertices right, and possibly remove first and last
C vertices due to collinearity with eyepoint.
C
ANGSP2 = 2.0D0*ANGSPC
CUR = MAXN + 1
N = MAXN
DO 10 I = NVIS,0,-1
CUR = CUR - 1
XC(CUR) = XC(I)
YC(CUR) = YC(I)
IVIS(CUR) = IVIS(I)
10 CONTINUE
LR = LRLINE(XC(CUR+1),YC(CUR+1),XEYE,YEYE,XC(CUR),YC(CUR),0.0D0)
IF (LR .GE. 0) THEN
CUR = CUR + 1
XC(0) = XC(CUR)
YC(0) = YC(CUR)
IVIS(0) = IVIS(CUR)
ENDIF
LR = LRLINE(XC(N-1),YC(N-1),XEYE,YEYE,XC(N),YC(N),0.0D0)
IF (LR .LE. 0) N = N - 1
ALPHA = ATAN2(YC(0)-YEYE,XC(0)-XEYE)
ANG2 = 0.0D0
THETA(0) = 0.0D0
TOP = 0
CUR = CUR + 1
C
C Process edge from vertices of indices CUR-1, CUR.
C
20 CONTINUE
ANG1 = ANG2
ANG2 = ANGLE(XC(CUR),YC(CUR),XEYE,YEYE,XC(0),YC(0))
ANGDIF = ANG2 - ANG1
IF (ANGDIF .LE. TOL) THEN
DIFF = ((XC(CUR) - XEYE)**2 + (YC(CUR) - YEYE)**2) -
$ ((XC(CUR-1) - XEYE)**2 + (YC(CUR-1) - YEYE)**2)
IF (DIFF .LT. 0.0D0) THEN
XC(TOP) = XC(CUR)
YC(TOP) = YC(CUR)
IVIS(TOP) = IVIS(CUR)
THETA(TOP) = ANG2
ENDIF
ELSE
IF (ANGDIF .GE. ANGSP2) THEN
K = INT(ANGDIF/ANGSPC)
IND = -ABS(IVIS(CUR))
ANGDIF = ANGDIF/DBLE(K)
DX = XC(CUR) - XC(CUR-1)
DY = YC(CUR) - YC(CUR-1)
NUMER = (XC(CUR) - XEYE)*DY - (YC(CUR) - YEYE)*DX
DO 30 I = 1,K-1
TOP = TOP + 1
THETA(TOP) = ANG1 + DBLE(I)*ANGDIF
ANG = THETA(TOP) + ALPHA
COSANG = COS(ANG)
SINANG = SIN(ANG)
R = NUMER/(DY*COSANG - DX*SINANG)
XC(TOP) = R*COSANG + XEYE
YC(TOP) = R*SINANG + YEYE
IVIS(TOP) = IND
30 CONTINUE
ENDIF
TOP = TOP + 1
XC(TOP) = XC(CUR)
YC(TOP) = YC(CUR)
IVIS(TOP) = IVIS(CUR)
THETA(TOP) = ANG2
ENDIF
CUR = CUR + 1
IF (CUR .LE. N) GO TO 20
NVSVRT = TOP
END
C
C The following code was excerpted from: vornbr.f
C
SUBROUTINE VORNBR(XEYE,YEYE,NVRT,XC,YC,NVOR,IVOR,XVOR,YVOR)
IMPLICIT LOGICAL (A-Z)
INTEGER NVOR,NVRT
INTEGER IVOR(0:NVRT)
DOUBLE PRECISION XEYE,YEYE
DOUBLE PRECISION XC(0:NVRT),XVOR(0:NVRT),YC(0:NVRT),YVOR(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 the Voronoi neighbours of (XEYE,YEYE) from a
C list of vertices which are in increasing "polar angle" order.
C The Voronoi neighbours are a sublist of this list. The
C Voronoi polygon is restricted to the sector formed from the
C the edges joining (XEYE,YEYE) to the first and last vertices
C of this list. Each Voronoi neighbour corresponds to an edge
C of the Voronoi polygon.
C
C Input parameters:
C XEYE,YEYE - coordinates of eyepoint
C NVRT - (number of vertices in list) - 1
C XC(0:NVRT),YC(0:NVRT) - vertex coordinates from which
C Voronoi neighbours are determined; (XC(0),YC(0)),...,
C (XC(NVRT),YC(NVRT)) are in increasing angular
C displacement order w.r.t. (XEYE,YEYE)
C
C Output parameters:
C NVOR - (number of Voronoi neighbours) - 1 [<= NVRT]
C IVOR(0:NVOR) - indices of Voronoi neighbours in XC, YC
C arrays; 0 <= IVOR(0) < ... < IVOR(NVOR) <= NVRT
C
C Working parameters:
C XVOR(0:NVRT),YVOR(0:NVRT) - arrays for storing the vertex
C coordinates of the Voronoi polygon
C
C Abnormal return:
C IERR is set to 212
C
C Routines called:
C LRLINE
C
INTEGER IERR
DOUBLE PRECISION PI,TOL
COMMON /GERROR/ IERR
COMMON /GCONST/ PI,TOL
SAVE /GERROR/,/GCONST/
C
INTEGER IM,K,LR,LRLINE,M
DOUBLE PRECISION A11,A12,A21,A22,B1,B2,DET,TOLABS,XI,YI
C
K = 1
M = 0
IVOR(0) = 0
XVOR(0) = (XEYE + XC(0))*0.5D0
YVOR(0) = (YEYE + YC(0))*0.5D0
C
C Beginning of main loop
C
10 CONTINUE
IF (K .GT. NVRT) GO TO 20
C
C Determine the intersection of the perpendicular bisectors
C of edges from (XEYE,YEYE) to (XC(K),YC(K)) and from
C (XEYE,YEYE) to (XC(IM),YC(IM)).
C
IM = IVOR(M)
A11 = XC(K) - XEYE
A12 = YC(K) - YEYE
A21 = XC(IM) - XEYE
A22 = YC(IM) - YEYE
TOLABS = TOL*MAX(ABS(A11),ABS(A12),ABS(A21),ABS(A22))
DET = A11*A22 - A21*A12
IF (ABS(DET) .LE. TOLABS) THEN
IERR = 212
RETURN
ENDIF
B1 = (A11**2 + A12**2)*0.5D0
B2 = (A21**2 + A22**2)*0.5D0
XI = (B1*A22 - B2*A12)/DET
YI = (B2*A11 - B1*A21)/DET
C
C Determine whether (XVOR(M+1),YVOR(M+1)) is to the left of or
C on the directed line from (XEYE,YEYE) to (XVOR(M),YVOR(M)).
C
XVOR(M+1) = XI + XEYE
YVOR(M+1) = YI + YEYE
LR = LRLINE(XVOR(M+1),YVOR(M+1),XEYE,YEYE,XVOR(M),YVOR(M),
1 0.0D0)
IF (LR .LE. 0) THEN
M = M + 1
IVOR(M) = K
K = K + 1
ELSE IF (M .GT. 0) THEN
M = M - 1
ELSE
C
C Determine the intersection of edge from (XEYE,YEYE) to
C (XC(0),YC(0)) and the perpendicular bisector of the edge
C from (XEYE,YEYE) to (XC(K),YC(K)).
C
A11 = XC(K) - XEYE
A12 = YC(K) - YEYE
A21 = YC(0) - YEYE
A22 = XEYE - XC(0)
TOLABS = TOL*MAX(ABS(A11),ABS(A12),ABS(A21),ABS(A22))
DET = A11*A22 - A21*A12
IF (ABS(DET) .LE. TOLABS) THEN
IERR = 212
RETURN
ENDIF
B1 = (A11**2 + A12**2)*0.5D0
B2 = 0.0D0
XI = (B1*A22 - B2*A12)/DET
YI = (B2*A11 - B1*A21)/DET
XVOR(M) = XI + XEYE
YVOR(M) = YI + YEYE
IVOR(M) = K
K = K + 1
ENDIF
GO TO 10
C
C The following short loop determines which vertices at the end
C of list are not Voronoi neighbours.
C
20 CONTINUE
LR = LRLINE(XVOR(M),YVOR(M),XEYE,YEYE,XC(NVRT),YC(NVRT),0.0D0)
IF (LR .GE. 0) GO TO 30
M = M - 1
IF (M .GE. 0) GO TO 20
30 CONTINUE
NVOR = M
END
C
C The following code was excerpted from: vpleft.f
C
SUBROUTINE VPLEFT(XC,YC,IVIS)
IMPLICIT LOGICAL (A-Z)
INTEGER IVIS(0:*)
DOUBLE PRECISION 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: This routine is called by routine VISPOL for the LEFT
C operation (OPER = 1).
C
C Input and updated parameters:
C XC,YC,IVIS - see comments in routine VISPOL
C
C Routines called:
C LRLINE, XEDGE
C
INTEGER CUR,NV,OPER,TOP
DOUBLE PRECISION XE,XW,YE,YW
LOGICAL BEYE
COMMON /GVPVAR/ NV,OPER,CUR,TOP,XE,YE,XW,YW,BEYE
SAVE /GVPVAR/
C
INTEGER J,LR,LR1,LR2,LRLINE
DOUBLE PRECISION XU,YU
LOGICAL INTSCT
C
C EYE-V(CUR-1)-V(CUR) is a left turn, S(TOP) = V(CUR), TOP <= CUR,
C S(TOP-1) = V(CUR-1) or on interior of edge V(CUR-1)-V(CUR).
C
10 CONTINUE
IF (CUR .EQ. NV) THEN
OPER = 7
RETURN
ENDIF
IF (.NOT. BEYE .AND. TOP .LE. 2) GO TO 20
C
C Check if angular displacement of stack chain >= 2*PI or
C interior angle at boundary viewpoint.
C
CALL XEDGE(1,XE,YE,XC(NV),YC(NV),XC(TOP-1),YC(TOP-1),XC(TOP),
$ YC(TOP),XU,YU,INTSCT)
IF (INTSCT) THEN
OPER = 4
XW = XC(CUR)
YW = YC(CUR)
LR = LRLINE(XC(TOP),YC(TOP),XE,YE,XC(NV),YC(NV),0.0D0)
IF (LR .EQ. -1) THEN
XC(TOP) = XU
YC(TOP) = YU
IVIS(TOP) = -CUR
ENDIF
RETURN
ENDIF
C
C Process next edge.
C
20 CONTINUE
LR = LRLINE(XC(CUR+1),YC(CUR+1),XE,YE,XC(CUR),YC(CUR),0.0D0)
IF (LR .EQ. -1) THEN
CUR = CUR + 1
TOP = TOP + 1
XC(TOP) = XC(CUR)
YC(TOP) = YC(CUR)
IVIS(TOP) = CUR
ELSE
J = CUR + 1
LR1 = LRLINE(XC(J),YC(J),XC(TOP-1),YC(TOP-1),XC(CUR),YC(CUR),
$ 0.0D0)
IF (LR1 .EQ. 1) THEN
OPER = 3
CUR = J
ELSE
IF (LR .EQ. 1) THEN
LR2 = 1
GO TO 40
ENDIF
30 CONTINUE
J = J + 1
LR2 = LRLINE(XC(J),YC(J),XE,YE,XC(CUR),YC(CUR),0.0D0)
IF (LR2 .EQ. 0) GO TO 30
40 CONTINUE
IF (LR2 .EQ. -1) THEN
TOP = TOP + 1
XC(TOP) = XC(J-1)
YC(TOP) = YC(J-1)
IVIS(TOP) = J - 1 + NV
TOP = TOP + 1
XC(TOP) = XC(J)
YC(TOP) = YC(J)
IVIS(TOP) = J
ELSE
OPER = 2
ENDIF
CUR = J
ENDIF
ENDIF
C
C This test avoids extra subroutine calls.
C
IF (OPER .EQ. 1) GO TO 10
END
C
C The following code was excerpted from: vprght.f
C
SUBROUTINE VPRGHT(XC,YC,IVIS)
IMPLICIT LOGICAL (A-Z)
INTEGER IVIS(0:*)
DOUBLE PRECISION 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: This routine is called by routine VISPOL for the RIGHT
C operation (OPER = 2).
C
C Input and updated parameters:
C XC,YC,IVIS - see comments in routine VISPOL
C
C Abnormal return:
C IERR is set to 206
C
C Routines called:
C LRLINE, XEDGE
C
INTEGER CUR,IERR,NV,OPER,TOP
DOUBLE PRECISION XE,XW,YE,YW
LOGICAL BEYE
COMMON /GERROR/ IERR
COMMON /GVPVAR/ NV,OPER,CUR,TOP,XE,YE,XW,YW,BEYE
SAVE /GERROR/,/GVPVAR/
C
INTEGER CASE,J,LR,LR1,LR2,LRLINE
DOUBLE PRECISION XU,YU
LOGICAL INTSCT
C
C EYE-V(CUR-1)-V(CUR) is a right turn, EYE-S(TOP)-V(CUR) is a right
C turn, EYE-S(TOP-1)-S(TOP) is a left turn, TOP < CUR, S(TOP) =
C V(CUR-1) and S(TOP-1)-S(TOP)-V(CUR) is a left turn or S(TOP) is
C not on edge V(CUR-1)-V(CUR) and V(CUR-1)-V(CUR) intersects
C EYE-S(TOP).
C Pop points from stack. If BEYE, it is not possible for
C (XC(CUR),YC(CUR)) to be identical to any stack points.
C
10 CONTINUE
CASE = 0
J = TOP
20 CONTINUE
IF (ABS(IVIS(J)) .LE. NV) THEN
LR = LRLINE(XC(CUR),YC(CUR),XE,YE,XC(J-1),YC(J-1),0.0D0)
IF (LR .EQ. -1) THEN
CASE = 1
ELSE IF (LR .EQ. 0) THEN
IF (ABS(IVIS(J-1)) .LE. NV) THEN
J = J - 1
CASE = 2
ELSE IF ((XC(J-2) - XE)**2 + (YC(J-2) - YE)**2 .GE.
$ (XC(J-1) - XE)**2 + (YC(J-1) - YE)**2) THEN
J = J - 2
CASE = 2
ELSE
CASE = -1
ENDIF
ENDIF
ELSE IF (CASE .EQ. -1) THEN
IF ((XC(J-1) - XE)**2 + (YC(J-1) - YE)**2 .GE.
$ (XC(CUR) - XE)**2 + (YC(CUR) - YE)**2) THEN
J = J - 1
CASE = 2
ELSE
XW = XC(CUR)
YW = YC(CUR)
CASE = 3
ENDIF
ELSE
CALL XEDGE(0,XC(CUR-1),YC(CUR-1),XC(CUR),YC(CUR),
$ XC(J-1),YC(J-1),XC(J),YC(J),XW,YW,INTSCT)
IF (INTSCT) CASE = 3
ENDIF
IF (CASE .GT. 0) GO TO 30
J = J - 1
IF (J .GE. 1) GO TO 20
C
C Error from no more edges in stack.
C
IERR = 206
RETURN
C
C Process next edge.
C
30 CONTINUE
IF (CASE .EQ. 3) THEN
OPER = 6
TOP = J - 1
ELSE
TOP = J
XW = XC(CUR-1)
YW = YC(CUR-1)
IF (CASE .EQ. 1) THEN
CALL XEDGE(1,XE,YE,XC(CUR),YC(CUR),XC(TOP-1),YC(TOP-1),
$ XC(TOP),YC(TOP),XU,YU,INTSCT)
XC(TOP) = XU
YC(TOP) = YU
IVIS(TOP) = -ABS(IVIS(TOP))
ENDIF
LR = LRLINE(XC(CUR+1),YC(CUR+1),XE,YE,XC(CUR),YC(CUR),0.0D0)
IF (LR .EQ. 1) THEN
CUR = CUR + 1
ELSE
J = CUR + 1
LR1 = LRLINE(XC(J),YC(J),XW,YW,XC(CUR),YC(CUR),0.0D0)
IF (LR1 .EQ. -1) THEN
OPER = 5
CUR = J
ELSE
IF (LR .EQ. -1) THEN
LR2 = -1
GO TO 50
ENDIF
40 CONTINUE
J = J + 1
LR2 = LRLINE(XC(J),YC(J),XE,YE,XC(CUR),YC(CUR),0.0D0)
IF (LR2 .EQ. 0) GO TO 40
50 CONTINUE
IF (LR2 .EQ. -1) THEN
OPER = 1
TOP = TOP + 1
XC(TOP) = XC(J-1)
YC(TOP) = YC(J-1)
IVIS(TOP) = J - 1 + NV
TOP = TOP + 1
XC(TOP) = XC(J)
YC(TOP) = YC(J)
IVIS(TOP) = J
ENDIF
CUR = J
ENDIF
ENDIF
ENDIF
C
C This test avoids extra subroutine calls.
C
IF (OPER .EQ. 2) GO TO 10
END
C
C The following code was excerpted from: vpscna.f
C
SUBROUTINE VPSCNA(XC,YC,IVIS)
IMPLICIT LOGICAL (A-Z)
INTEGER IVIS(0:*)
DOUBLE PRECISION 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: This routine is called by routine VISPOL for the SCANA
C operation (OPER = 3).
C
C Input and updated parameters:
C XC,YC,IVIS - see comments in routine VISPOL
C
C Abnormal return:
C IERR is set to 207
C
C Routines called:
C LRLINE, XEDGE
C
INTEGER CUR,IERR,NV,OPER,TOP
DOUBLE PRECISION XE,XW,YE,YW
LOGICAL BEYE
COMMON /GERROR/ IERR
COMMON /GVPVAR/ NV,OPER,CUR,TOP,XE,YE,XW,YW,BEYE
SAVE /GERROR/,/GVPVAR/
C
INTEGER CASE,J,K,LR,LR1,LR2,LR3,LRLINE
LOGICAL INTSCT
C
C EYE-V(CUR-1)-V(CUR) is a right turn or forward move, S(TOP) =
C V(CUR-1) or EYE-S(TOP)-V(CUR-1) is a forward move and TOP = 0,
C TOP < CUR; S(TOP-1)-S(TOP)-V(CUR) is a right turn if TOP >= 1
C or EYE-S(TOP)-V(CUR) is a right turn if TOP = 0.
C If BEYE, it is possible that (XC(TOP),YC(TOP)) is a non-simple
C vertex but any edge incident on this vertex encountered during
C scan must be invisible from (XE,YE).
C
K = CUR
10 CONTINUE
IF (XC(K+1) .EQ. XC(TOP) .AND. YC(K+1) .EQ. YC(TOP)) THEN
K = K + 2
ELSE
CALL XEDGE(1,XE,YE,XC(TOP),YC(TOP),XC(K),YC(K),XC(K+1),
$ YC(K+1),XW,YW,INTSCT)
IF (INTSCT) THEN
LR = LRLINE(XC(K+1),YC(K+1),XE,YE,XC(K),YC(K),0.0D0)
IF (LR .EQ. 1) THEN
IF ((XC(TOP) - XE)**2 + (YC(TOP) - YE)**2 .GE.
$ (XW - XE)**2 + (YW - YE)**2) THEN
IF (TOP .GT. 0) THEN
CASE = 1
GO TO 20
ENDIF
ELSE
LR1 = LRLINE(XC(K),YC(K),XE,YE,XC(TOP),YC(TOP),
$ 0.0D0)
IF (LR1 .EQ. -1) THEN
CASE = 2
GO TO 20
ENDIF
ENDIF
ELSE
LR1 = LRLINE(XC(K+1),YC(K+1),XE,YE,XC(TOP),YC(TOP),
$ 0.0D0)
IF (LR1 .EQ. -1) THEN
CASE = 3
GO TO 20
ENDIF
ENDIF
ENDIF
K = K + 1
ENDIF
IF (K .LT. NV) GO TO 10
C
C Error from unsuccessful scan.
C
IERR = 207
RETURN
C
C Process current edge.
C
20 CONTINUE
IF (CASE .EQ. 3) THEN
OPER = 1
CUR = K + 1
LR = LRLINE(XC(K),YC(K),XE,YE,XC(TOP),YC(TOP),0.0D0)
TOP = TOP + 1
IF (LR .EQ. 0) THEN
XC(TOP) = XC(K)
YC(TOP) = YC(K)
IVIS(TOP) = K + NV
ELSE
XC(TOP) = XW
YC(TOP) = YW
IVIS(TOP) = -(K + 1 + NV)
ENDIF
TOP = TOP + 1
XC(TOP) = XC(CUR)
YC(TOP) = YC(CUR)
IVIS(TOP) = CUR
ELSE IF (CASE .EQ. 1) THEN
CUR = K + 1
LR = LRLINE(XC(CUR),YC(CUR),XE,YE,XC(TOP),YC(TOP),0.0D0)
IF (LR .EQ. 1) THEN
OPER = 2
ELSE
J = CUR + 1
LR1 = LRLINE(XC(J),YC(J),XE,YE,XC(CUR),YC(CUR),0.0D0)
LR2 = LRLINE(XC(J),YC(J),XC(K),YC(K),XC(CUR),YC(CUR),0.0D0)
IF (LR1 .LE. 0 .AND. LR2 .EQ. -1) THEN
OPER = 5
XW = XC(K)
YW = YC(K)
CUR = J
ELSE
IF (LR1 .NE. 0) THEN
LR3 = LR1
GO TO 40
ENDIF
30 CONTINUE
J = J + 1
LR3 = LRLINE(XC(J),YC(J),XE,YE,XC(CUR),YC(CUR),0.0D0)
IF (LR3 .EQ. 0) GO TO 30
40 CONTINUE
IF (LR3 .EQ. 1) THEN
OPER = 2
ELSE
OPER = 1
TOP = TOP + 1
XC(TOP) = XC(J-1)
YC(TOP) = YC(J-1)
IVIS(TOP) = J - 1 + NV
TOP = TOP + 1
XC(TOP) = XC(J)
YC(TOP) = YC(J)
IVIS(TOP) = J
ENDIF
CUR = J
ENDIF
ENDIF
ELSE
OPER = 6
CUR = K + 1
LR = LRLINE(XC(CUR),YC(CUR),XE,YE,XC(TOP),YC(TOP),0.0D0)
IF (LR .EQ. 0) THEN
XW = XC(CUR)
YW = YC(CUR)
ENDIF
ENDIF
END
C
C The following code was excerpted from: vpscnb.f
C
SUBROUTINE VPSCNB(XC,YC,IVIS)
IMPLICIT LOGICAL (A-Z)
INTEGER IVIS(0:*)
DOUBLE PRECISION 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: This routine is called by routine VISPOL for the SCANB
C operation (OPER = 4).
C
C Input and updated parameters:
C XC,YC,IVIS - see comments in routine VISPOL
C
C Abnormal return:
C IERR is set to 208
C
C Routines called:
C LRLINE, XEDGE
C
INTEGER CUR,IERR,NV,OPER,TOP
DOUBLE PRECISION PI,TOL,XE,XW,YE,YW
LOGICAL BEYE
COMMON /GERROR/ IERR
COMMON /GCONST/ PI,TOL
COMMON /GVPVAR/ NV,OPER,CUR,TOP,XE,YE,XW,YW,BEYE
SAVE /GERROR/,/GCONST/,/GVPVAR/
C
INTEGER K,LR,LR1,LRLINE
DOUBLE PRECISION TOLABS,XU,YU
LOGICAL INTSCT
C
C EYE-V(CUR-1)-V(CUR) is a left turn, S(TOP) = V(CUR) or S(TOP) is
C on interior of edge V(CUR-1)-V(CUR), TOP <= CUR, S(TOP) has
C angular displacement of 2*PI or interior angle at boundary eye.
C (XW,YW) is the input version of (XC(CUR),YC(CUR)).
C If BEYE, it is possible that (XC(TOP),YC(TOP)) is a non-simple
C point but any edge containing this point encountered during scan
C must be invisible from (XE,YE), except for 1 case where K = CUR.
C
TOLABS = TOL*((XC(NV) - XC(TOP))**2 + (YC(NV) - YC(TOP))**2)
K = CUR
IF (IVIS(TOP) .LT. 0 .OR. K + 1 .EQ. NV) GO TO 10
LR = LRLINE(XC(K+1),YC(K+1),XE,YE,XC(TOP),YC(TOP),0.0D0)
LR1 = LRLINE(XC(K+1),YC(K+1),XC(TOP-1),YC(TOP-1),XC(TOP),YC(TOP),
$ 0.0D0)
IF (LR .EQ. 1 .AND. LR1 .EQ. -1) THEN
OPER = 2
CUR = K + 1
RETURN
ELSE
K = K + 1
ENDIF
C
10 CONTINUE
IF (K + 1 .EQ. NV) THEN
OPER = 7
CUR = NV
TOP = TOP + 1
XC(TOP) = XC(NV)
YC(TOP) = YC(NV)
IVIS(TOP) = NV
RETURN
ELSE
IF (K .EQ. CUR) THEN
CALL XEDGE(0,XC(NV),YC(NV),XC(TOP),YC(TOP),XW,YW,
$ XC(K+1),YC(K+1),XU,YU,INTSCT)
ELSE
CALL XEDGE(0,XC(NV),YC(NV),XC(TOP),YC(TOP),XC(K),YC(K),
$ XC(K+1),YC(K+1),XU,YU,INTSCT)
ENDIF
IF (INTSCT) THEN
IF ((XC(TOP) - XU)**2 + (YC(TOP) - YU)**2 .LE. TOLABS)
$ GO TO 20
LR = LRLINE(XC(K+1),YC(K+1),XE,YE,XC(NV),YC(NV),0.0D0)
IF (LR .EQ. 1) THEN
OPER = 2
CUR = K + 1
RETURN
ENDIF
ENDIF
20 CONTINUE
K = K + 1
ENDIF
IF (K .LT. NV) GO TO 10
C
C Error from unsuccessful scan.
C
IERR = 208
END
C
C The following code was excerpted from: vpscnc.f
C
SUBROUTINE VPSCNC(XC,YC,IVIS)
IMPLICIT LOGICAL (A-Z)
INTEGER IVIS(0:*)
DOUBLE PRECISION 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: This routine is called by routine VISPOL for the SCANC
C operation (OPER = 5).
C
C Input and updated parameters:
C XC,YC,IVIS - see comments in routine VISPOL
C
C Abnormal return:
C IERR is set to 209
C
C Routines called:
C LRLINE, XEDGE
C
INTEGER CUR,IERR,NV,OPER,TOP
DOUBLE PRECISION XE,XW,YE,YW
LOGICAL BEYE
COMMON /GERROR/ IERR
COMMON /GVPVAR/ NV,OPER,CUR,TOP,XE,YE,XW,YW,BEYE
SAVE /GERROR/,/GVPVAR/
C
INTEGER J,K,LR,LR1,LR2,LRLINE
DOUBLE PRECISION XP,XU,YP,YU
LOGICAL INTSCT
C
C EYE-V(CUR-1)-V(CUR) is a left turn or forward move, EYE-V(CUR-2)-
C V(CUR-1) is a right turn, V(CUR-2)-V(CUR-1)-V(CUR) is a left turn,
C TOP < CUR-1, W = V(CUR-2), S(TOP) is not on V(CUR-1)-V(CUR), EYE-
C S(TOP)-V(CUR-1) is a backward move, EYE-S(TOP-1)-S(TOP) is a left
C turn. If BEYE, it is possible that V(CUR-1) is a non-simple point,
C but intersection at (XC(TOP),YC(TOP)) cannot occur.
C
XP = XC(CUR-1)
YP = YC(CUR-1)
K = CUR
10 CONTINUE
IF (XC(K+1) .EQ. XP .AND. YC(K+1) .EQ. YP) THEN
GO TO 40
ELSE IF (XC(K) .EQ. XP .AND. YC(K) .EQ. YP) THEN
J = K + 1
LR = LRLINE(XC(J),YC(J),XE,YE,XP,YP,0.0D0)
LR1 = LRLINE(XC(J),YC(J),XW,YW,XP,YP,0.0D0)
IF (LR .LE. 0 .AND. LR1 .EQ. -1) GO TO 40
IF (LR .NE. 0) THEN
LR2 = LR
GO TO 30
ENDIF
20 CONTINUE
J = J + 1
LR2 = LRLINE(XC(J),YC(J),XE,YE,XP,YP,0.0D0)
IF (LR2 .EQ. 0) GO TO 20
30 CONTINUE
IF (LR2 .EQ. 1) THEN
OPER = 2
ELSE
OPER = 1
TOP = TOP + 1
XC(TOP) = XC(J-1)
YC(TOP) = YC(J-1)
IVIS(TOP) = J - 1 + NV
TOP = TOP + 1
XC(TOP) = XC(J)
YC(TOP) = YC(J)
IVIS(TOP) = J
ENDIF
CUR = J
RETURN
ELSE
CALL XEDGE(0,XP,YP,XC(TOP),YC(TOP),XC(K),YC(K),XC(K+1),
$ YC(K+1),XU,YU,INTSCT)
IF (INTSCT) THEN
LR = LRLINE(XC(K+1),YC(K+1),XE,YE,XP,YP,0.0D0)
IF (LR .EQ. 1) THEN
OPER = 2
CUR = K + 1
RETURN
ENDIF
ENDIF
ENDIF
40 CONTINUE
K = K + 1
IF (K .LT. NV) GO TO 10
C
C Error from unsuccessful scan.
C
IERR = 209
END
C
C The following code was excerpted from: vpscnd.f
C
SUBROUTINE VPSCND(XC,YC,IVIS)
IMPLICIT LOGICAL (A-Z)
INTEGER IVIS(0:*)
DOUBLE PRECISION 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: This routine is called by routine VISPOL for the SCAND
C operation (OPER = 6).
C
C Input and updated parameters:
C XC,YC,IVIS - see comments in routine VISPOL
C
C Abnormal return:
C IERR is set to 210
C
C Routines called:
C LRLINE, XEDGE
C
INTEGER CUR,IERR,NV,OPER,TOP
DOUBLE PRECISION XE,XW,YE,YW
LOGICAL BEYE
COMMON /GERROR/ IERR
COMMON /GVPVAR/ NV,OPER,CUR,TOP,XE,YE,XW,YW,BEYE
SAVE /GERROR/,/GVPVAR/
C
INTEGER K,LR,LR1,LR2,LRLINE
DOUBLE PRECISION XP,XU,YP,YU
LOGICAL INTSCT
C
C EYE-V(CUR-1)-V(CUR) is a right turn, S(TOP) is a V vertex not on
C V(CUR-1)-V(CUR), TOP < CUR, W is intersection of V(CUR-1)-V(CUR)
C and ray EYE-S(TOP), EYE-S(TOP)-W is a forward move, and
C EYE-S(TOP-1)-S(TOP) is a left turn if TOP >= 1.
C If BEYE, it is possible that (XW,YW) is a non-simple point,
C but intersection at (XC(TOP),YC(TOP)) cannot occur.
C
XP = XC(CUR-1)
YP = YC(CUR-1)
K = CUR
10 CONTINUE
CALL XEDGE(0,XW,YW,XC(TOP),YC(TOP),XC(K),YC(K),XC(K+1),
$ YC(K+1),XU,YU,INTSCT)
IF (INTSCT) THEN
LR = LRLINE(XC(K+1),YC(K+1),XE,YE,XC(K),YC(K),0.0D0)
LR1 = LRLINE(XC(K+1),YC(K+1),XE,YE,XC(TOP),YC(TOP),0.0D0)
IF (LR .EQ. -1 .AND. LR1 .EQ. -1) THEN
IF (XC(K) .NE. XW .OR. YC(K) .NE. YW) GO TO 20
LR2 = LRLINE(XC(K+1),YC(K+1),XP,YP,XW,YW,0.0D0)
IF (LR2 .EQ. -1) GO TO 30
20 CONTINUE
OPER = 1
CUR = K + 1
LR2 = LRLINE(XC(K),YC(K),XE,YE,XC(TOP),YC(TOP),0.0D0)
TOP = TOP + 1
IF (LR2 .EQ. 0) THEN
XC(TOP) = XC(K)
YC(TOP) = YC(K)
IVIS(TOP) = K + NV
ELSE
XC(TOP) = XU
YC(TOP) = YU
IVIS(TOP) = -(K + 1 + NV)
ENDIF
TOP = TOP + 1
XC(TOP) = XC(CUR)
YC(TOP) = YC(CUR)
IVIS(TOP) = CUR
RETURN
ENDIF
ENDIF
30 CONTINUE
K = K + 1
IF (K .LT. NV) GO TO 10
C
C Error from unsuccessful scan.
C
IERR = 210
END
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