MODULE TRIPACK
! ALGORITHM 751, COLLECTED ALGORITHMS FROM ACM.
! THIS WORK PUBLISHED IN TRANSACTIONS ON MATHEMATICAL SOFTWARE,
! VOL. 22, NO. 1, March, 1996, P. 1--8.
! ####### With remark from renka (to appear) 4/dec/1998
! Code converted using TO_F90 by Alan Miller
! Date: 2000-05-25 Time: 18:21:09
IMPLICIT NONE
! Tolerance stored by TRMESH or TRMSHR.
! COMMON/swpcom/swtol
REAL, SAVE, PRIVATE :: swtol
! REAL :: y
! COMMON/stcom/y
REAL, SAVE, PRIVATE :: stcom
! Random number seeds
INTEGER, SAVE , PRIVATE :: ix = 1, iy = 2, iz = 3
CONTAINS
SUBROUTINE addcst (ncc, lcc, n, x, y, lwk, list, lptr, lend, ier)
! N.B. Argument IWK has been removed.
INTEGER, INTENT(IN) :: ncc
INTEGER, INTENT(IN) :: lcc(:)
INTEGER, INTENT(IN) :: n
REAL, INTENT(IN OUT) :: x(:)
REAL, INTENT(IN OUT) :: y(:)
INTEGER, INTENT(IN OUT) :: lwk
INTEGER, INTENT(IN OUT) :: list(:)
INTEGER, INTENT(IN OUT) :: lptr(:)
INTEGER, INTENT(IN OUT) :: lend(:)
INTEGER, INTENT(OUT) :: ier
!*******************************************************************
! From TRIPACK
! Robert J. Renka
! Dept. of Computer Science
! Univ. of North Texas
! renka@cs.unt.edu
! 11/12/94
! This subroutine provides for creation of a constrained Delaunay
! triangulation which, in some sense, covers an arbitrary connected
! region R rather than the convex hull of the nodes.
! This is achieved simply by forcing the presence of certain
! adjacencies (triangulation arcs) corresponding to constraint curves.
! The union of triangles coincides with the convex hull of the nodes,
! but triangles in R can be distinguished from those outside of R.
! The only modification required to generalize the definition of the
! Delaunay triangulation is replacement of property 5 (refer to TRMESH)
! by the following:
! 5') If a node is contained in the interior of the circum]circle
! of a triangle, then every interior point of the triangle
! is separated from the node by a constraint arc.
! In order to be explicit, we make the following definitions.
! A constraint region is the open interior of a simple closed
! positively oriented polygonal curve defined by an ordered
! sequence of three or more distinct nodes (constraint nodes)
! P(1),P(2),...,P(K), such that P(I) is adjacent to P(I+1) for
! I = 1,...,K with P(K+1) = P(1).
! Thus, the constraint region is on the left (and may have nonfinite
! area) as the sequence of constraint nodes is traversed in the
! specified order. The constraint regions must not contain nodes
! and must not overlap. The region R is the convex hull of the nodes
! with constraint regions excluded.
! Note that the terms boundary node and boundary arc are reserved
! for nodes and arcs on the boundary of the convex hull of the nodes.
! The algorithm is as follows: given a triangulation which includes
! one or more sets of constraint nodes, the corresponding adjacencies
! (constraint arcs) are forced to be present (Subroutine EDGE).
! Any additional new arcs required are chosen to be locally optimal
! (satisfy the modified circumcircle property).
! On input:
! NCC = Number of constraint curves (constraint regions)
! NCC >= 0.
! LCC = Array of length NCC (or dummy array of length
! 1 if NCC = 0) containing the index (for X, Y,
! and LEND) of the first node of constraint I in
! LCC(I) for I = 1 to NCC. Thus, constraint I
! contains K = LCC(I+1) - LCC(I) nodes, K >=
! 3, stored in (X,Y) locations LCC(I), ...,
! LCC(I+1)-1, where LCC(NCC+1) = N+1.
! N = Number of nodes in the triangulation, including
! constraint nodes. N >= 3.
! X,Y = Arrays of length N containing the coordinates of the nodes with
! non-constraint nodes in the first LCC(1)-1 locations, followed
! by NCC sequences of constraint nodes. Only one of these
! sequences may be specified in clockwise order to represent an
! exterior constraint curve (a constraint region with nonfinite
! area).
! The above parameters are not altered by this routine.
! LWK = Length of IWK. This must be at least 2*NI where NI is the
! maximum number of arcs which intersect a constraint arc to be
! added. NI is bounded by N-3.
! IWK = Integer work array of length LWK (used by
! Subroutine EDGE to add constraint arcs).
! LIST,LPTR,LEND = Data structure defining the triangulation.
! Refer to Subroutine TRMESH.
! On output:
! LWK = Required length of IWK unless IER = 1 or IER = 3.
! In the case of IER = 1, LWK is not altered
! from its input value.
! IWK = Array containing the endpoint indexes of the new arcs
! which were swapped in by the last call to Subroutine EDGE.
! LIST,LPTR,LEND = Triangulation data structure with all constraint
! arcs present unless IER .NE. 0.
! These arrays are not altered if IER = 1.
! IER = Error indicator:
! IER = 0 if no errors were encountered.
! IER = 1 if NCC, N, or an LCC entry is outside
! its valid range, or LWK < 0 on input.
! IER = 2 if more space is required in IWK.
! IER = 3 if the triangulation data structure is invalid,
! or failure (in EDGE or OPTIM) was caused by
! collinear nodes on the convex hull boundary.
! An error message is written to logical unit 6
! in this case.
! IER = 4 if intersecting constraint arcs were encountered.
! IER = 5 if a constraint region contains a node.
! Modules required by ADDCST: EDGE, LEFT, LSTPTR, OPTIM, SWAP, SWPTST
! Intrinsic functions called by ADDCST: ABS, MAX
!***********************************************************
INTEGER :: i, ifrst, ilast, k, kbak, kfor, kn, lccip1, &
lp, lpb, lpf, lpl, lw, lwd2, n1, n2
lwd2 = lwk/2
! Test for errors in input parameters.
ier = 1
IF (ncc < 0 .OR. lwk < 0) RETURN
IF (ncc == 0) THEN
IF (n < 3) RETURN
lwk = 0
GO TO 9
ELSE
lccip1 = n+1
DO i = ncc,1,-1
IF (lccip1 - lcc(i) < 3) RETURN
lccip1 = lcc(i)
END DO
IF (lccip1 < 1) RETURN
END IF
! Force the presence of constraint arcs. The outer loop is
! on constraints in reverse order. IFRST and ILAST are
! the first and last nodes of constraint I.
lwk = 0
ifrst = n+1
DO i = ncc,1,-1
ilast = ifrst - 1
ifrst = lcc(i)
! Inner loop on constraint arcs N1-N2 in constraint I.
n1 = ilast
DO n2 = ifrst,ilast
lw = lwd2
CALL edge (n1,n2,x,y, lw,list,lptr,lend, ier)
lwk = MAX(lwk,2*lw)
IF (ier == 4) ier = 3
IF (ier /= 0) RETURN
n1 = n2
END DO
END DO
! Test for errors. The outer loop is on constraint I with first and
! last nodes IFRST and ILAST, and the inner loop is on constraint nodes K
! with (KBAK,K,KFOR) a subsequence of constraint I.
ier = 4
ifrst = n+1
DO i = ncc,1,-1
ilast = ifrst - 1
ifrst = lcc(i)
kbak = ilast
DO k = ifrst,ilast
kfor = k + 1
IF (k == ilast) kfor = ifrst
! Find the LIST pointers LPF and LPB of KFOR and KBAK as neighbors of K.
lpf = 0
lpb = 0
lpl = lend(k)
lp = lpl
DO
lp = lptr(lp)
kn = ABS(list(lp))
IF (kn == kfor) lpf = lp
IF (kn == kbak) lpb = lp
IF (lp == lpl) EXIT
END DO
! A pair of intersecting constraint arcs was encountered
! if and only if a constraint arc is missing (introduction
! of the second caused the first to be swapped out).
IF (lpf == 0 .OR. lpb == 0) RETURN
! Loop on neighbors KN of node K which follow KFOR and precede KBAK.
! The constraint region contains no nodes
! if and only if all such nodes KN are in constraint I.
lp = lpf
DO
lp = lptr(lp)
IF (lp == lpb) EXIT
kn = ABS(list(lp))
IF (kn < ifrst .OR. kn > ilast) GO TO 10
END DO
! Bottom of loop.
kbak = k
END DO
END DO
! No errors encountered.
9 ier = 0
RETURN
! A constraint region contains a node.
10 ier = 5
RETURN
END SUBROUTINE addcst
SUBROUTINE addnod (k, xk, yk, ist, ncc, lcc, n, x, y, list, lptr, lend, &
lnew, ier)
INTEGER, INTENT(IN) :: k
REAL, INTENT(IN) :: xk
REAL, INTENT(IN) :: yk
INTEGER, INTENT(IN) :: ist
INTEGER, INTENT(IN) :: ncc
INTEGER, INTENT(IN OUT) :: lcc(:)
INTEGER, INTENT(IN OUT) :: n
REAL, INTENT(IN OUT) :: x(:)
REAL, INTENT(IN OUT) :: y(:)
INTEGER, INTENT(IN OUT) :: list(:)
INTEGER, INTENT(IN OUT) :: lptr(:)
INTEGER, INTENT(IN OUT) :: lend(:)
INTEGER, INTENT(IN OUT) :: lnew
INTEGER, INTENT(OUT) :: ier
!*******************************************************************
! From TRIPACK
! Robert J. Renka
! Dept. of Computer Science
! Univ. of North Texas
! renka@cs.unt.edu
! 06/27/98
! Given a triangulation of N nodes in the plane created by
! Subroutine TRMESH or TRMSHR, this subroutine updates the data
! structure with the addition of a new node in position K.
! If node K is inserted into X and Y (K <= N) rather than appended
! (K = N+1), then a corresponding insertion must be performed in
! any additional arrays associated with the nodes.
! For example, an array of data values Z must be shifted down
! to open up position K for the new value:
! set Z(I+1) to Z(I) for I = N,N-1,...,K. For optimal efficiency,
! new nodes should be appended whenever possible.
! Insertion is necessary, however, to add a non-constraint node
! when constraints are present (refer to Subroutine ADDCST).
! Note that a constraint node cannot be added by this routine.
! In order to insert a constraint node, it is necessary to add the node with
! no constraints present (call this routine with NCC = 0), update LCC by
! incrementing the appropriate entries, and then create (or restore) the
! constraints by a call to ADDCST.
! The algorithm consists of the following steps: node K is located
! relative to the triangulation (TRFIND), its index is added to the data
! structure (INTADD or BDYADD), and a sequence of swaps (SWPTST and SWAP) are
! applied to the arcs opposite K so that all arcs incident on node K and
! opposite node K (excluding constraint arcs) are locally optimal (satisfy
! the circumcircle test). Thus, if a (constrained) Delaunay triangulation is
! input, a (constrained) Delaunay triangulation will result.
! All indexes are incremented as necessary for an insertion.
! On input:
! K = Nodal index (index for X, Y, and LEND) of the
! new node to be added. 1 <= K <= LCC(1).
! (K <= N+1 if NCC=0).
! XK,YK = Cartesian coordinates of the new node (to be stored in X(K)
! and Y(K)). The node must not lie in a constraint region.
! IST = Index of a node at which TRFIND begins the search.
! Search time depends on the proximity of this node to node K.
! 1 <= IST <= N.
! NCC = Number of constraint curves. NCC >= 0.
! The above parameters are not altered by this routine.
! LCC = List of constraint curve starting indexes (or dummy array of
! length 1 if NCC = 0). Refer to Subroutine ADDCST.
! N = Number of nodes in the triangulation before K is added. N >= 3.
! Note that N will be incremented following the addition of node K.
! X,Y = Arrays of length at least N+1 containing the Cartesian
! coordinates of the nodes in the first N positions with non-
! constraint nodes in the first LCC(1)-1 locations if NCC > 0.
! LIST,LPTR,LEND,LNEW = Data structure associated with the triangulation
! of nodes 1 to N. The arrays must have
! sufficient length for N+1 nodes.
! Refer to TRMESH.
! On output:
! LCC = List of constraint curve starting indexes incremented by 1
! to reflect the insertion of K unless NCC = 0 or
! (IER .NE. 0 and IER .NE. -4).
! N = Number of nodes in the triangulation including K
! unless IER .NE. 0 and IER .NE. -4. Note that
! all comments refer to the input value of N.
! X,Y = Arrays updated with the insertion of XK and YK in the K-th
! positions (node I+1 was node I be fore the insertion for
! I = K to N if K <= N) unless IER .NE. 0 and IER .NE. -4.
! LIST,LPTR,LEND,LNEW = Data structure updated with the addition of
! node K unless IER .NE. 0 and IER .NE. -4.
! IER = Error indicator:
! IER = 0 if no errors were encountered.
! IER = -1 if K, IST, NCC, N, or an LCC entry is
! outside its valid range on input.
! IER = -2 if all nodes (including K) are collinear.
! IER = L if nodes L and K coincide for some L.
! IER = -3 if K lies in a constraint region.
! IER = -4 if an error flag is returned by SWAP implying that the
! triangulation (geometry) was bad on input.
! The errors conditions are tested in the order specified.
! Modules required by ADDNOD: BDYADD, CRTRI, INDXCC, INSERT, INTADD, JRAND,
! LEFT, LSTPTR, SWAP, SWPTST, TRFIND
! Intrinsic function called by ADDNOD: ABS
!***********************************************************
INTEGER :: i, i1, i2, i3, ibk, io1, io2, in1, kk, l, lccip1, lp, lpf, &
lpo1, nm1
kk = k
! Test for an invalid input parameter.
IF (kk < 1 .OR. ist < 1 .OR. ist > n .OR. ncc < 0 .OR. n < 3) GO TO 7
lccip1 = n+1
DO i = ncc,1,-1
IF (lccip1-lcc(i) < 3) GO TO 7
lccip1 = lcc(i)
END DO
IF (kk > lccip1) GO TO 7
! Find a triangle (I1,I2,I3) containing K or the rightmost (I1)
! and leftmost (I2) visible boundary nodes as viewed from node K.
CALL trfind (ist, xk, yk, n, x, y, list, lptr, lend, i1, i2, i3)
! Test for collinear nodes, duplicate nodes, and K lying in
! a constraint region.
IF (i1 == 0) GO TO 8
IF (i3 /= 0) THEN
l = i1
IF (xk == x(l) .AND. yk == y(l)) GO TO 9
l = i2
IF (xk == x(l) .AND. yk == y(l)) GO TO 9
l = i3
IF (xk == x(l) .AND. yk == y(l)) GO TO 9
IF (ncc > 0 .AND. crtri(ncc, lcc, i1, i2, i3) ) GO TO 10
ELSE
! K is outside the convex hull of the nodes and lies in a
! constraint region iff an exterior constraint curve is present.
IF (ncc > 0 .AND. indxcc(ncc,lcc,n,list,lend) /= 0) GO TO 10
END IF
! No errors encountered.
ier = 0
nm1 = n
n = n + 1
IF (kk < n) THEN
! Open a slot for K in X, Y, and LEND, and increment all
! nodal indexes which are greater than or equal to K.
! Note that LIST, LPTR, and LNEW are not yet updated with
! either the neighbors of K or the edges terminating on K.
DO ibk = nm1,kk,-1
x(ibk+1) = x(ibk)
y(ibk+1) = y(ibk)
lend(ibk+1) = lend(ibk)
END DO
DO i = 1,ncc
lcc(i) = lcc(i) + 1
END DO
l = lnew - 1
DO i = 1,l
IF (list(i) >= kk) list(i) = list(i) + 1
IF (list(i) <= -kk) list(i) = list(i) - 1
END DO
IF (i1 >= kk) i1 = i1 + 1
IF (i2 >= kk) i2 = i2 + 1
IF (i3 >= kk) i3 = i3 + 1
END IF
! Insert K into X and Y, and update LIST, LPTR, LEND, and
! LNEW with the arcs containing node K.
x(kk) = xk
y(kk) = yk
IF (i3 == 0) THEN
CALL bdyadd (kk, i1, i2, list, lptr, lend, lnew )
ELSE
CALL intadd (kk, i1, i2, i3, list, lptr, lend, lnew )
END IF
! Initialize variables for optimization of the triangulation.
lp = lend(kk)
lpf = lptr(lp)
io2 = list(lpf)
lpo1 = lptr(lpf)
io1 = ABS(list(lpo1))
! Begin loop: find the node opposite K.
5 lp = lstptr(lend(io1),io2,list,lptr)
IF (list(lp) < 0) GO TO 6
lp = lptr(lp)
in1 = ABS(list(lp))
IF ( crtri(ncc,lcc,io1,io2,in1) ) GO TO 6
! Swap test: if a swap occurs, two new arcs are opposite K and must be tested.
IF ( .NOT. swptst(in1,kk,io1,io2,x,y) ) GO TO 6
CALL swap (in1,kk,io1,io2, list,lptr,lend, lpo1)
IF (lpo1 == 0) GO TO 11
io1 = in1
GO TO 5
! No swap occurred. Test for termination and reset IO2 and IO1.
6 IF (lpo1 == lpf .OR. list(lpo1) < 0) RETURN
io2 = io1
lpo1 = lptr(lpo1)
io1 = ABS(list(lpo1))
GO TO 5
! A parameter is outside its valid range on input.
7 ier = -1
RETURN
! All nodes are collinear.
8 ier = -2
RETURN
! Nodes L and K coincide.
9 ier = l
RETURN
! Node K lies in a constraint region.
10 ier = -3
RETURN
! Zero pointer returned by SWAP.
11 ier = -4
RETURN
END SUBROUTINE addnod
FUNCTION areap (x, y, nb, nodes) RESULT(fn_val)
REAL, INTENT(IN) :: x(:)
REAL, INTENT(IN) :: y(:)
INTEGER, INTENT(IN) :: nb
INTEGER, INTENT(IN) :: nodes(:)
REAL :: fn_val
!*******************************************************************
! From TRIPACK
! Robert J. Renka
! Dept. of Computer Science
! Univ. of North Texas
! renka@cs.unt.edu
! 09/21/90
! Given a sequence of NB points in the plane, this function computes
! the signed area bounded by the closed polygonal curve which passes
! through the points in the specified order.
! Each simple closed curve is positively oriented (bounds positive area)
! if and only if the points are specified in counterclockwise order.
! The last point of the curve is taken to be the first point specified,
! and this point should therefore not be specified twice.
! The area of a triangulation may be computed by calling
! AREAP with values of NB and NODES determined by Subroutine BNODES.
! On input:
! X,Y = Arrays of length N containing the Cartesian coordinates of a
! set of points in the plane for some N >= NB.
! NB = Length of NODES.
! NODES = Array of length NB containing the ordered sequence of nodal
! indexes (in the range 1 to N) which define the polygonal curve.
! Input parameters are not altered by this function.
! On output:
! AREAP = Signed area bounded by the polygonal curve, or zero if NB < 3.
! Modules required by AREAP: None
!***********************************************************
INTEGER :: i, nd1, nd2, nnb
REAL :: a
! Local parameters:
! A = Partial sum of signed (and doubled) trapezoid areas
! I = DO-loop and NODES index
! ND1,ND2 = Elements of NODES
! NNB = Local copy of NB
nnb = nb
a = 0.
IF (nnb < 3) GO TO 2
nd2 = nodes(nnb)
! Loop on line segments NODES(I-1) -> NODES(I), where
! NODES(0) = NODES(NB), adding twice the signed trapezoid
! areas (integrals of the linear interpolants) to A.
DO i = 1,nnb
nd1 = nd2
nd2 = nodes(i)
a = a + (x(nd2)-x(nd1))*(y(nd1)+y(nd2))
END DO
! A contains twice the negative signed area of the region.
2 fn_val = -a/2.
RETURN
END FUNCTION areap
SUBROUTINE bdyadd (kk, i1, i2, list, lptr, lend, lnew )
INTEGER, INTENT(IN) :: kk
INTEGER, INTENT(IN) :: i1
INTEGER, INTENT(IN) :: i2
INTEGER, INTENT(OUT) :: list(:)
INTEGER, INTENT(IN OUT) :: lptr(:)
INTEGER, INTENT(IN OUT) :: lend(:)
INTEGER, INTENT(IN OUT) :: lnew
!*******************************************************************
! From TRIPACK
! Robert J. Renka
! Dept. of Computer Science
! Univ. of North Texas
! renka@cs.unt.edu
! 02/22/91
! This subroutine adds a boundary node to a triangulation of a set
! of points in the plane. The data structure is updated with the
! insertion of node KK, but no optimization is performed.
! On input:
! KK = Index of a node to be connected to the sequence
! of all visible boundary nodes. KK >= 1 and
! KK must not be equal to I1 or I2.
! I1 = First (rightmost as viewed from KK) boundary
! node in the triangulation which is visible from
! node KK (the line segment KK-I1 intersects no arcs.
! I2 = Last (leftmost) boundary node which is visible from node KK.
! I1 and I2 may be determined by Subroutine TRFIND.
! The above parameters are not altered by this routine.
! LIST,LPTR,LEND,LNEW = Triangulation data structure created by TRMESH
! or TRMSHR. Nodes I1 and I2 must be included
! in the triangulation.
! On output:
! LIST,LPTR,LEND,LNEW = Data structure updated with the addition of
! node KK. Node KK is connected to I1, I2, and
! all boundary nodes in between.
! Module required by BDYADD: INSERT
!***********************************************************
INTEGER :: k, lp, lsav, n1, n2, next, nsav
k = kk
n1 = i1
n2 = i2
! Add K as the last neighbor of N1.
lp = lend(n1)
lsav = lptr(lp)
lptr(lp) = lnew
list(lnew) = -k
lptr(lnew) = lsav
lend(n1) = lnew
lnew = lnew + 1
next = -list(lp)
list(lp) = next
nsav = next
! Loop on the remaining boundary nodes between N1 and N2,
! adding K as the first neighbor.
1 lp = lend(next)
CALL insert (k,lp,list,lptr,lnew)
IF (next == n2) GO TO 2
next = -list(lp)
list(lp) = next
GO TO 1
! Add the boundary nodes between N1 and N2 as neighbors of node K.
2 lsav = lnew
list(lnew) = n1
lptr(lnew) = lnew + 1
lnew = lnew + 1
next = nsav
3 IF (next == n2) GO TO 4
list(lnew) = next
lptr(lnew) = lnew + 1
lnew = lnew + 1
lp = lend(next)
next = list(lp)
GO TO 3
4 list(lnew) = -n2
lptr(lnew) = lsav
lend(k) = lnew
lnew = lnew + 1
RETURN
END SUBROUTINE bdyadd
SUBROUTINE bnodes (n, list, lptr, lend, nodes, nb, na, nt)
INTEGER, INTENT(IN) :: n
INTEGER, INTENT(IN) :: list(:)
INTEGER, INTENT(IN) :: lptr(:)
INTEGER, INTENT(IN) :: lend(:)
INTEGER, INTENT(OUT) :: nodes(:)
INTEGER, INTENT(OUT) :: nb
INTEGER, INTENT(OUT) :: na
INTEGER, INTENT(OUT) :: nt
!*******************************************************************
! From TRIPACK
! Robert J. Renka
! Dept. of Computer Science
! Univ. of North Texas
! renka@cs.unt.edu
! 09/01/88
! Given a triangulation of N points in the plane, this subroutine
! returns an array containing the indexes, in counterclockwise order,
! of the nodes on the boundary of the convex hull of the set of points.
! On input:
! N = Number of nodes in the triangulation. N >= 3.
! LIST,LPTR,LEND = Data structure defining the triangulation.
! Refer to Subroutine TRMESH.
! The above parameters are not altered by this routine.
! NODES = Integer array of length at least NB
! (NB <= N).
! On output:
! NODES = Ordered sequence of boundary node indexes in the range 1 to N.
! NB = Number of boundary nodes.
! NA,NT = Number of arcs and triangles, respectively,
! in the triangulation.
! Modules required by BNODES: None
!***********************************************************
INTEGER :: k, lp, n0, nst
! Set NST to the first boundary node encountered.
nst = 1
1 lp = lend(nst)
IF (list(lp) < 0) GO TO 2
nst = nst + 1
GO TO 1
! Initialization.
2 nodes(1) = nst
k = 1
n0 = nst
! Traverse the boundary in counterclockwise order.
3 lp = lend(n0)
lp = lptr(lp)
n0 = list(lp)
IF (n0 == nst) GO TO 4
k = k + 1
nodes(k) = n0
GO TO 3
! Termination.
4 nb = k
nt = 2*n - nb - 2
na = nt + n - 1
RETURN
END SUBROUTINE bnodes
SUBROUTINE circum (x1, y1, x2, y2, x3, y3, ratio, xc, yc, cr, sa, ar)
REAL, INTENT(IN) :: x1
REAL, INTENT(IN) :: y1
REAL, INTENT(IN) :: x2
REAL, INTENT(IN) :: y2
REAL, INTENT(IN) :: x3
REAL, INTENT(IN) :: y3
LOGICAL, INTENT(IN) :: ratio
REAL, INTENT(OUT) :: xc
REAL, INTENT(OUT) :: yc
REAL, INTENT(OUT) :: cr
REAL, INTENT(OUT) :: sa
REAL, INTENT(OUT) :: ar
!***********************************************************
! From TRIPACK
! Robert J. Renka
! Dept. of Computer Science
! Univ. of North Texas
! renka@cs.unt.edu
! 12/10/96
! Given three vertices defining a triangle, this subroutine returns
! the circumcenter, circumradius, signed triangle area, and,
! optionally, the aspect ratio of the triangle.
! On input:
! X1,...,Y3 = Cartesian coordinates of the vertices.
! RATIO = Logical variable with value TRUE if and only
! if the aspect ratio is to be computed.
! Input parameters are not altered by this routine.
! On output:
! XC,YC = Cartesian coordinates of the circumcenter
! (center of the circle defined by the three points)
! unless SA = 0, in which XC and YC are not altered.
! CR = Circumradius (radius of the circle defined by
! the three points) unless SA = 0 (infinite
! radius), in which case CR is not altered.
! SA = Signed triangle area with positive value if and only if
! the vertices are specified in counterclockwise order:
! (X3,Y3) is strictly to the left of the directed line
! from (X1,Y1) toward (X2,Y2).
! AR = Aspect ratio r/CR, where r is the radius of the inscribed
! circle, unless RATIO = FALSE, in which case AR is not
! altered. AR is in the range 0 to .5, with value 0 iff
! SA = 0 and value .5 iff the vertices define an equilateral
! triangle.
! Modules required by CIRCUM: None
! Intrinsic functions called by CIRCUM: ABS, SQRT
!***********************************************************
INTEGER :: i
REAL :: ds(3), fx, fy, u(3), v(3)
! Set U(K) and V(K) to the x and y components, respectively,
! of the directed edge opposite vertex K.
u(1) = x3 - x2
u(2) = x1 - x3
u(3) = x2 - x1
v(1) = y3 - y2
v(2) = y1 - y3
v(3) = y2 - y1
! Set SA to the signed triangle area.
sa = (u(1)*v(2) - u(2)*v(1))/2.
IF (sa == 0.) THEN
IF (ratio) ar = 0.
RETURN
END IF
! Set DS(K) to the squared distance from the origin to vertex K.
ds(1) = x1*x1 + y1*y1
ds(2) = x2*x2 + y2*y2
ds(3) = x3*x3 + y3*y3
! Compute factors of XC and YC.
fx = 0.
fy = 0.
DO i = 1,3
fx = fx - ds(i)*v(i)
fy = fy + ds(i)*u(i)
END DO
xc = fx/(4.*sa)
yc = fy/(4.*sa)
cr = SQRT( (xc-x1)**2 + (yc-y1)**2 )
IF (.NOT. ratio) RETURN
! Compute the squared edge lengths and aspect ratio.
DO i = 1,3
ds(i) = u(i)*u(i) + v(i)*v(i)
END DO
ar = 2.*ABS(sa)/ ( (SQRT(ds(1)) + SQRT(ds(2)) + SQRT(ds(3)))*cr )
RETURN
END SUBROUTINE circum
FUNCTION crtri (ncc, lcc, i1, i2, i3) RESULT(fn_val)
INTEGER, INTENT(IN) :: ncc
INTEGER, INTENT(IN) :: lcc(:)
INTEGER, INTENT(IN) :: i1
INTEGER, INTENT(IN) :: i2
INTEGER, INTENT(IN) :: i3
LOGICAL :: fn_val
!***********************************************************
! From TRIPACK
! Robert J. Renka
! Dept. of Computer Science
! Univ. of North Texas
! renka@cs.unt.edu
! 08/14/91
! This function returns TRUE if and only if triangle (I1,
! I2,I3) lies in a constraint region.
! On input:
! NCC,LCC = Constraint data structure. Refer to Subroutine ADDCST.
! I1,I2,I3 = Nodal indexes of the counterclockwise-
! ordered vertices of a triangle.
! Input parameters are altered by this function.
! CRTRI = TRUE iff (I1,I2,I3) is a constraint region triangle.
! Note that input parameters are not tested for validity.
! Modules required by CRTRI: None
! Intrinsic functions called by CRTRI: MAX, MIN
!***********************************************************
INTEGER :: i, imax, imin
imax = MAX(i1, i2, i3)
! Find the index I of the constraint containing IMAX.
i = ncc + 1
1 i = i - 1
IF (i <= 0) GO TO 2
IF (imax < lcc(i)) GO TO 1
imin = MIN(i1, i2, i3)
! P lies in a constraint region iff I1, I2, and I3 are nodes of the same
! constraint (IMIN >= LCC(I)), and (IMIN,IMAX) is (I1,I3), (I2,I1),
! or (I3,I2).
fn_val = imin >= lcc(i) .AND. ((imin == i1 .AND. imax == i3) .OR. &
(imin == i2 .AND. imax == i1) .OR. (imin == i3 .AND. imax == i2))
RETURN
! NCC <= 0 or all vertices are non-constraint nodes.
2 fn_val = .false.
RETURN
END FUNCTION crtri
SUBROUTINE delarc (n, io1, io2, list, lptr, lend, lnew, ier)
INTEGER, INTENT(IN) :: n
INTEGER, INTENT(IN) :: io1
INTEGER, INTENT(IN) :: io2
INTEGER, INTENT(IN OUT) :: list(:)
INTEGER, INTENT(IN OUT) :: lptr(:)
INTEGER, INTENT(IN OUT) :: lend(:)
INTEGER, INTENT(IN OUT) :: lnew
INTEGER, INTENT(OUT) :: ier
!***********************************************************
! From TRIPACK
! Robert J. Renka
! Dept. of Computer Science
! Univ. of North Texas
! renka@cs.unt.edu
! 11/12/94
! This subroutine deletes a boundary arc from a triangulation.
! It may be used to remove a null triangle from the convex hull boundary.
! Note, however, that if the union of triangles is rendered nonconvex,
! Subroutines DELNOD, EDGE, and TRFIND may fail.
! Thus, Subroutines ADDCST, ADDNOD, DELNOD, EDGE, and NEARND should not be
! called following an arc deletion.
! On input:
! N = Number of nodes in the triangulation. N >= 4.
! IO1,IO2 = Indexes (in the range 1 to N) of a pair of adjacent
! boundary nodes defining the arc to be removed.
! The above parameters are not altered by this routine.
! LIST,LPTR,LEND,LNEW = Triangulation data structure created by
! TRMESH or TRMSHR.
! On output:
! LIST,LPTR,LEND,LNEW = Data structure updated with the removal of
! arc IO1-IO2 unless IER > 0.
! IER = Error indicator:
! IER = 0 if no errors were encountered.
! IER = 1 if N, IO1, or IO2 is outside its valid range,
! or IO1 = IO2.
! IER = 2 if IO1-IO2 is not a boundary arc.
! IER = 3 if the node opposite IO1-IO2 is already a boundary node,
! and thus IO1 or IO2 has only two neighbors or a
! deletion would result in two triangulations sharing
! a single node.
! IER = 4 if one of the nodes is a neighbor of the other,
! but not vice versa, implying an invalid triangulation
! data structure.
! Modules required by DELARC: DELNB, LSTPTR
! Intrinsic function called by DELARC: ABS
!***********************************************************
INTEGER :: lp, lph, lpl, n1, n2, n3
n1 = io1
n2 = io2
! Test for errors, and set N1->N2 to the directed boundary edge
! associated with IO1-IO2: (N1,N2,N3) is a triangle for some N3.
IF (n < 4 .OR. n1 < 1 .OR. n1 > n .OR. n2 < 1 .OR. n2 > n .OR. n1 == n2) THEN
ier = 1
RETURN
END IF
lpl = lend(n2)
IF (-list(lpl) /= n1) THEN
n1 = n2
n2 = io1
lpl = lend(n2)
IF (-list(lpl) /= n1) THEN
ier = 2
RETURN
END IF
END IF
! Set N3 to the node opposite N1->N2 (the second neighbor
! of N1), and test for error 3 (N3 already a boundary node).
lpl = lend(n1)
lp = lptr(lpl)
lp = lptr(lp)
n3 = ABS(list(lp))
lpl = lend(n3)
IF (list(lpl) <= 0) THEN
ier = 3
RETURN
END IF
! Delete N2 as a neighbor of N1, making N3 the first neighbor, and test for
! error 4 (N2 not a neighbor of N1).
! Note that previously computed pointers may no longer be valid following
! the call to DELNB.
CALL delnb (n1,n2,n, list,lptr,lend,lnew, lph)
IF (lph < 0) THEN
ier = 4
RETURN
END IF
! Delete N1 as a neighbor of N2, making N3 the new last neighbor.
CALL delnb (n2,n1,n, list,lptr,lend,lnew, lph)
! Make N3 a boundary node with first neighbor N2 and last neighbor N1.
lp = lstptr(lend(n3), n1, list, lptr)
lend(n3) = lp
list(lp) = -n1
! No errors encountered.
ier = 0
RETURN
END SUBROUTINE delarc
SUBROUTINE delnb (n0, nb, n, list, lptr, lend, lnew, lph)
INTEGER, INTENT(IN) :: n0
INTEGER, INTENT(IN) :: nb
INTEGER, INTENT(IN) :: n
INTEGER, INTENT(IN OUT) :: list(:)
INTEGER, INTENT(IN OUT) :: lptr(:)
INTEGER, INTENT(IN OUT) :: lend(:)
INTEGER, INTENT(IN OUT) :: lnew
INTEGER, INTENT(OUT) :: lph
!***********************************************************
! From TRIPACK
! Robert J. Renka
! Dept. of Computer Science
! Univ. of North Texas
! renka@cs.unt.edu
! 07/30/98
! This subroutine deletes a neighbor NB from the adjacency list of node N0
! (but N0 is not deleted from the adjacency list of NB) and, if NB is a
! boundary node, makes N0 a boundary node. For pointer (LIST index) LPH to NB
! as a neighbor of N0, the empty LIST,LPTR location LPH is filled in with the
! values at LNEW-1, pointer LNEW-1 (in LPTR and possibly in LEND) is changed
! to LPH, and LNEW is decremented. This requires a search of LEND and LPTR
! entailing an expected operation count of O(N).
! On input:
! N0,NB = Indexes, in the range 1 to N, of a pair of
! nodes such that NB is a neighbor of N0.
! (N0 need not be a neighbor of NB.)
! N = Number of nodes in the triangulation. N >= 3.
! The above parameters are not altered by this routine.
! LIST,LPTR,LEND,LNEW = Data structure defining the triangulation.
! On output:
! LIST,LPTR,LEND,LNEW = Data structure updated with the removal of
! NB from the adjacency list of N0 unless LPH < 0.
! LPH = List pointer to the hole (NB as a neighbor of
! N0) filled in by the values at LNEW-1 or error indicator:
! LPH > 0 if no errors were encountered.
! LPH = -1 if N0, NB, or N is outside its valid range.
! LPH = -2 if NB is not a neighbor of N0.
! Modules required by DELNB: None
! Intrinsic function called by DELNB: ABS
!***********************************************************
INTEGER :: i, lnw, lp, lpb, lpl, lpp, nn
! Local parameters:
! I = DO-loop index
! LNW = LNEW-1 (output value of LNEW)
! LP = LIST pointer of the last neighbor of NB
! LPB = Pointer to NB as a neighbor of N0
! LPL = Pointer to the last neighbor of N0
! LPP = Pointer to the neighbor of N0 that precedes NB
! NN = Local copy of N
nn = n
! Test for error 1.
IF (n0 < 1 .OR. n0 > nn .OR. nb < 1 .OR. nb > nn .OR. nn < 3) THEN
lph = -1
RETURN
END IF
! Find pointers to neighbors of N0:
! LPL points to the last neighbor,
! LPP points to the neighbor NP preceding NB, and
! LPB points to NB.
lpl = lend(n0)
lpp = lpl
lpb = lptr(lpp)
1 IF (list(lpb) == nb) GO TO 2
lpp = lpb
lpb = lptr(lpp)
IF (lpb /= lpl) GO TO 1
! Test for error 2 (NB not found).
IF (ABS(list(lpb)) /= nb) THEN
lph = -2
RETURN
END IF
! NB is the last neighbor of N0. Make NP the new last neighbor and,
! if NB is a boundary node, then make N0 a boundary node.
lend(n0) = lpp
lp = lend(nb)
IF (list(lp) < 0) list(lpp) = -list(lpp)
GO TO 3
! NB is not the last neighbor of N0. If NB is a boundary node and
! N0 is not, then make N0 a boundary node with last neighbor NP.
2 lp = lend(nb)
IF (list(lp) < 0 .AND. list(lpl) > 0) THEN
lend(n0) = lpp
list(lpp) = -list(lpp)
END IF
! Update LPTR so that the neighbor following NB now follows NP,
! and fill in the hole at location LPB.
3 lptr(lpp) = lptr(lpb)
lnw = lnew-1
list(lpb) = list(lnw)
lptr(lpb) = lptr(lnw)
DO i = nn,1,-1
IF (lend(i) == lnw) THEN
lend(i) = lpb
GO TO 5
END IF
END DO
5 DO i = 1,lnw-1
IF (lptr(i) == lnw) THEN
lptr(i) = lpb
END IF
END DO
! No errors encountered.
lnew = lnw
lph = lpb
RETURN
END SUBROUTINE delnb
SUBROUTINE delnod (k, ncc, lcc, n, x, y, list, lptr, lend, lnew, lwk, iwk, ier)
INTEGER, INTENT(IN) :: k
INTEGER, INTENT(IN) :: ncc
INTEGER, INTENT(IN OUT) :: lcc(:)
INTEGER, INTENT(IN OUT) :: n
REAL, INTENT(IN OUT) :: x(:)
REAL, INTENT(IN OUT) :: y(:)
INTEGER, INTENT(IN OUT) :: list(:)
INTEGER, INTENT(IN OUT) :: lptr(:)
INTEGER, INTENT(IN OUT) :: lend(:)
INTEGER, INTENT(IN OUT) :: lnew
INTEGER, INTENT(IN OUT) :: lwk
INTEGER, INTENT(OUT) :: iwk(:,:)
INTEGER, INTENT(OUT) :: ier
!*******************************************************************
! From TRIPACK
! Robert J. Renka
! Dept. of Computer Science
! Univ. of North Texas
! renka@cs.unt.edu
! 06/28/98
! This subroutine deletes node K (along with all arcs incident on
! node K) from a triangulation of N nodes in the plane, and inserts arcs
! as necessary to produce a triangulation of the remaining N-1 nodes.
! If a Delaunay triangulation is input, a Delaunay triangulation will result,
! and thus, DELNOD reverses the effect of a call to Subroutine ADDNOD.
! Note that a constraint node cannot be deleted by this routine.
! In order to delete a constraint node, it is necessary to call this
! routine with NCC = 0, decrement the appropriate LCC entries (LCC(I)
! such that LCC(I) > K), and then create (or restore) the constraints
! by a call to Subroutine ADDCST.
! On input:
! K = Index (for X and Y) of the node to be deleted.
! 1 <= K < LCC(1). (K <= N if NCC=0).
! NCC = Number of constraint curves. NCC >= 0.
! The above parameters are not altered by this routine.
! LCC = List of constraint curve starting indexes (or dummy array of
! length 1 if NCC = 0). Refer to Subroutine ADDCST.
! N = Number of nodes in the triangulation on input.
! N >= 4. Note that N will be decremented following the deletion.
! X,Y = Arrays of length N containing the coordinates of the nodes with
! non-constraint nodes in the first LCC(1)-1 locations if NCC > 0.
! LIST,LPTR,LEND,LNEW = Data structure defining the triangulation.
! Refer to Subroutine TRMESH.
! LWK = Number of columns reserved for IWK. LWK must be at least NNB-3,
! where NNB is the number of neighbors of node K, including an
! extra pseudo-node if K is a boundary node.
! IWK = Integer work array dimensioned 2 by LWK (or array of
! length >= 2*LWK).
! On output:
! LCC = List of constraint curve starting indexes decremented by 1 to
! reflect the deletion of K unless NCC = 0 or 1 <= IER <= 4.
! N = New number of nodes (input value minus one) unless 1 <= IER <= 4.
!
! X,Y = Updated arrays of length N-1 containing nodal coordinates
! (with elements K+1,...,N shifted up a position and thus
! overwriting element K) unless 1 <= IER <= 4. (N here denotes
! the input value.)
! LIST,LPTR,LEND,LNEW = Updated triangulation data structure
! reflecting the deletion unless IER .NE. 0.
! Note that the data structure may
! have been altered if IER >= 3.
! LWK = Number of IWK columns required unless IER = 1 or IER = 3.
! IWK = Indexes of the endpoints of the new arcs added unless LWK = 0
! or 1 <= IER <= 4. (Arcs are associated with columns, or
! pairs of adjacent elements if IWK is declared as a
! singly-subscripted array.)
! IER = Error indicator:
! IER = 0 if no errors were encountered.
! IER = 1 if K, NCC, N, or an LCC entry is outside its valid
! range or LWK < 0 on input.
! IER = 2 if more space is required in IWK. Refer to LWK.
! IER = 3 if the triangulation data structure is invalid on input.
! IER = 4 if K is an interior node with 4 or more neighbors, and
! the number of neighbors could not be reduced to 3 by
! swaps. This could be caused by floating point errors
! with collinear nodes or by an invalid data structure.
! IER = 5 if an error flag was returned by OPTIM.
! An error message is written to the standard output unit
! in this event.
! Note that the deletion may result in all remaining nodes being collinear.
! This situation is not flagged.
! Modules required by DELNOD: DELNB, LEFT, LSTPTR, NBCNT, OPTIM, SWAP, SWPTST
! Intrinsic function called by DELNOD: ABS
!***********************************************************
INTEGER :: i, ierr, iwl, j, lccip1, lnw, lp, lp21, lpf, &
lph, lpl, lpl2, lpn, lwkl, n1, n2, nfrst, nit, nl, nn, nnb, nr
LOGICAL :: bdry
REAL :: x1, x2, xl, xr, y1, y2, yl, yr
! Set N1 to K and NNB to the number of neighbors of N1 (plus
! one if N1 is a boundary node), and test for errors. LPF
! and LPL are LIST indexes of the first and last neighbors
! of N1, IWL is the number of IWK columns containing arcs,
! and BDRY is TRUE iff N1 is a boundary node.
n1 = k
nn = n
IF (ncc < 0 .OR. n1 < 1 .OR. nn < 4 .OR. lwk < 0) GO TO 21
lccip1 = nn+1
DO i = ncc,1,-1
IF (lccip1-lcc(i) < 3) GO TO 21
lccip1 = lcc(i)
END DO
IF (n1 >= lccip1) GO TO 21
lpl = lend(n1)
lpf = lptr(lpl)
nnb = nbcnt(lpl,lptr)
bdry = list(lpl) < 0
IF (bdry) nnb = nnb + 1
IF (nnb < 3) GO TO 23
lwkl = lwk
lwk = nnb - 3
IF (lwkl < lwk) GO TO 22
iwl = 0
IF (nnb == 3) GO TO 5
! Initialize for loop on arcs N1-N2 for neighbors N2 of N1, beginning with the
! second neighbor. NR and NL are the neighbors preceding and following N2,
! respectively, and LP indexes NL. The loop is exited when all possible
! swaps have been applied to arcs incident on N1. If N1 is interior,
! the number of neighbors will be reduced to 3.
x1 = x(n1)
y1 = y(n1)
nfrst = list(lpf)
nr = nfrst
xr = x(nr)
yr = y(nr)
lp = lptr(lpf)
n2 = list(lp)
x2 = x(n2)
y2 = y(n2)
lp = lptr(lp)
! Top of loop: set NL to the neighbor following N2.
2 nl = ABS(list(lp))
IF (nl == nfrst .AND. bdry) GO TO 5
xl = x(nl)
yl = y(nl)
! Test for a convex quadrilateral. To avoid an incorrect test caused by
! collinearity, use the fact that if N1 is a boundary node, then
! N1 LEFT NR->NL and if N2 is a boundary node, then N2 LEFT NL->NR.
lpl2 = lend(n2)
IF ( (bdry .OR. left(xr, yr, xl, yl, x1, y1)) .AND. (list(lpl2) < 0 .OR. &
left(xl, yl, xr, yr, x2, y2)) ) GO TO 3
! Nonconvex quadrilateral -- no swap is possible.
nr = n2
xr = x2
yr = y2
GO TO 4
! The quadrilateral defined by adjacent triangles (N1,N2,NL) and (N2,N1,NR)
! is convex. Swap in NL-NR and store it in IWK. Indexes larger than N1
! must be decremented since N1 will be deleted from X and Y.
3 CALL swap (nl, nr, n1, n2, list, lptr, lend, lp21)
iwl = iwl + 1
IF (nl <= n1) THEN
iwk(1,iwl) = nl
ELSE
iwk(1,iwl) = nl - 1
END IF
IF (nr <= n1) THEN
iwk(2,iwl) = nr
ELSE
iwk(2,iwl) = nr - 1
END IF
! Recompute the LIST indexes LPL,LP and decrement NNB.
lpl = lend(n1)
nnb = nnb - 1
IF (nnb == 3) GO TO 5
lp = lstptr(lpl, nl, list, lptr)
IF (nr == nfrst) GO TO 4
! NR is not the first neighbor of N1.
! Back up and test N1-NR for a swap again: Set N2 to NR and NR to the
! previous neighbor of N1 -- the neighbor of NR which follows N1.
! LP21 points to NL as a neighbor of NR.
n2 = nr
x2 = xr
y2 = yr
lp21 = lptr(lp21)
lp21 = lptr(lp21)
nr = ABS(list(lp21))
xr = x(nr)
yr = y(nr)
GO TO 2
! Bottom of loop -- test for invalid termination.
4 IF (n2 == nfrst) GO TO 24
n2 = nl
x2 = xl
y2 = yl
lp = lptr(lp)
GO TO 2
! Delete N1 from the adjacency list of N2 for all neighbors N2 of N1.
! LPL points to the last neighbor of N1.
! LNEW is stored in local variable LNW.
5 lp = lpl
lnw = lnew
! Loop on neighbors N2 of N1, beginning with the first.
6 lp = lptr(lp)
n2 = ABS(list(lp))
CALL delnb (n2,n1,n, list,lptr,lend,lnw, lph)
IF (lph < 0) GO TO 23
! LP and LPL may require alteration.
IF (lpl == lnw) lpl = lph
IF (lp == lnw) lp = lph
IF (lp /= lpl) GO TO 6
! Delete N1 from X, Y, and LEND, and remove its adjacency list from LIST and
! LPTR. LIST entries (nodal indexes) which are larger than N1 must be
! decremented.
nn = nn - 1
IF (n1 > nn) GO TO 9
DO i = n1,nn
x(i) = x(i+1)
y(i) = y(i+1)
lend(i) = lend(i+1)
END DO
DO i = 1,lnw-1
IF (list(i) > n1) list(i) = list(i) - 1
IF (list(i) < -n1) list(i) = list(i) + 1
END DO
! For LPN = first to last neighbors of N1, delete the preceding neighbor
! (indexed by LP).
! Each empty LIST,LPTR location LP is filled in with the values at LNW-1,
! and LNW is decremented. All pointers (including those in LPTR and LEND)
! with value LNW-1 must be changed to LP.
! LPL points to the last neighbor of N1.
9 IF (bdry) nnb = nnb - 1
lpn = lpl
DO j = 1,nnb
lnw = lnw - 1
lp = lpn
lpn = lptr(lp)
list(lp) = list(lnw)
lptr(lp) = lptr(lnw)
IF (lptr(lpn) == lnw) lptr(lpn) = lp
IF (lpn == lnw) lpn = lp
DO i = nn,1,-1
IF (lend(i) == lnw) THEN
lend(i) = lp
GO TO 11
END IF
END DO
11 DO i = lnw-1,1,-1
IF (lptr(i) == lnw) lptr(i) = lp
END DO
END DO
! Decrement LCC entries.
DO i = 1,ncc
lcc(i) = lcc(i) - 1
END DO
! Update N and LNEW, and optimize the patch of triangles
! containing K (on input) by applying swaps to the arcs in IWK.
n = nn
lnew = lnw
IF (iwl > 0) THEN
nit = 4*iwl
CALL optim (x, y, iwl, list, lptr, lend, nit, iwk, ierr)
IF (ierr /= 0) GO TO 25
END IF
! Successful termination.
ier = 0
RETURN
! Invalid input parameter.
21 ier = 1
RETURN
! Insufficient space reserved for IWK.
22 ier = 2
RETURN
! Invalid triangulation data structure. NNB < 3 on input or
! N2 is a neighbor of N1 but N1 is not a neighbor of N2.
23 ier = 3
RETURN
! K is an interior node with 4 or more neighbors, but the
! number of neighbors could not be reduced.
24 ier = 4
RETURN
! Error flag returned by OPTIM.
25 ier = 5
WRITE (*,100) nit, ierr
RETURN
100 FORMAT (//t6, '*** Error in OPTIM: NIT = ', i4, ', IER = ', i1, ' ***'/)
END SUBROUTINE delnod
SUBROUTINE edge (in1, in2, x, y, lwk, list, lptr, lend, ier)
! N.B. Argument IWK has been removed.
INTEGER, INTENT(IN) :: in1
INTEGER, INTENT(IN) :: in2
REAL, INTENT(IN) :: x(:)
REAL, INTENT(IN) :: y(:)
INTEGER, INTENT(IN OUT) :: lwk
INTEGER, INTENT(IN OUT) :: list(:)
INTEGER, INTENT(IN OUT) :: lptr(:)
INTEGER, INTENT(IN OUT) :: lend(:)
INTEGER, INTENT(OUT) :: ier
!***********************************************************
! From TRIPACK
! Robert J. Renka
! Dept. of Computer Science
! Univ. of North Texas
! renka@cs.unt.edu
! 06/23/98
! Given a triangulation of N nodes and a pair of nodal indexes IN1 and IN2,
! this routine swaps arcs as necessary to force IN1 and IN2 to be adjacent.
! Only arcs which intersect IN1-IN2 are swapped out. If a Delaunay
! triangulation is input, the resulting triangulation is as close as possible
! to a Delaunay triangulation in the sense that all arcs other than IN1-IN2
! are locally optimal.
! A sequence of calls to EDGE may be used to force the presence of a set of
! edges defining the boundary of a non-convex and/or multiply connected region
! (refer to Subroutine ADDCST), or to introduce barriers into the
! triangulation. Note that Subroutine GETNP will not necessarily return
! closest nodes if the triangulation has been constrained by a call to EDGE.
! However, this is appropriate in some applications, such as triangle-based
! interpolation on a nonconvex domain.
! On input:
! IN1,IN2 = Indexes (of X and Y) in the range 1 to N
! defining a pair of nodes to be connected by an arc.
! X,Y = Arrays of length N containing the Cartesian coordinates of the
! nodes.
! The above parameters are not altered by this routine.
! LWK = Number of columns reserved for IWK. This must be at least NI --
! the number of arcs which intersect IN1-IN2.
! (NI is bounded by N-3.)
! IWK = Integer work array of length at least 2*LWK.
! LIST,LPTR,LEND = Data structure defining the triangulation.
! Refer to Subroutine TRMESH.
! On output:
! LWK = Number of arcs which intersect IN1-IN2 (but not more than the
! input value of LWK) unless IER = 1 or IER = 3. LWK = 0 if and
! only if IN1 and IN2 were adjacent (or LWK=0) on input.
! IWK = Array containing the indexes of the endpoints of the new arcs
! other than IN1-IN2 unless IER > 0 or LWK = 0. New arcs to the
! left of IN2-IN1 are stored in the first K-1 columns
! (left portion of IWK), column K contains zeros, and new arcs to
! the right of IN2-IN1 occupy columns K+1,...,LWK. (K can be
! determined by searching IWK for the zeros.)
! LIST,LPTR,LEND = Data structure updated if necessary to reflect the
! presence of an arc connecting IN1 and IN2 unless
! IER.NE. 0. The data structure has been altered if
! IER = 4.
! IER = Error indicator:
! IER = 0 if no errors were encountered.
! IER = 1 if IN1 < 1, IN2 < 1, IN1 = IN2, or LWK < 0 on input.
! IER = 2 if more space is required in IWK.
! IER = 3 if IN1 and IN2 could not be connected due to
! either an invalid data structure or
! collinear nodes (and floating point error).
! IER = 4 if an error flag was returned by OPTIM.
! An error message is written to the standard output unit
! in the case of IER = 3 or IER = 4.
! Modules required by EDGE: LEFT, LSTPTR, OPTIM, SWAP, SWPTST
! Intrinsic function called by EDGE: ABS
!***********************************************************
INTEGER :: i, ierr, iwc, iwcp1, iwend, iwf, iwk(2,lwk), iwl, lft, lp, &
lpl, lp21, next, nit, nl, nr, n0, n1, n2, n1frst, n1lst
REAL :: dx, dy, x0, y0, x1, y1, x2, y2
! Local parameters:
! DX,DY = Components of arc N1-N2
! I = DO-loop index and column index for IWK
! IERR = Error flag returned by Subroutine OPTIM
! IWC = IWK index between IWF and IWL -- NL->NR is
! stored in IWK(1,IWC)->IWK(2,IWC)
! IWCP1 = IWC + 1
! IWEND = Input or output value of LWK
! IWF = IWK (column) index of the first (leftmost) arc
! which intersects IN1->IN2
! IWL = IWK (column) index of the last (rightmost) are
! which intersects IN1->IN2
! LFT = Flag used to determine if a swap results in the new arc
! intersecting IN1-IN2 -- LFT = 0 iff N0 = IN1, LFT = -1 implies
! N0 LEFT IN1->IN2, and LFT = 1 implies N0 LEFT IN2->IN1
! LP21 = Unused parameter returned by SWAP
! LP = List pointer (index) for LIST and LPTR
! LPL = Pointer to the last neighbor of IN1 or NL
! N0 = Neighbor of N1 or node opposite NR->NL
! N1,N2 = Local copies of IN1 and IN2
! N1FRST = First neighbor of IN1
! N1LST = (Signed) last neighbor of IN1
! NEXT = Node opposite NL->NR
! NIT = Flag or number of iterations employed by OPTIM
! NL,NR = Endpoints of an arc which intersects IN1-IN2 with NL LEFT IN1->IN2
! X0,Y0 = Coordinates of N0
! X1,Y1 = Coordinates of IN1
! X2,Y2 = Coordinates of IN2
! Store IN1, IN2, and LWK in local variables and test for errors.
n1 = in1
n2 = in2
iwend = lwk
IF (n1 < 1 .OR. n2 < 1 .OR. n1 == n2 .OR. iwend < 0) GO TO 31
! Test for N2 as a neighbor of N1. LPL points to the last neighbor of N1.
lpl = lend(n1)
n0 = ABS(list(lpl))
lp = lpl
1 IF (n0 == n2) GO TO 30
lp = lptr(lp)
n0 = list(lp)
IF (lp /= lpl) GO TO 1
! Initialize parameters.
iwl = 0
nit = 0
! Store the coordinates of N1 and N2.
2 x1 = x(n1)
y1 = y(n1)
x2 = x(n2)
y2 = y(n2)
! Set NR and NL to adjacent neighbors of N1 such that NR LEFT N2->N1 and
! NL LEFT N1->N2, (NR Forward N1->N2 or NL Forward N1->N2), and
! (NR Forward N2->N1 or NL Forward N2->N1).
! Initialization: Set N1FRST and N1LST to the first and (signed) last
! neighbors of N1, respectively, and initialize NL to N1FRST.
lpl = lend(n1)
n1lst = list(lpl)
lp = lptr(lpl)
n1frst = list(lp)
nl = n1frst
IF (n1lst < 0) GO TO 4
! N1 is an interior node. Set NL to the first candidate
! for NR (NL LEFT N2->N1).
3 IF ( left(x2,y2,x1,y1,x(nl),y(nl)) ) GO TO 4
lp = lptr(lp)
nl = list(lp)
IF (nl /= n1frst) GO TO 3
! All neighbors of N1 are strictly left of N1->N2.
GO TO 5
! NL = LIST(LP) LEFT N2->N1. Set NR to NL and NL to the
! following neighbor of N1.
4 nr = nl
lp = lptr(lp)
nl = ABS(list(lp))
IF ( left(x1,y1,x2,y2,x(nl),y(nl)) ) THEN
! NL LEFT N1->N2 and NR LEFT N2->N1. The Forward tests are employed to
! avoid an error associated with collinear nodes.
dx = x2-x1
dy = y2-y1
IF ((dx*(x(nl)-x1)+dy*(y(nl)-y1) >= 0. .OR. &
dx*(x(nr)-x1)+dy*(y(nr)-y1) >= 0.) .AND. &
(dx*(x(nl)-x2)+dy*(y(nl)-y2) <= 0. .OR. &
dx*(x(nr)-x2)+dy*(y(nr)-y2) <= 0.)) GO TO 6
! NL-NR does not intersect N1-N2. However, there is another
! candidate for the first arc if NL lies on the line N1-N2.
IF ( .NOT. left(x2,y2,x1,y1,x(nl),y(nl)) ) GO TO 5
END IF
! Bottom of loop.
IF (nl /= n1frst) GO TO 4
! Either the triangulation is invalid or N1-N2 lies on the convex hull
! boundary and an edge NR->NL (opposite N1 and intersecting N1-N2)
! was not found due to floating point error.
! Try interchanging N1 and N2 -- NIT > 0 iff this has already been done.
5 IF (nit > 0) GO TO 33
nit = 1
n1 = n2
n2 = in1
GO TO 2
! Store the ordered sequence of intersecting edges NL->NR in
! IWK(1,IWL)->IWK(2,IWL).
6 iwl = iwl + 1
IF (iwl > iwend) GO TO 32
iwk(1,iwl) = nl
iwk(2,iwl) = nr
! Set NEXT to the neighbor of NL which follows NR.
lpl = lend(nl)
lp = lptr(lpl)
! Find NR as a neighbor of NL. The search begins with the first neighbor.
7 IF (list(lp) == nr) GO TO 8
lp = lptr(lp)
IF (lp /= lpl) GO TO 7
! NR must be the last neighbor, and NL->NR cannot be a boundary edge.
IF (list(lp) /= nr) GO TO 33
! Set NEXT to the neighbor following NR, and test for
! termination of the store loop.
8 lp = lptr(lp)
next = ABS(list(lp))
IF (next == n2) GO TO 9
! Set NL or NR to NEXT.
IF ( left(x1,y1,x2,y2,x(next),y(next)) ) THEN
nl = next
ELSE
nr = next
END IF
GO TO 6
! IWL is the number of arcs which intersect N1-N2.
! Store LWK.
9 lwk = iwl
iwend = iwl
! Initialize for edge swapping loop -- all possible swaps are applied
! (even if the new arc again intersects N1-N2), arcs to the left of N1->N2
! are stored in the left portion of IWK, and arcs to the right are stored
! in the right portion. IWF and IWL index the first and last
! intersecting arcs.
iwf = 1
! Top of loop -- set N0 to N1 and NL->NR to the first edge.
! IWC points to the arc currently being processed.
! LFT <= 0 iff N0 LEFT N1->N2.
10 lft = 0
n0 = n1
x0 = x1
y0 = y1
nl = iwk(1,iwf)
nr = iwk(2,iwf)
iwc = iwf
! Set NEXT to the node opposite NL->NR unless IWC is the last arc.
11 IF (iwc == iwl) GO TO 21
iwcp1 = iwc + 1
next = iwk(1,iwcp1)
IF (next /= nl) GO TO 16
next = iwk(2,iwcp1)
! NEXT RIGHT N1->N2 and IWC < IWL. Test for a possible swap.
IF ( .NOT. left(x0,y0,x(nr),y(nr),x(next),y(next)) ) GO TO 14
IF (lft >= 0) GO TO 12
IF ( .NOT. left(x(nl),y(nl),x0,y0,x(next),y(next)) ) GO TO 14
! Replace NL->NR with N0->NEXT.
CALL swap (next,n0,nl,nr, list,lptr,lend, lp21)
iwk(1,iwc) = n0
iwk(2,iwc) = next
GO TO 15
! Swap NL-NR for N0-NEXT, shift columns IWC+1,...,IWL to
! the left, and store N0-NEXT in the right portion of IWK.
12 CALL swap (next,n0,nl,nr, list,lptr,lend, lp21)
DO i = iwcp1,iwl
iwk(1,i-1) = iwk(1,i)
iwk(2,i-1) = iwk(2,i)
END DO
iwk(1,iwl) = n0
iwk(2,iwl) = next
iwl = iwl - 1
nr = next
GO TO 11
! A swap is not possible. Set N0 to NR.
14 n0 = nr
x0 = x(n0)
y0 = y(n0)
lft = 1
! Advance to the next arc.
15 nr = next
iwc = iwc + 1
GO TO 11
! NEXT LEFT N1->N2, NEXT .NE. N2, and IWC < IWL.
! Test for a possible swap.
16 IF ( .NOT. left(x(nl),y(nl),x0,y0,x(next),y(next)) ) GO TO 19
IF (lft <= 0) GO TO 17
IF ( .NOT. left(x0,y0,x(nr),y(nr),x(next),y(next)) ) GO TO 19
! Replace NL->NR with NEXT->N0.
CALL swap (next, n0, nl, nr, list, lptr, lend, lp21)
iwk(1,iwc) = next
iwk(2,iwc) = n0
GO TO 20
! Swap NL-NR for N0-NEXT, shift columns IWF,...,IWC-1 to
! the right, and store N0-NEXT in the left portion of
! IWK.
17 CALL swap (next, n0, nl, nr, list, lptr, lend, lp21)
DO i = iwc-1,iwf,-1
iwk(1,i+1) = iwk(1,i)
iwk(2,i+1) = iwk(2,i)
END DO
iwk(1,iwf) = n0
iwk(2,iwf) = next
iwf = iwf + 1
GO TO 20
! A swap is not possible. Set N0 to NL.
19 n0 = nl
x0 = x(n0)
y0 = y(n0)
lft = -1
! Advance to the next arc.
20 nl = next
iwc = iwc + 1
GO TO 11
! N2 is opposite NL->NR (IWC = IWL).
21 IF (n0 == n1) GO TO 24
IF (lft < 0) GO TO 22
! N0 RIGHT N1->N2. Test for a possible swap.
IF ( .NOT. left(x0, y0, x(nr), y(nr), x2, y2) ) GO TO 10
! Swap NL-NR for N0-N2 and store N0-N2 in the right portion of IWK.
CALL swap (n2, n0, nl, nr, list, lptr, lend, lp21)
iwk(1,iwl) = n0
iwk(2,iwl) = n2
iwl = iwl - 1
GO TO 10
! N0 LEFT N1->N2. Test for a possible swap.
22 IF ( .NOT. left(x(nl), y(nl), x0, y0, x2, y2) ) GO TO 10
! Swap NL-NR for N0-N2, shift columns IWF,...,IWL-1 to the
! right, and store N0-N2 in the left portion of IWK.
CALL swap (n2, n0, nl, nr, list, lptr, lend, lp21)
i = iwl
23 iwk(1,i) = iwk(1,i-1)
iwk(2,i) = iwk(2,i-1)
i = i - 1
IF (i > iwf) GO TO 23
iwk(1,iwf) = n0
iwk(2,iwf) = n2
iwf = iwf + 1
GO TO 10
! IWF = IWC = IWL. Swap out the last arc for N1-N2 and store zeros in IWK.
24 CALL swap (n2, n1, nl, nr, list, lptr, lend, lp21)
iwk(1,iwc) = 0
iwk(2,iwc) = 0
! Optimization procedure --
IF (iwc > 1) THEN
! Optimize the set of new arcs to the left of IN1->IN2.
nit = 3*(iwc-1)
CALL optim (x, y, iwc-1, list, lptr, lend, nit, iwk, ierr)
IF (ierr /= 0) GO TO 34
END IF
IF (iwc < iwend) THEN
! Optimize the set of new arcs to the right of IN1->IN2.
nit = 3*(iwend-iwc)
CALL optim (x, y, iwend-iwc, list, lptr, lend, nit, iwk(1:,iwc+1:), ierr)
IF (ierr /= 0) GO TO 34
END IF
! Successful termination.
ier = 0
RETURN
! IN1 and IN2 were adjacent on input.
30 ier = 0
RETURN
! Invalid input parameter.
31 ier = 1
RETURN
! Insufficient space reserved for IWK.
32 ier = 2
RETURN
! Invalid triangulation data structure or collinear nodes
! on convex hull boundary.
33 ier = 3
WRITE (*,130) in1, in2
130 FORMAT (//t6, '*** Error in EDGE: Invalid triangulation', &
' or null triangles on boundary'/ t10, 'IN1 =', i4, ', IN2 =', i4/)
RETURN
! Error flag returned by OPTIM.
34 ier = 4
WRITE (*,140) nit, ierr
140 FORMAT (//t6, '*** Error in OPTIM: NIT = ', i4, ', IER = ', i1, ' ***'/)
RETURN
END SUBROUTINE edge
SUBROUTINE getnp (ncc, lcc, n, x, y, list, lptr, lend, l, npts, ds, ier)
INTEGER, INTENT(IN) :: ncc
INTEGER, INTENT(IN) :: lcc(:)
INTEGER, INTENT(IN) :: n
REAL, INTENT(IN) :: x(:)
REAL, INTENT(IN) :: y(:)
INTEGER, INTENT(IN OUT) :: list(:)
INTEGER, INTENT(IN) :: lptr(:)
INTEGER, INTENT(OUT) :: lend(:)
INTEGER, INTENT(IN) :: l
INTEGER, INTENT(IN OUT) :: npts(:)
REAL, INTENT(IN OUT) :: ds(:)
INTEGER, INTENT(OUT) :: ier
!***********************************************************
! From TRIPACK
! Robert J. Renka
! Dept. of Computer Science
! Univ. of North Texas
! renka@cs.unt.edu
! 11/12/94
! Given a triangulation of N nodes and an array NPTS con-
! taining the indexes of L-1 nodes ordered by distance from
! NPTS(1), this subroutine sets NPTS(L) to the index of the
! next node in the sequence -- the node, other than NPTS(1),
! ...,NPTS(L-1), which is closest to NPTS(1). Thus, the
! ordered sequence of K closest nodes to N1 (including N1)
! may be determined by K-1 calls to GETNP with NPTS(1) = N1
! and L = 2,3,...,K for K >= 2. Note that NPTS must in-
! clude constraint nodes as well as non-constraint nodes.
! Thus, a sequence of K1 closest non-constraint nodes to N1
! must be obtained as a subset of the closest K2 nodes to N1
! for some K2 >= K1.
! The terms closest and distance have special definitions
! when constraint nodes are present in the triangulation.
! Nodes N1 and N2 are said to be visible from each other if
! and only if the line segment N1-N2 intersects no con-
! straint arc (except possibly itself) and is not an interi-
! or constraint arc (arc whose interior lies in a constraint
! region). A path from N1 to N2 is an ordered sequence of
! nodes, with N1 first and N2 last, such that adjacent path
! elements are visible from each other. The path length is
! the sum of the Euclidean distances between adjacent path
! nodes. Finally, the distance from N1 to N2 is defined to
! be the length of the shortest path from N1 to N2.
! The algorithm uses the property of a Delaunay triangula-
! tion that the K-th closest node to N1 is a neighbor of one
! of the K-1 closest nodes to N1. With the definition of
! distance used here, this property holds when constraints
! are present as long as non-constraint arcs are locally optimal.
! On input:
! NCC = Number of constraints. NCC >= 0.
! LCC = List of constraint curve starting indexes (or dummy array of
! length 1 if NCC = 0). Refer to Subroutine ADDCST.
! N = Number of nodes in the triangulation. N >= 3.
! X,Y = Arrays of length N containing the coordinates
! of the nodes with non-constraint nodes in the
! first LCC(1)-1 locations if NCC > 0.
! LIST,LPTR,LEND = Triangulation data structure. Refer to
! Subroutine TRMESH.
! L = Number of nodes in the sequence on output. 2 <= L <= N.
! NPTS = Array of length >= L containing the indexes of the L-1 closest
! nodes to NPTS(1) in the first L-1 locations.
! DS = Array of length >= L containing the distance
! (defined above) between NPTS(1) and NPTS(I) in
! the I-th position for I = 1,...,L-1. Thus, DS(1) = 0.
! Input parameters other than NPTS(L) and DS(L) are not
! altered by this routine.
! On output:
! NPTS = Array updated with the index of the L-th closest node
! to NPTS(1) in position L unless IER .NE. 0.
! DS = Array updated with the distance between NPTS(1)
! and NPTS(L) in position L unless IER .NE. 0.
! IER = Error indicator:
! IER = 0 if no errors were encountered.
! IER = -1 if NCC, N, L, or an LCC entry is
! outside its valid range on input.
! IER = K if NPTS(K) is not a valid index in the range 1 to N.
! Module required by GETNP: INTSEC
! Intrinsic functions called by GETNP: ABS, MIN, SQRT
!***********************************************************
INTEGER :: i, ifrst, ilast, j, k, km1, lcc1, lm1, lp, &
lpcl, lpk, lpkl, n1, nc, nf1, nf2, nj, nk, nkbak, nkfor, nl, nn
LOGICAL :: isw, vis, ncf, njf, skip, sksav, lft1, lft2, lft12
REAL :: dc, dl, x1, xc, xj, xk, y1, yc, yj, yk
! Store parameters in local variables and test for errors.
! LCC1 indexes the first constraint node.
ier = -1
nn = n
lcc1 = nn+1
lm1 = l-1
IF (ncc < 0 .OR. lm1 < 1 .OR. lm1 >= nn) RETURN
IF (ncc == 0) THEN
IF (nn < 3) RETURN
ELSE
DO i = ncc,1,-1
IF (lcc1 - lcc(i) < 3) RETURN
lcc1 = lcc(i)
END DO
IF (lcc1 < 1) RETURN
END IF
! Test for an invalid index in NPTS.
DO k = 1,lm1
nk = npts(k)
IF (nk < 1 .OR. nk > nn) THEN
ier = k
RETURN
END IF
END DO
! Store N1 = NPTS(1) and mark the elements of NPTS.
n1 = npts(1)
x1 = x(n1)
y1 = y(n1)
DO k = 1,lm1
nk = npts(k)
lend(nk) = -lend(nk)
END DO
! Candidates NC for NL = NPTS(L) are the unmarked visible
! neighbors of nodes NK in NPTS. ISW is an initialization
! switch set to .TRUE. when NL and its distance DL from N1
! have been initialized with the first candidate encountered.
isw = .false.
dl = 0.
! Loop on marked nodes NK = NPTS(K). LPKL indexes the last
! neighbor of NK in LIST.
DO k = 1,lm1
km1 = k - 1
nk = npts(k)
xk = x(nk)
yk = y(nk)
lpkl = -lend(nk)
nkfor = 0
nkbak = 0
vis = .true.
IF (nk >= lcc1) THEN
! NK is a constraint node. Set NKFOR and NKBAK to the constraint nodes
! which follow and precede NK. IFRST and ILAST are set to the first and
! last nodes in the constraint containing NK.
ifrst = nn + 1
DO i = ncc,1,-1
ilast = ifrst - 1
ifrst = lcc(i)
IF (nk >= ifrst) GO TO 5
END DO
5 IF (nk < ilast) THEN
nkfor = nk + 1
ELSE
nkfor = ifrst
END IF
IF (nk > ifrst) THEN
nkbak = nk - 1
ELSE
nkbak = ilast
END IF
! Initialize VIS to TRUE iff NKFOR precedes NKBAK in the adjacency list for
! NK -- the first neighbor is visible and is not NKBAK.
lpk = lpkl
6 lpk = lptr(lpk)
nc = ABS(list(lpk))
IF (nc /= nkfor .AND. nc /= nkbak) GO TO 6
vis = nc == nkfor
END IF
! Loop on neighbors NC of NK, bypassing marked and nonvisible neighbors.
lpk = lpkl
7 lpk = lptr(lpk)
nc = ABS(list(lpk))
IF (nc == nkbak) vis = .true.
! VIS = .FALSE. iff NK-NC is an interior constraint arc
! (NK is a constraint node and NC lies strictly between NKFOR and NKBAK).
IF (.NOT. vis) GO TO 15
IF (nc == nkfor) vis = .false.
IF (lend(nc) < 0) GO TO 15
! Initialize distance DC between N1 and NC to Euclidean distance.
xc = x(nc)
yc = y(nc)
dc = SQRT((xc-x1)*(xc-x1) + (yc-y1)*(yc-y1))
IF (isw .AND. dc >= dl) GO TO 15
IF (k == 1) GO TO 14
! K >= 2. Store the pointer LPCL to the last neighbor of NC.
lpcl = lend(nc)
! Set DC to the length of the shortest path from N1 to NC
! which has not previously been encountered and which is
! a viable candidate for the shortest path from N1 to NL.
! This is Euclidean distance iff NC is visible from N1.
! Since the shortest path from N1 to NL contains only ele-
! ments of NPTS which are constraint nodes (in addition to
! N1 and NL), only these need be considered for the path
! from N1 to NC. Thus, for distance function D(A,B) and
! J = 1,...,K, DC = min(D(N1,NJ) + D(NJ,NC)) over con-
! straint nodes NJ = NPTS(J) which are visible from NC.
DO j = 1,km1
nj = npts(j)
IF (j > 1 .AND. nj < lcc1) CYCLE
! If NC is a visible neighbor of NJ, a path from N1 to NC
! containing NJ has already been considered. Thus, NJ may
! be bypassed if it is adjacent to NC.
lp = lpcl
8 lp = lptr(lp)
IF ( nj == ABS(list(lp)) ) GO TO 12
IF (lp /= lpcl) GO TO 8
! NJ is a constraint node (unless J=1) not adjacent to NC,
! and is visible from NC iff NJ-NC is not intersected by
! a constraint arc. Loop on constraints I in reverse order --
xj = x(nj)
yj = y(nj)
ifrst = nn+1
DO i = ncc,1,-1
ilast = ifrst - 1
ifrst = lcc(i)
nf1 = ilast
ncf = nf1 == nc
njf = nf1 == nj
skip = ncf .OR. njf
! Loop on boundary constraint arcs NF1-NF2 which contain neither NC nor NJ.
! NCF and NJF are TRUE iff NC (or NJ) has been encountered in the
! constraint, and SKIP = .TRUE. iff NF1 = NC or NF1 = NJ.
DO nf2 = ifrst,ilast
IF (nf2 == nc) ncf = .true.
IF (nf2 == nj) njf = .true.
sksav = skip
skip = nf2 == nc .OR. nf2 == nj
! The last constraint arc in the constraint need not be
! tested if none of the arcs have been skipped.
IF ( sksav .OR. skip .OR. (nf2 == ilast .AND. &
.NOT. ncf .AND. .NOT. njf) ) GO TO 9
IF ( intsec(x(nf1),y(nf1),x(nf2),y(nf2), xc,yc,xj,yj) ) GO TO 12
9 nf1 = nf2
END DO
IF (.NOT. ncf .OR. .NOT. njf) CYCLE
! NC and NJ are constraint nodes in the same constraint.
! NC-NJ is intersected by an interior constraint arc iff
! 1) NC LEFT NF2->NF1 and (NJ LEFT NF1->NC and NJ LEFT NC->NF2) or
! 2) NC .NOT. LEFT NF2->NF1 and (NJ LEFT NF1->NC or NJ LEFT NC->NF2),
! where NF1, NC, NF2 are consecutive constraint nodes.
IF (nc /= ifrst) THEN
nf1 = nc - 1
ELSE
nf1 = ilast
END IF
IF (nc /= ilast) THEN
nf2 = nc + 1
ELSE
nf2 = ifrst
END IF
lft1 = (xc-x(nf1))*(yj-y(nf1)) >= (xj-x(nf1))*(yc-y(nf1))
lft2 = (x(nf2)-xc)*(yj-yc) >= (xj-xc)*(y(nf2)-yc)
lft12 = (x(nf1)-x(nf2))*(yc-y(nf2)) >= (xc-x(nf2))*(y(nf1)-y(nf2))
IF ( (lft1 .AND. lft2) .OR. (.NOT. lft12 &
.AND. (lft1 .OR. lft2)) ) GO TO 12
END DO
! NJ is visible from NC. Exit the loop with DC = Euclidean distance if J = 1.
IF (j == 1) GO TO 14
dc = MIN(dc,ds(j) + SQRT((xc-xj)*(xc-xj) + (yc-yj)*(yc-yj)))
CYCLE
! NJ is not visible from NC or is adjacent to NC. Initial-
! ize DC with D(N1,NK) + D(NK,NC) if J = 1.
12 IF (j == 1) dc = ds(k) + SQRT((xc-xk)*(xc-xk) + (yc-yk)*(yc-yk))
END DO
! Compare DC with DL.
IF (isw .AND. dc >= dl) GO TO 15
! The first (or a closer) candidate for NL has been encountered.
14 nl = nc
dl = dc
isw = .true.
15 IF (lpk /= lpkl) GO TO 7
END DO
! Unmark the elements of NPTS and store NL and DL.
DO k = 1,lm1
nk = npts(k)
lend(nk) = -lend(nk)
END DO
npts(l) = nl
ds(l) = dl
ier = 0
RETURN
END SUBROUTINE getnp
FUNCTION indxcc (ncc, lcc, n, list, lend) RESULT(fn_val)
INTEGER, INTENT(IN) :: ncc
INTEGER, INTENT(IN) :: lcc(:)
INTEGER, INTENT(IN) :: n
INTEGER, INTENT(IN) :: list(:)
INTEGER, INTENT(IN) :: lend(:)
INTEGER :: fn_val
!***********************************************************
! From TRIPACK
! Robert J. Renka
! Dept. of Computer Science
! Univ. of North Texas
! renka@cs.unt.edu
! 08/25/91
! Given a constrained Delaunay triangulation, this func-
! tion returns the index, if any, of an exterior constraint
! curve (an unbounded constraint region). An exterior con-
! straint curve is assumed to be present if and only if the
! clockwise-ordered sequence of boundary nodes is a subse-
! quence of a constraint node sequence. The triangulation
! adjacencies corresponding to constraint edges may or may
! not have been forced by a call to ADDCST, and the con-
! straint region may or may not be valid (contain no nodes).
! On input:
! NCC = Number of constraints. NCC >= 0.
! LCC = List of constraint curve starting indexes (or dummy array of
! length 1 if NCC = 0). Refer to Subroutine ADDCST.
! N = Number of nodes in the triangulation. N >= 3.
! LIST,LEND = Data structure defining the triangulation.
! Refer to Subroutine TRMESH.
! Input parameters are not altered by this function. Note
! that the parameters are not tested for validity.
! On output:
! INDXCC = Index of the exterior constraint curve, if
! present, or 0 otherwise.
! Modules required by INDXCC: None
!***********************************************************
INTEGER :: i, ifrst, ilast, lp, n0, nst, nxt
fn_val = 0
IF (ncc < 1) RETURN
! Set N0 to the boundary node with smallest index.
n0 = 0
1 n0 = n0 + 1
lp = lend(n0)
IF (list(lp) > 0) GO TO 1
! Search in reverse order for the constraint I, if any, that contains N0.
! IFRST and ILAST index the first and last nodes in constraint I.
i = ncc
ilast = n
2 ifrst = lcc(i)
IF (n0 >= ifrst) GO TO 3
IF (i == 1) RETURN
i = i - 1
ilast = ifrst - 1
GO TO 2
! N0 is in constraint I which indexes an exterior constraint curve iff the
! clockwise-ordered sequence of boundary node indexes beginning with N0 is
! increasing and bounded above by ILAST.
3 nst = n0
4 nxt = -list(lp)
IF (nxt == nst) GO TO 5
IF (nxt <= n0 .OR. nxt > ilast) RETURN
n0 = nxt
lp = lend(n0)
GO TO 4
! Constraint I contains the boundary node sequence as a subset.
5 fn_val = i
RETURN
END FUNCTION indxcc
SUBROUTINE insert (k, lp, list, lptr, lnew )
INTEGER, INTENT(IN) :: k
INTEGER, INTENT(IN OUT) :: lp
INTEGER, INTENT(OUT) :: list(:)
INTEGER, INTENT(IN OUT) :: lptr(:)
INTEGER, INTENT(IN OUT) :: lnew
!***********************************************************
! From TRIPACK
! Robert J. Renka
! Dept. of Computer Science
! Univ. of North Texas
! renka@cs.unt.edu
! 09/01/88
! This subroutine inserts K as a neighbor of N1 following
! N2, where LP is the LIST pointer of N2 as a neighbor of
! N1. Note that, if N2 is the last neighbor of N1, K will
! become the first neighbor (even if N1 is a boundary node).
! On input:
! K = Index of the node to be inserted.
! LP = LIST pointer of N2 as a neighbor of N1.
! The above parameters are not altered by this routine.
! LIST,LPTR,LNEW = Data structure defining the triangulation.
! Refer to Subroutine TRMESH.
! On output:
! LIST,LPTR,LNEW = Data structure updated with the
! addition of node K.
! Modules required by INSERT: None
!***********************************************************
INTEGER :: lsav
lsav = lptr(lp)
lptr(lp) = lnew
list(lnew) = k
lptr(lnew) = lsav
lnew = lnew + 1
RETURN
END SUBROUTINE insert
SUBROUTINE intadd (kk, i1, i2, i3, list, lptr, lend, lnew )
INTEGER, INTENT(IN) :: kk
INTEGER, INTENT(IN) :: i1
INTEGER, INTENT(IN) :: i2
INTEGER, INTENT(IN) :: i3
INTEGER, INTENT(IN OUT) :: list(:)
INTEGER, INTENT(OUT) :: lptr(:)
INTEGER, INTENT(OUT) :: lend(:)
INTEGER, INTENT(IN OUT) :: lnew
!***********************************************************
! From TRIPACK
! Robert J. Renka
! Dept. of Computer Science
! Univ. of North Texas
! renka@cs.unt.edu
! 02/22/91
! This subroutine adds an interior node to a triangulation
! of a set of points in the plane. The data structure is
! updated with the insertion of node KK into the triangle
! whose vertices are I1, I2, and I3. No optimization of the
! triangulation is performed.
! On input:
! KK = Index of the node to be inserted. KK >= 1
! and KK must not be equal to I1, I2, or I3.
! I1,I2,I3 = Indexes of the counterclockwise-ordered sequence of
! vertices of a triangle which contains node KK.
! The above parameters are not altered by this routine.
! LIST,LPTR,LEND,LNEW = Data structure defining the triangulation.
! Refer to Subroutine TRMESH. Triangle (I1,I2,I3)
! must be included in the triangulation.
! On output:
! LIST,LPTR,LEND,LNEW = Data structure updated with
! the addition of node KK. KK
! will be connected to nodes I1,
! I2, and I3.
! Modules required by INTADD: INSERT, LSTPTR
!***********************************************************
INTEGER :: k, lp, n1, n2, n3
k = kk
! Initialization.
n1 = i1
n2 = i2
n3 = i3
! Add K as a neighbor of I1, I2, and I3.
lp = lstptr(lend(n1),n2,list,lptr)
CALL insert (k,lp,list,lptr,lnew)
lp = lstptr(lend(n2),n3,list,lptr)
CALL insert (k,lp,list,lptr,lnew)
lp = lstptr(lend(n3),n1,list,lptr)
CALL insert (k,lp,list,lptr,lnew)
! Add I1, I2, and I3 as neighbors of K.
list(lnew) = n1
list(lnew+1) = n2
list(lnew+2) = n3
lptr(lnew) = lnew + 1
lptr(lnew+1) = lnew + 2
lptr(lnew+2) = lnew
lend(k) = lnew + 2
lnew = lnew + 3
RETURN
END SUBROUTINE intadd
FUNCTION intsec (x1, y1, x2, y2, x3, y3, x4, y4) RESULT(fn_val)
REAL, INTENT(IN) :: x1
REAL, INTENT(IN) :: y1
REAL, INTENT(IN) :: x2
REAL, INTENT(IN) :: y2
REAL, INTENT(IN) :: x3
REAL, INTENT(IN) :: y3
REAL, INTENT(IN) :: x4
REAL, INTENT(IN) :: y4
LOGICAL :: fn_val
!***********************************************************
! From TRIPACK
! Robert J. Renka
! Dept. of Computer Science
! Univ. of North Texas
! renka@cs.unt.edu
! 09/01/88
! Given a pair of line segments P1-P2 and P3-P4, this
! function returns the value .TRUE. if and only if P1-P2
! shares one or more points with P3-P4. The line segments
! include their endpoints, and the four points need not be
! distinct. Thus, either line segment may consist of a
! single point, and the segments may meet in a V (which is
! treated as an intersection). Note that an incorrect
! decision may result from floating point error if the four
! endpoints are nearly collinear.
! On input:
! X1,Y1 = Coordinates of P1.
! X2,Y2 = Coordinates of P2.
! X3,Y3 = Coordinates of P3.
! X4,Y4 = Coordinates of P4.
! Input parameters are not altered by this function.
! On output:
! INTSEC = Logical value defined above.
! Modules required by INTSEC: None
!***********************************************************
REAL :: a, b, d, dx12, dx31, dx34, dy12, dy31, dy34
! Test for overlap between the smallest rectangles that
! contain the line segments and have sides parallel to the axes.
IF ((x1 < x3 .AND. x1 < x4 .AND. x2 < x3 .AND. x2 < x4) .OR. &
(x1 > x3 .AND. x1 > x4 .AND. x2 > x3 .AND. x2 > x4) .OR. &
(y1 < y3 .AND. y1 < y4 .AND. y2 < y3 .AND. y2 < y4) .OR. &
(y1 > y3 .AND. y1 > y4 .AND. y2 > y3 .AND. y2 > y4)) THEN
fn_val = .false.
RETURN
END IF
! Compute A = P4-P3 X P1-P3, B = P2-P1 X P1-P3, and
! D = P2-P1 X P4-P3 (Z components).
dx12 = x2 - x1
dy12 = y2 - y1
dx34 = x4 - x3
dy34 = y4 - y3
dx31 = x1 - x3
dy31 = y1 - y3
a = dx34*dy31 - dx31*dy34
b = dx12*dy31 - dx31*dy12
d = dx12*dy34 - dx34*dy12
IF (d == 0.) GO TO 1
! D .NE. 0 and the point of intersection of the lines defined by the line
! segments is P = P1 + (A/D)*(P2-P1) = P3 + (B/D)*(P4-P3).
fn_val = a/d >= 0. .AND. a/d <= 1. .AND. b/d >= 0. .AND. b/d <= 1.
RETURN
! D .EQ. 0 and thus either the line segments are parallel,
! or one (or both) of them is a single point.
1 fn_val = a == 0. .AND. b == 0.
RETURN
END FUNCTION intsec
FUNCTION jrand (n) RESULT(fn_val)
! N.B. Arguments IX, IY & IZ have been removed.
INTEGER, INTENT(IN) :: n
INTEGER :: fn_val
!***********************************************************
! From STRIPACK
! Robert J. Renka
! Dept. of Computer Science
! Univ. of North Texas
! renka@cs.unt.edu
! 07/28/98
! This function returns a uniformly distributed pseudo-
! random integer in the range 1 to N.
! On input:
! N = Maximum value to be returned.
! N is not altered by this function.
! IX,IY,IZ = Integer seeds initialized to values in the range
! 1 to 30,000 before the first call to JRAND, and not
! altered between subsequent calls (unless a sequence of
! random numbers is to be repeated by reinitializing the
! seeds).
! On output:
! IX,IY,IZ = Updated integer seeds.
! JRAND = Random integer in the range 1 to N.
! Reference: B. A. Wichmann and I. D. Hill, "An Efficient
! and Portable Pseudo-random Number Generator",
! Applied Statistics, Vol. 31, No. 2, 1982, pp. 188-190.
! Modules required by JRAND: None
! Intrinsic functions called by JRAND: INT, MOD, REAL
!***********************************************************
REAL :: u, x
! Local parameters:
! U = Pseudo-random number uniformly distributed in the interval (0,1).
! X = Pseudo-random number in the range 0 to 3 whose fractional part is U.
ix = MOD(171*ix,30269)
iy = MOD(172*iy,30307)
iz = MOD(170*iz,30323)
x = (REAL(ix)/30269.) + (REAL(iy)/30307.) + (REAL(iz)/30323.)
u = x - INT(x)
fn_val = REAL(n)*u + 1.
RETURN
END FUNCTION jrand
FUNCTION left (x1, y1, x2, y2, x0, y0) RESULT(fn_val)
REAL, INTENT(IN) :: x1
REAL, INTENT(IN) :: y1
REAL, INTENT(IN) :: x2
REAL, INTENT(IN) :: y2
REAL, INTENT(IN) :: x0
REAL, INTENT(IN) :: y0
LOGICAL :: fn_val
!***********************************************************
! From TRIPACK
! Robert J. Renka
! Dept. of Computer Science
! Univ. of North Texas
! renka@cs.unt.edu
! 09/01/88
! This function determines whether node N0 is to the left
! or to the right of the line through N1-N2 as viewed by an
! observer at N1 facing N2.
! On input:
! X1,Y1 = Coordinates of N1.
! X2,Y2 = Coordinates of N2.
! X0,Y0 = Coordinates of N0.
! Input parameters are not altered by this function.
! On output:
! LEFT = .TRUE. if and only if (X0,Y0) is on or to the
! left of the directed line N1->N2.
! Modules required by LEFT: None
!***********************************************************
REAL :: dx1, dy1, dx2, dy2
! Local parameters:
! DX1,DY1 = X,Y components of the vector N1->N2
! DX2,DY2 = X,Y components of the vector N1->N0
dx1 = x2-x1
dy1 = y2-y1
dx2 = x0-x1
dy2 = y0-y1
! If the sign of the vector cross product of N1->N2 and N1->N0 is positive,
! then sin(A) > 0, where A is the angle between the vectors, and thus A is
! in the range (0,180) degrees.
fn_val = dx1*dy2 >= dx2*dy1
RETURN
END FUNCTION left
FUNCTION lstptr (lpl, nb, list, lptr) RESULT(fn_val)
INTEGER, INTENT(IN) :: lpl
INTEGER, INTENT(IN) :: nb
INTEGER, INTENT(IN) :: list(:)
INTEGER, INTENT(IN) :: lptr(:)
INTEGER :: fn_val
!***********************************************************
! From TRIPACK
! Robert J. Renka
! Dept. of Computer Science
! Univ. of North Texas
! renka@cs.unt.edu
! 09/01/88
! This function returns the index (LIST pointer) of NB in
! the adjacency list for N0, where LPL = LEND(N0).
! On input:
! LPL = LEND(N0)
! NB = Index of the node whose pointer is to be returned.
! NB must be connected to N0.
! LIST,LPTR = Data structure defining the triangulation
! Refer to Subroutine TRMESH.
! Input parameters are not altered by this function.
! On output:
! LSTPTR = Pointer such that LIST(LSTPTR) = NB or
! LIST(LSTPTR) = -NB, unless NB is not a
! neighbor of N0, in which case LSTPTR = LPL.
! Modules required by LSTPTR: None
!***********************************************************
INTEGER :: lp, nd
lp = lptr(lpl)
1 nd = list(lp)
IF (nd == nb) GO TO 2
lp = lptr(lp)
IF (lp /= lpl) GO TO 1
2 fn_val = lp
RETURN
END FUNCTION lstptr
FUNCTION nbcnt (lpl, lptr) RESULT(fn_val)
INTEGER, INTENT(IN) :: lpl
INTEGER, INTENT(IN) :: lptr(:)
INTEGER :: fn_val
!***********************************************************
! From TRIPACK
! Robert J. Renka
! Dept. of Computer Science
! Univ. of North Texas
! renka@cs.unt.edu
! 09/01/88
! This function returns the number of neighbors of a node
! N0 in a triangulation created by Subroutine TRMESH (or TRMSHR).
! On input:
! LPL = LIST pointer to the last neighbor of N0 --
! LPL = LEND(N0).
! LPTR = Array of pointers associated with LIST.
! Input parameters are not altered by this function.
! On output:
! NBCNT = Number of neighbors of N0.
! Modules required by NBCNT: None
!***********************************************************
INTEGER :: k, lp
lp = lpl
k = 1
1 lp = lptr(lp)
IF (lp == lpl) GO TO 2
k = k + 1
GO TO 1
2 fn_val = k
RETURN
END FUNCTION nbcnt
FUNCTION nearnd (xp, yp, ist, n, x, y, list, lptr, lend, dsq) RESULT(fn_val)
REAL, INTENT(IN) :: xp
REAL, INTENT(IN) :: yp
INTEGER, INTENT(IN) :: ist
INTEGER, INTENT(IN) :: n
REAL, INTENT(IN) :: x(:)
REAL, INTENT(IN) :: y(:)
INTEGER, INTENT(IN) :: list(:)
INTEGER, INTENT(IN) :: lptr(:)
INTEGER, INTENT(IN) :: lend(:)
REAL, INTENT(OUT) :: dsq
INTEGER :: fn_val
!***********************************************************
! From TRIPACK
! Robert J. Renka
! Dept. of Computer Science
! Univ. of North Texas
! renka@cs.unt.edu
! 06/27/98
! Given a point P in the plane and a Delaunay triangulation created by
! Subroutine TRMESH or TRMSHR, this function returns the index of the nearest
! triangulation node to P.
! The algorithm consists of implicitly adding P to the triangulation,
! finding the nearest neighbor to P, and implicitly deleting P from the
! triangulation. Thus, it is based on the fact that, if P is a node in
! a Delaunay triangulation, the nearest node to P is a neighbor of P.
! On input:
! XP,YP = Cartesian coordinates of the point P to be
! located relative to the triangulation.
! IST = Index of a node at which TRFIND begins the search.
! Search time depends on the proximity of this node to P.
! N = Number of nodes in the triangulation. N >= 3.
! X,Y = Arrays of length N containing the Cartesian
! coordinates of the nodes.
! LIST,LPTR,LEND = Data structure defining the triangulation.
! Refer to TRMESH.
! Input parameters are not altered by this function.
! On output:
! NEARND = Nodal index of the nearest node to P, or 0
! if N < 3 or the triangulation data structure is invalid.
! DSQ = Squared distance between P and NEARND unless NEARND = 0.
! Note that the number of candidates for NEARND (neighbors of P)
! is limited to LMAX defined in the PARAMETER statement below.
! Modules required by NEARND: JRAND, LEFT, LSTPTR, TRFIND
! Intrinsic function called by NEARND: ABS
!***********************************************************
INTEGER, PARAMETER :: lmax=25
INTEGER :: i1, i2, i3, l, listp(lmax), lp, lp1, lp2, &
lpl, lptrp(lmax), n1, n2, n3, nr, nst
REAL :: cos1, cos2, ds1, dsr, dx11, dx12, dx21, &
dx22, dy11, dy12, dy21, dy22, sin1, sin2
! Store local parameters and test for N invalid.
IF (n < 3) GO TO 7
nst = ist
IF (nst < 1 .OR. nst > n) nst = 1
! Find a triangle (I1,I2,I3) containing P, or the rightmost
! (I1) and leftmost (I2) visible boundary nodes as viewed from P.
CALL trfind (nst, xp, yp, n, x, y, list, lptr, lend, i1, i2, i3)
! Test for collinear nodes.
IF (i1 == 0) GO TO 7
! Store the linked list of 'neighbors' of P in LISTP and
! LPTRP. I1 is the first neighbor, and 0 is stored as
! the last neighbor if P is not contained in a triangle.
! L is the length of LISTP and LPTRP, and is limited to LMAX.
IF (i3 /= 0) THEN
listp(1) = i1
lptrp(1) = 2
listp(2) = i2
lptrp(2) = 3
listp(3) = i3
lptrp(3) = 1
l = 3
ELSE
n1 = i1
l = 1
lp1 = 2
listp(l) = n1
lptrp(l) = lp1
! Loop on the ordered sequence of visible boundary nodes N1 from I1 to I2.
1 lpl = lend(n1)
n1 = -list(lpl)
l = lp1
lp1 = l+1
listp(l) = n1
lptrp(l) = lp1
IF (n1 /= i2 .AND. lp1 < lmax) GO TO 1
l = lp1
listp(l) = 0
lptrp(l) = 1
END IF
! Initialize variables for a loop on arcs N1-N2 opposite P in which new
! 'neighbors' are 'swapped' in. N1 follows N2 as a neighbor of P, and LP1
! and LP2 are the LISTP indexes of N1 and N2.
lp2 = 1
n2 = i1
lp1 = lptrp(1)
n1 = listp(lp1)
! Begin loop: find the node N3 opposite N1->N2.
2 lp = lstptr(lend(n1),n2,list,lptr)
IF (list(lp) < 0) GO TO 4
lp = lptr(lp)
n3 = ABS(list(lp))
! Swap test: Exit the loop if L = LMAX.
IF (l == lmax) GO TO 5
dx11 = x(n1) - x(n3)
dx12 = x(n2) - x(n3)
dx22 = x(n2) - xp
dx21 = x(n1) - xp
dy11 = y(n1) - y(n3)
dy12 = y(n2) - y(n3)
dy22 = y(n2) - yp
dy21 = y(n1) - yp
cos1 = dx11*dx12 + dy11*dy12
cos2 = dx22*dx21 + dy22*dy21
IF (cos1 >= 0. .AND. cos2 >= 0.) GO TO 4
IF (cos1 < 0. .AND. cos2 < 0.) GO TO 3
sin1 = dx11*dy12 - dx12*dy11
sin2 = dx22*dy21 - dx21*dy22
IF (sin1*cos2 + cos1*sin2 >= 0.) GO TO 4
! Swap: Insert N3 following N2 in the adjacency list for P.
! The two new arcs opposite P must be tested.
3 l = l+1
lptrp(lp2) = l
listp(l) = n3
lptrp(l) = lp1
lp1 = l
n1 = n3
GO TO 2
! No swap: Advance to the next arc and test for termination
! on N1 = I1 (LP1 = 1) or N1 followed by 0.
4 IF (lp1 == 1) GO TO 5
lp2 = lp1
n2 = n1
lp1 = lptrp(lp1)
n1 = listp(lp1)
IF (n1 == 0) GO TO 5
GO TO 2
! Set NR and DSR to the index of the nearest node to P and
! its squared distance from P, respectively.
5 nr = i1
dsr = (x(nr)-xp)**2 + (y(nr)-yp)**2
DO lp = 2,l
n1 = listp(lp)
IF (n1 == 0) CYCLE
ds1 = (x(n1)-xp)**2 + (y(n1)-yp)**2
IF (ds1 < dsr) THEN
nr = n1
dsr = ds1
END IF
END DO
dsq = dsr
fn_val = nr
RETURN
! Invalid input.
7 fn_val = 0
RETURN
END FUNCTION nearnd
SUBROUTINE optim (x, y, na, list, lptr, lend, nit, iwk, ier)
REAL, INTENT(IN) :: x(:)
REAL, INTENT(IN) :: y(:)
INTEGER, INTENT(IN) :: na
INTEGER, INTENT(IN OUT) :: list(:)
INTEGER, INTENT(IN OUT) :: lptr(:)
INTEGER, INTENT(IN OUT) :: lend(:)
INTEGER, INTENT(IN OUT) :: nit
INTEGER, INTENT(IN OUT) :: iwk(:,:)
INTEGER, INTENT(OUT) :: ier
!***********************************************************
! From TRIPACK
! Robert J. Renka
! Dept. of Computer Science
! Univ. of North Texas
! renka@cs.unt.edu
! 06/27/98
! Given a set of NA triangulation arcs, this subroutine
! optimizes the portion of the triangulation consisting of
! the quadrilaterals (pairs of adjacent triangles) which
! have the arcs as diagonals by applying the circumcircle
! test and appropriate swaps to the arcs.
! An iteration consists of applying the swap test and
! swaps to all NA arcs in the order in which they are
! stored. The iteration is repeated until no swap occurs
! or NIT iterations have been performed. The bound on the
! number of iterations may be necessary to prevent an
! infinite loop caused by cycling (reversing the effect of a
! previous swap) due to floating point inaccuracy when four
! or more nodes are nearly cocircular.
! On input:
! X,Y = Arrays containing the nodal coordinates.
! NA = Number of arcs in the set. NA >= 0.
! The above parameters are not altered by this routine.
! LIST,LPTR,LEND = Data structure defining the trian-
! gulation. Refer to Subroutine TRMESH.
! NIT = Maximum number of iterations to be performed.
! A reasonable value is 3*NA. NIT >= 1.
! IWK = Integer array dimensioned 2 by NA containing the nodal indexes
! of the arc endpoints (pairs of endpoints are stored in columns).
! On output:
! LIST,LPTR,LEND = Updated triangulation data structure reflecting the
! swaps.
! NIT = Number of iterations performed.
! IWK = Endpoint indexes of the new set of arcs reflecting the swaps.
! IER = Error indicator:
! IER = 0 if no errors were encountered.
! IER = 1 if a swap occurred on the last of
! MAXIT iterations, where MAXIT is the
! value of NIT on input. The new set
! of arcs in not necessarily optimal in this case.
! IER = 2 if NA < 0 or NIT < 1 on input.
! IER = 3 if IWK(2,I) is not a neighbor of
! IWK(1,I) for some I in the range 1
! to NA. A swap may have occurred in this case.
! IER = 4 if a zero pointer was returned by Subroutine SWAP.
! Modules required by OPTIM: LSTPTR, SWAP, SWPTST
! Intrinsic function called by OPTIM: ABS
!***********************************************************
INTEGER :: i, io1, io2, iter, lp, lp21, lpl, lpp, maxit, n1, n2, nna
LOGICAL :: swp
! Local parameters:
! I = Column index for IWK
! IO1,IO2 = Nodal indexes of the endpoints of an arc in IWK
! ITER = Iteration count
! LP = LIST pointer
! LP21 = Parameter returned by SWAP (not used)
! LPL = Pointer to the last neighbor of IO1
! LPP = Pointer to the node preceding IO2 as a neighbor of IO1
! MAXIT = Input value of NIT
! N1,N2 = Nodes opposite IO1->IO2 and IO2->IO1, respectively
! NNA = Local copy of NA
! SWP = Flag set to TRUE iff a swap occurs in the optimization loop
nna = na
maxit = nit
IF (nna < 0 .OR. maxit < 1) GO TO 7
! Initialize iteration count ITER and test for NA = 0.
iter = 0
IF (nna == 0) GO TO 5
! Top of loop --
! SWP = TRUE iff a swap occurred in the current iteration.
1 IF (iter == maxit) GO TO 6
iter = iter + 1
swp = .false.
! Inner loop on arcs IO1-IO2 --
DO i = 1,nna
io1 = iwk(1,i)
io2 = iwk(2,i)
! Set N1 and N2 to the nodes opposite IO1->IO2 and
! IO2->IO1, respectively. Determine the following:
! LPL = pointer to the last neighbor of IO1,
! LP = pointer to IO2 as a neighbor of IO1, and
! LPP = pointer to the node N2 preceding IO2.
lpl = lend(io1)
lpp = lpl
lp = lptr(lpp)
2 IF (list(lp) == io2) GO TO 3
lpp = lp
lp = lptr(lpp)
IF (lp /= lpl) GO TO 2
! IO2 should be the last neighbor of IO1. Test for no
! arc and bypass the swap test if IO1 is a boundary node.
IF (ABS(list(lp)) /= io2) GO TO 8
IF (list(lp) < 0) CYCLE
! Store N1 and N2, or bypass the swap test if IO1 is a
! boundary node and IO2 is its first neighbor.
3 n2 = list(lpp)
IF (n2 < 0) CYCLE
lp = lptr(lp)
n1 = ABS(list(lp))
! Test IO1-IO2 for a swap, and update IWK if necessary.
IF ( .NOT. swptst(n1,n2,io1,io2,x,y) ) CYCLE
CALL swap (n1,n2,io1,io2, list,lptr,lend, lp21)
IF (lp21 == 0) GO TO 9
swp = .true.
iwk(1,i) = n1
iwk(2,i) = n2
END DO
IF (swp) GO TO 1
! Successful termination.
5 nit = iter
ier = 0
RETURN
! MAXIT iterations performed without convergence.
6 nit = maxit
ier = 1
RETURN
! Invalid input parameter.
7 nit = 0
ier = 2
RETURN
! IO2 is not a neighbor of IO1.
8 nit = iter
ier = 3
RETURN
! Zero pointer returned by SWAP.
9 nit = iter
ier = 4
RETURN
END SUBROUTINE optim
FUNCTION store (x) RESULT(fn_val)
REAL, INTENT(IN) :: x
REAL :: fn_val
!***********************************************************
! From TRIPACK
! Robert J. Renka
! Dept. of Computer Science
! Univ. of North Texas
! renka@cs.unt.edu
! 03/18/90
! This function forces its argument X to be stored in a memory location,
! thus providing a means of determining floating point number characteristics
! (such as the machine precision) when it is necessary to avoid computation
! in high precision registers.
! On input:
! X = Value to be stored.
! X is not altered by this function.
! On output:
! STORE = Value of X after it has been stored and
! possibly truncated or rounded to the single
! precision word length.
! Modules required by STORE: None
!***********************************************************
stcom = x
fn_val = stcom
RETURN
END FUNCTION store
SUBROUTINE swap (in1, in2, io1, io2, list, lptr, lend, lp21)
INTEGER, INTENT(IN) :: in1
INTEGER, INTENT(IN) :: in2
INTEGER, INTENT(IN) :: io1
INTEGER, INTENT(IN) :: io2
INTEGER, INTENT(IN OUT) :: list(:)
INTEGER, INTENT(IN OUT) :: lptr(:)
INTEGER, INTENT(IN OUT) :: lend(:)
INTEGER, INTENT(OUT) :: lp21
!***********************************************************
! From TRIPACK
! Robert J. Renka
! Dept. of Computer Science
! Univ. of North Texas
! renka@cs.unt.edu
! 06/22/98
! Given a triangulation of a set of points on the unit sphere,
! this subroutine replaces a diagonal arc in a strictly convex
! quadrilateral (defined by a pair of adjacent triangles) with the
! other diagonal. Equivalently, a pair of adjacent triangles is
! replaced by another pair having the same union.
! On input:
! IN1,IN2,IO1,IO2 = Nodal indexes of the vertices of
! the quadrilateral. IO1-IO2 is re-
! placed by IN1-IN2. (IO1,IO2,IN1)
! and (IO2,IO1,IN2) must be trian-
! gles on input.
! The above parameters are not altered by this routine.
! LIST,LPTR,LEND = Data structure defining the triangulation.
! Refer to Subroutine TRMESH.
! On output:
! LIST,LPTR,LEND = Data structure updated with the swap --
! triangles (IO1,IO2,IN1) and (IO2,IO1,IN2) are
! replaced by (IN1,IN2,IO2) and (IN2,IN1,IO1)
! unless LP21 = 0.
! LP21 = Index of IN1 as a neighbor of IN2 after the
! swap is performed unless IN1 and IN2 are
! adjacent on input, in which case LP21 = 0.
! Module required by SWAP: LSTPTR
! Intrinsic function called by SWAP: ABS
!***********************************************************
INTEGER :: lp, lph, lpsav
! Local parameters:
! LP,LPH,LPSAV = LIST pointers
! Test for IN1 and IN2 adjacent.
lp = lstptr(lend(in1), in2, list, lptr)
IF (ABS(list(lp)) == in2) THEN
lp21 = 0
RETURN
END IF
! Delete IO2 as a neighbor of IO1.
lp = lstptr(lend(io1), in2, list, lptr)
lph = lptr(lp)
lptr(lp) = lptr(lph)
! If IO2 is the last neighbor of IO1, make IN2 the last neighbor.
IF (lend(io1) == lph) lend(io1) = lp
! Insert IN2 as a neighbor of IN1 following IO1 using the hole created above.
lp = lstptr(lend(in1), io1, list, lptr)
lpsav = lptr(lp)
lptr(lp) = lph
list(lph) = in2
lptr(lph) = lpsav
! Delete IO1 as a neighbor of IO2.
lp = lstptr(lend(io2), in1, list, lptr)
lph = lptr(lp)
lptr(lp) = lptr(lph)
! If IO1 is the last neighbor of IO2, make IN1 the last neighbor.
IF (lend(io2) == lph) lend(io2) = lp
! Insert IN1 as a neighbor of IN2 following IO2.
lp = lstptr(lend(in2),io2,list,lptr)
lpsav = lptr(lp)
lptr(lp) = lph
list(lph) = in1
lptr(lph) = lpsav
lp21 = lph
RETURN
END SUBROUTINE swap
FUNCTION swptst (in1, in2, io1, io2, x, y) RESULT(fn_val)
INTEGER, INTENT(IN) :: in1
INTEGER, INTENT(IN) :: in2
INTEGER, INTENT(IN) :: io1
INTEGER, INTENT(IN) :: io2
REAL, INTENT(IN) :: x(:)
REAL, INTENT(IN) :: y(:)
LOGICAL :: fn_val
!***********************************************************
! From TRIPACK
! Robert J. Renka
! Dept. of Computer Science
! Univ. of North Texas
! renka@cs.unt.edu
! 09/01/88
! This function applies the circumcircle test to a quadri-
! lateral defined by a pair of adjacent triangles. The
! diagonal arc (shared triangle side) should be swapped for
! the other diagonl if and only if the fourth vertex is
! strictly interior to the circumcircle of one of the
! triangles (the decision is independent of the choice of
! triangle). Equivalently, the diagonal is chosen to maxi-
! mize the smallest of the six interior angles over the two
! pairs of possible triangles (the decision is for no swap
! if the quadrilateral is not strictly convex).
! When the four vertices are nearly cocircular (the
! neutral case), the preferred decision is no swap -- in
! order to avoid unnecessary swaps and, more important, to
! avoid cycling in Subroutine OPTIM which is called by
! DELNOD and EDGE. Thus, a tolerance SWTOL (stored in
! SWPCOM by TRMESH or TRMSHR) is used to define 'nearness'
! to the neutral case.
! On input:
! IN1,IN2,IO1,IO2 = Nodal indexes of the vertices of
! the quadrilateral. IO1-IO2 is the
! triangulation arc (shared triangle
! side) to be replaced by IN1-IN2 if
! the decision is to swap. The
! triples (IO1,IO2,IN1) and (IO2,
! IO1,IN2) must define triangles (be
! in counterclockwise order) on input.
! X,Y = Arrays containing the nodal coordinates.
! Input parameters are not altered by this routine.
! On output:
! SWPTST = .TRUE. if and only if the arc connecting
! IO1 and IO2 is to be replaced.
! Modules required by SWPTST: None
!***********************************************************
REAL :: dx11, dx12, dx22, dx21, dy11, dy12, dy22, dy21, &
sin1, sin2, cos1, cos2, sin12
! Local parameters:
! DX11,DY11 = X,Y components of the vector IN1->IO1
! DX12,DY12 = X,Y components of the vector IN1->IO2
! DX22,DY22 = X,Y components of the vector IN2->IO2
! DX21,DY21 = X,Y components of the vector IN2->IO1
! SIN1 = Cross product of the vectors IN1->IO1 and
! IN1->IO2 -- proportional to sin(T1), where
! T1 is the angle at IN1 formed by the vectors
! COS1 = Inner product of the vectors IN1->IO1 and
! IN1->IO2 -- proportional to cos(T1)
! SIN2 = Cross product of the vectors IN2->IO2 and
! IN2->IO1 -- proportional to sin(T2), where
! T2 is the angle at IN2 formed by the vectors
! COS2 = Inner product of the vectors IN2->IO2 and
! IN2->IO1 -- proportional to cos(T2)
! SIN12 = SIN1*COS2 + COS1*SIN2 -- proportional to
! sin(T1+T2)
! Compute the vectors containing the angles T1 and T2.
dx11 = x(io1) - x(in1)
dx12 = x(io2) - x(in1)
dx22 = x(io2) - x(in2)
dx21 = x(io1) - x(in2)
dy11 = y(io1) - y(in1)
dy12 = y(io2) - y(in1)
dy22 = y(io2) - y(in2)
dy21 = y(io1) - y(in2)
! Compute inner products.
cos1 = dx11*dx12 + dy11*dy12
cos2 = dx22*dx21 + dy22*dy21
! The diagonals should be swapped iff (T1+T2) > 180 degrees.
! The following two tests ensure numerical stability:
! the decision must be FALSE when both angles are close to 0,
! and TRUE when both angles are close to 180 degrees.
IF (cos1 >= 0. .AND. cos2 >= 0.) GO TO 2
IF (cos1 < 0. .AND. cos2 < 0.) GO TO 1
! Compute vector cross products (Z-components).
sin1 = dx11*dy12 - dx12*dy11
sin2 = dx22*dy21 - dx21*dy22
sin12 = sin1*cos2 + cos1*sin2
IF (sin12 >= -swtol) GO TO 2
! Swap.
1 fn_val = .true.
RETURN
! No swap.
2 fn_val = .false.
RETURN
END FUNCTION swptst
SUBROUTINE trfind (nst, px, py, n, x, y, list, lptr, lend, i1, i2, i3)
INTEGER, INTENT(IN) :: nst
REAL, INTENT(IN) :: px
REAL, INTENT(IN) :: py
INTEGER, INTENT(IN) :: n
REAL, INTENT(IN) :: x(:)
REAL, INTENT(IN) :: y(:)
INTEGER, INTENT(IN) :: list(:)
INTEGER, INTENT(IN) :: lptr(:)
INTEGER, INTENT(IN) :: lend(:)
INTEGER, INTENT(OUT) :: i1
INTEGER, INTENT(OUT) :: i2
INTEGER, INTENT(OUT) :: i3
!***********************************************************
! From TRIPACK
! Robert J. Renka
! Dept. of Computer Science
! Univ. of North Texas
! renka@cs.unt.edu
! 07/28/98
! This subroutine locates a point P relative to a triangu-
! lation created by Subroutine TRMESH or TRMSHR. If P is
! contained in a triangle, the three vertex indexes are
! returned. Otherwise, the indexes of the rightmost and
! leftmost visible boundary nodes are returned.
! On input:
! NST = Index of a node at which TRFIND begins the
! search. Search time depends on the proximity
! of this node to P.
! PX,PY = X and y coordinates of the point P to be located.
! N = Number of nodes in the triangulation. N >= 3.
! X,Y = Arrays of length N containing the coordinates
! of the nodes in the triangulation.
! LIST,LPTR,LEND = Data structure defining the triangulation.
! Refer to Subroutine TRMESH.
! Input parameters are not altered by this routine.
! On output:
! I1,I2,I3 = Nodal indexes, in counterclockwise order,
! of the vertices of a triangle containing
! P if P is contained in a triangle. If P
! is not in the convex hull of the nodes,
! I1 indexes the rightmost visible boundary
! node, I2 indexes the leftmost visible
! boundary node, and I3 = 0. Rightmost and
! leftmost are defined from the perspective
! of P, and a pair of points are visible
! from each other if and only if the line
! segment joining them intersects no trian-
! gulation arc. If P and all of the nodes
! lie on a common line, then I1 = I2 = I3 =
! 0 on output.
! Modules required by TRFIND: JRAND, LEFT, LSTPTR, STORE
! Intrinsic function called by TRFIND: ABS
!***********************************************************
INTEGER :: lp, n0, n1, n1s, n2, n2s, n3, n4, nb, nf, nl, np, npp
REAL :: b1, b2, xp, yp
! Local parameters:
! B1,B2 = Unnormalized barycentric coordinates of P with
! respect to (N1,N2,N3)
! IX,IY,IZ = Integer seeds for JRAND
! LP = LIST pointer
! N0,N1,N2 = Nodes in counterclockwise order defining a
! cone (with vertex N0) containing P
! N1S,N2S = Saved values of N1 and N2
! N3,N4 = Nodes opposite N1->N2 and N2->N1, respectively
! NB = Index of a boundary node -- first neighbor of
! NF or last neighbor of NL in the boundary traversal loops
! NF,NL = First and last neighbors of N0, or first
! (rightmost) and last (leftmost) nodes
! visible from P when P is exterior to the triangulation
! NP,NPP = Indexes of boundary nodes used in the boundary traversal loops
! XA,XB,XC = Dummy arguments for FRWRD
! YA,YB,YC = Dummy arguments for FRWRD
! XP,YP = Local variables containing the components of P
! Statement function:
! FRWRD = TRUE iff C is forward of A->B
! iff B,A->C> >= 0.
! frwrd(xa,ya,xb,yb,xc,yc) = (xb-xa)*(xc-xa) + (yb-ya)*(yc-ya) >= 0.
! Initialize variables.
xp = px
yp = py
n0 = nst
IF (n0 < 1 .OR. n0 > n) n0 = jrand(n)
! Set NF and NL to the first and last neighbors of N0, and initialize N1 = NF.
1 lp = lend(n0)
nl = list(lp)
lp = lptr(lp)
nf = list(lp)
n1 = nf
! Find a pair of adjacent neighbors N1,N2 of N0 that define
! a wedge containing P: P LEFT N0->N1 and P RIGHT N0->N2.
IF (nl > 0) GO TO 2
! N0 is a boundary node. Test for P exterior.
nl = -nl
IF ( .NOT. left(x(n0),y(n0),x(nf),y(nf),xp,yp) ) THEN
nl = n0
GO TO 9
END IF
IF ( .NOT. left(x(nl),y(nl),x(n0),y(n0),xp,yp) ) THEN
nb = nf
nf = n0
np = nl
npp = n0
GO TO 11
END IF
GO TO 3
! N0 is an interior node. Find N1.
2 IF ( left(x(n0), y(n0), x(n1), y(n1), xp, yp) ) GO TO 3
lp = lptr(lp)
n1 = list(lp)
IF (n1 == nl) GO TO 6
GO TO 2
! P is to the left of edge N0->N1. Initialize N2 to the
! next neighbor of N0.
3 lp = lptr(lp)
n2 = ABS(list(lp))
IF ( .NOT. left(x(n0),y(n0),x(n2),y(n2),xp,yp) ) GO TO 7
n1 = n2
IF (n1 /= nl) GO TO 3
IF ( .NOT. left(x(n0),y(n0),x(nf),y(nf),xp,yp) ) GO TO 6
IF (xp == x(n0) .AND. yp == y(n0)) GO TO 5
! P is left of or on edges N0->NB for all neighbors NB of N0.
! All points are collinear iff P is left of NB->N0 for
! all neighbors NB of N0. Search the neighbors of N0.
! NOTE -- N1 = NL and LP points to NL.
4 IF ( .NOT. left(x(n1), y(n1), x(n0), y(n0), xp, yp) ) GO TO 5
lp = lptr(lp)
n1 = ABS(list(lp))
IF (n1 == nl) GO TO 17
GO TO 4
! P is to the right of N1->N0, or P=N0. Set N0 to N1 and start over.
5 n0 = n1
GO TO 1
! P is between edges N0->N1 and N0->NF.
6 n2 = nf
! P is contained in the wedge defined by line segments
! N0->N1 and N0->N2, where N1 is adjacent to N2. Set
! N3 to the node opposite N1->N2, and save N1 and N2 to
! test for cycling.
7 n3 = n0
n1s = n1
n2s = n2
! Top of edge hopping loop. Test for termination.
8 IF ( left(x(n1), y(n1), x(n2), y(n2), xp, yp) ) THEN
! P LEFT N1->N2 and hence P is in (N1,N2,N3) unless an
! error resulted from floating point inaccuracy and
! collinearity. Compute the unnormalized barycentric
! coordinates of P with respect to (N1,N2,N3).
b1 = (x(n3)-x(n2))*(yp-y(n2)) - (xp-x(n2))*(y(n3)-y(n2))
b2 = (x(n1)-x(n3))*(yp-y(n3)) - (xp-x(n3))*(y(n1)-y(n3))
IF (store(b1+1.) >= 1. .AND. store(b2+1.) >= 1.) GO TO 16
! Restart with N0 randomly selected.
n0 = jrand(n)
GO TO 1
END IF
! Set N4 to the neighbor of N2 which follows N1 (node
! opposite N2->N1) unless N1->N2 is a boundary edge.
lp = lstptr(lend(n2), n1, list, lptr)
IF (list(lp) < 0) THEN
nf = n2
nl = n1
GO TO 9
END IF
lp = lptr(lp)
n4 = ABS(list(lp))
! Select the new edge N1->N2 which intersects the line
! segment N0-P, and set N3 to the node opposite N1->N2.
IF ( left(x(n0), y(n0), x(n4), y(n4), xp, yp) ) THEN
n3 = n1
n1 = n4
n2s = n2
IF (n1 /= n1s .AND. n1 /= n0) GO TO 8
ELSE
n3 = n2
n2 = n4
n1s = n1
IF (n2 /= n2s .AND. n2 /= n0) GO TO 8
END IF
! The starting node N0 or edge N1-N2 was encountered
! again, implying a cycle (infinite loop). Restart
! with N0 randomly selected.
n0 = jrand(n)
GO TO 1
! Boundary traversal loops. NL->NF is a boundary edge and
! P RIGHT NL->NF. Save NL and NF.
9 np = nl
npp = nf
! Find the first (rightmost) visible boundary node NF. NB
! is set to the first neighbor of NF, and NP is the last neighbor.
10 lp = lend(nf)
lp = lptr(lp)
nb = list(lp)
IF ( .NOT. left(x(nf),y(nf),x(nb),y(nb),xp,yp) ) GO TO 12
! P LEFT NF->NB and thus NB is not visible unless an error
! resulted from floating point inaccuracy and collinear-
! ity of the 4 points NP, NF, NB, and P.
11 IF ( frwrd(x(nf),y(nf),x(np),y(np),xp,yp) .OR. &
frwrd(x(nf),y(nf),x(np),y(np),x(nb),y(nb)) ) THEN
i1 = nf
GO TO 13
END IF
! Bottom of loop.
12 np = nf
nf = nb
GO TO 10
! Find the last (leftmost) visible boundary node NL. NB
! is set to the last neighbor of NL, and NPP is the first neighbor.
13 lp = lend(nl)
nb = -list(lp)
IF ( .NOT. left(x(nb),y(nb),x(nl),y(nl),xp,yp) ) GO TO 14
! P LEFT NB->NL and thus NB is not visible unless an error
! resulted from floating point inaccuracy and collinear-
! ity of the 4 points P, NB, NL, and NPP.
IF ( frwrd(x(nl),y(nl),x(npp),y(npp),xp,yp) .OR. &
frwrd(x(nl),y(nl),x(npp),y(npp),x(nb),y(nb)) ) GO TO 15
! Bottom of loop.
14 npp = nl
nl = nb
GO TO 13
! NL is the leftmost visible boundary node.
15 i2 = nl
i3 = 0
RETURN
! P is in the triangle (N1,N2,N3).
16 i1 = n1
i2 = n2
i3 = n3
RETURN
! All points are collinear.
17 i1 = 0
i2 = 0
i3 = 0
RETURN
END SUBROUTINE trfind
SUBROUTINE trlist (ncc, lcc, n, list, lptr, lend, nrow, nt, ltri, lct, ier)
INTEGER, INTENT(IN) :: ncc
INTEGER, INTENT(IN) :: lcc(:)
INTEGER, INTENT(IN) :: n
INTEGER, INTENT(IN) :: list(:)
INTEGER, INTENT(IN) :: lptr(:)
INTEGER, INTENT(IN) :: lend(:)
INTEGER, INTENT(IN) :: nrow
INTEGER, INTENT(OUT) :: nt
INTEGER, INTENT(OUT) :: ltri(:,:) ! ltri(nrow,*)
INTEGER, INTENT(OUT) :: lct(:)
INTEGER, INTENT(OUT) :: ier
!***********************************************************
! From TRIPACK
! Robert J. Renka
! Dept. of Computer Science
! Univ. of North Texas
! renka@cs.unt.edu
! 03/22/97
! This subroutine converts a triangulation data structure
! from the linked list created by Subroutine TRMESH or
! TRMSHR to a triangle list.
! On input:
! NCC = Number of constraints. NCC >= 0.
! LCC = List of constraint curve starting indexes (or
! dummy array of length 1 if NCC = 0). Refer to
! Subroutine ADDCST.
! N = Number of nodes in the triangulation. N >= 3.
! LIST,LPTR,LEND = Linked list data structure defin-
! ing the triangulation. Refer to
! Subroutine TRMESH.
! NROW = Number of rows (entries per triangle) reserved for the
! triangle list LTRI. The value must be 6 if only the vertex
! indexes and neighboring triangle indexes are to be stored,
! or 9 if arc indexes are also to be assigned and stored.
! Refer to LTRI.
! The above parameters are not altered by this routine.
! LTRI = Integer array of length at least NROW*NT,
! where NT is at most 2N-5. (A sufficient
! length is 12N if NROW=6 or 18N if NROW=9.)
! LCT = Integer array of length NCC or dummy array of
! length 1 if NCC = 0.
! On output:
! NT = Number of triangles in the triangulation unless
! IER .NE. 0, in which case NT = 0. NT = 2N - NB
! - 2, where NB is the number of boundary nodes.
! LTRI = NROW by NT array whose J-th column contains
! the vertex nodal indexes (first three rows),
! neighboring triangle indexes (second three
! rows), and, if NROW = 9, arc indexes (last
! three rows) associated with triangle J for
! J = 1,...,NT. The vertices are ordered
! counterclockwise with the first vertex taken
! to be the one with smallest index. Thus,
! LTRI(2,J) and LTRI(3,J) are larger than
! LTRI(1,J) and index adjacent neighbors of
! node LTRI(1,J). For I = 1,2,3, LTRI(I+3,J)
! and LTRI(I+6,J) index the triangle and arc,
! respectively, which are opposite (not shared
! by) node LTRI(I,J), with LTRI(I+3,J) = 0 if
! LTRI(I+6,J) indexes a boundary arc. Vertex
! indexes range from 1 to N, triangle indexes
! from 0 to NT, and, if included, arc indexes
! from 1 to NA = NT+N-1. The triangles are or-
! dered on first (smallest) vertex indexes,
! except that the sets of constraint triangles
! (triangles contained in the closure of a con-
! straint region) follow the non-constraint triangles.
! LCT = Array of length NCC containing the triangle
! index of the first triangle of constraint J in
! LCT(J). Thus, the number of non-constraint
! triangles is LCT(1)-1, and constraint J con-
! tains LCT(J+1)-LCT(J) triangles, where
! LCT(NCC+1) = NT+1.
! IER = Error indicator.
! IER = 0 if no errors were encountered.
! IER = 1 if NCC, N, NROW, or an LCC entry is
! outside its valid range on input.
! IER = 2 if the triangulation data structure
! (LIST,LPTR,LEND) is invalid. Note,
! however, that these arrays are not
! completely tested for validity.
! Modules required by TRLIST: None
! Intrinsic function called by TRLIST: ABS
!***********************************************************
INTEGER :: i, i1, i2, i3, isv, j, jlast, ka, kn, kt, l, &
lcc1, lp, lp2, lpl, lpln1, n1, n1st, n2, n3, nm2, nn
LOGICAL :: arcs, cstri, pass2
! Test for invalid input parameters and store the index
! LCC1 of the first constraint node (if any).
nn = n
IF (ncc < 0 .OR. (nrow /= 6 .AND. nrow /= 9)) GO TO 12
lcc1 = nn+1
IF (ncc == 0) THEN
IF (nn < 3) GO TO 12
ELSE
DO i = ncc,1,-1
IF (lcc1-lcc(i) < 3) GO TO 12
lcc1 = lcc(i)
END DO
IF (lcc1 < 1) GO TO 12
END IF
! Initialize parameters for loop on triangles KT = (N1,N2,
! N3), where N1 < N2 and N1 < N3. This requires two
! passes through the nodes with all non-constraint
! triangles stored on the first pass, and the constraint
! triangles stored on the second.
! ARCS = TRUE iff arc indexes are to be stored.
! KA,KT = Numbers of currently stored arcs and triangles.
! N1ST = Starting index for the loop on nodes (N1ST = 1 on
! pass 1, and N1ST = LCC1 on pass 2).
! NM2 = Upper bound on candidates for N1.
! PASS2 = TRUE iff constraint triangles are to be stored.
arcs = nrow == 9
ka = 0
kt = 0
n1st = 1
nm2 = nn-2
pass2 = .false.
! Loop on nodes N1: J = constraint containing N1,
! JLAST = last node in constraint J.
2 j = 0
jlast = lcc1 - 1
DO n1 = n1st,nm2
IF (n1 > jlast) THEN
! N1 is the first node in constraint J+1. Update J and
! JLAST, and store the first constraint triangle index
! if in pass 2.
j = j + 1
IF (j < ncc) THEN
jlast = lcc(j+1) - 1
ELSE
jlast = nn
END IF
IF (pass2) lct(j) = kt + 1
END IF
! Loop on pairs of adjacent neighbors (N2,N3). LPLN1 points
! to the last neighbor of N1, and LP2 points to N2.
lpln1 = lend(n1)
lp2 = lpln1
3 lp2 = lptr(lp2)
n2 = list(lp2)
lp = lptr(lp2)
n3 = ABS(list(lp))
IF (n2 < n1 .OR. n3 < n1) GO TO 10
! (N1,N2,N3) is a constraint triangle iff the three nodes
! are in the same constraint and N2 < N3. Bypass con-
! straint triangles on pass 1 and non-constraint triangles
! on pass 2.
cstri = n1 >= lcc1 .AND. n2 < n3 .AND. n3 <= jlast
IF ((cstri .AND. .NOT. pass2) .OR. (.NOT. cstri .AND. pass2)) GO TO 10
! Add a new triangle KT = (N1,N2,N3).
kt = kt + 1
ltri(1,kt) = n1
ltri(2,kt) = n2
ltri(3,kt) = n3
! Loop on triangle sides (I1,I2) with neighboring triangles
! KN = (I1,I2,I3).
DO i = 1,3
IF (i == 1) THEN
i1 = n3
i2 = n2
ELSE IF (i == 2) THEN
i1 = n1
i2 = n3
ELSE
i1 = n2
i2 = n1
END IF
! Set I3 to the neighbor of I1 which follows I2 unless
! I2->I1 is a boundary arc.
lpl = lend(i1)
lp = lptr(lpl)
4 IF (list(lp) == i2) GO TO 5
lp = lptr(lp)
IF (lp /= lpl) GO TO 4
! I2 is the last neighbor of I1 unless the data structure
! is invalid. Bypass the search for a neighboring
! triangle if I2->I1 is a boundary arc.
IF (ABS(list(lp)) /= i2) GO TO 13
kn = 0
IF (list(lp) < 0) GO TO 8
! I2->I1 is not a boundary arc, and LP points to I2 as a neighbor of I1.
5 lp = lptr(lp)
i3 = ABS(list(lp))
! Find L such that LTRI(L,KN) = I3 (not used if KN > KT),
! and permute the vertex indexes of KN so that I1 is
! smallest.
IF (i1 < i2 .AND. i1 < i3) THEN
l = 3
ELSE IF (i2 < i3) THEN
l = 2
isv = i1
i1 = i2
i2 = i3
i3 = isv
ELSE
l = 1
isv = i1
i1 = i3
i3 = i2
i2 = isv
END IF
! Test for KN > KT (triangle index not yet assigned).
IF (i1 > n1 .AND. .NOT. pass2) CYCLE
! Find KN, if it exists, by searching the triangle list in
! reverse order.
DO kn = kt-1,1,-1
IF (ltri(1,kn) == i1 .AND. ltri(2,kn) == &
i2 .AND. ltri(3,kn) == i3) GO TO 7
END DO
CYCLE
! Store KT as a neighbor of KN.
7 ltri(l+3,kn) = kt
! Store KN as a neighbor of KT, and add a new arc KA.
8 ltri(i+3,kt) = kn
IF (arcs) THEN
ka = ka + 1
ltri(i+6,kt) = ka
IF (kn /= 0) ltri(l+6,kn) = ka
END IF
END DO
! Bottom of loop on triangles.
10 IF (lp2 /= lpln1) GO TO 3
END DO
! Bottom of loop on nodes.
IF (.NOT. pass2 .AND. ncc > 0) THEN
pass2 = .true.
n1st = lcc1
GO TO 2
END IF
! No errors encountered.
nt = kt
ier = 0
RETURN
! Invalid input parameter.
12 nt = 0
ier = 1
RETURN
! Invalid triangulation data structure: I1 is a neighbor of
! I2, but I2 is not a neighbor of I1.
13 nt = 0
ier = 2
RETURN
END SUBROUTINE trlist
SUBROUTINE trlprt (ncc, lct, n, x, y, nrow, nt, ltri, lout, prntx)
INTEGER, INTENT(IN) :: ncc
INTEGER, INTENT(IN OUT) :: lct(:)
INTEGER, INTENT(IN) :: n
REAL, INTENT(IN OUT) :: x(:)
REAL, INTENT(IN OUT) :: y(:)
INTEGER, INTENT(IN) :: nrow
INTEGER, INTENT(IN) :: nt
INTEGER, INTENT(IN OUT) :: ltri(:,:) ! ltri(nrow,nt)
INTEGER, INTENT(IN) :: lout
LOGICAL, INTENT(IN) :: prntx
!***********************************************************
! From TRLPACK
! Robert J. Renka
! Dept. of Computer Science
! Univ. of North Texas
! renka@cs.unt.edu
! 07/02/98
! Given a triangulation of a set of points in the plane,
! this subroutine prints the triangle list created by
! Subroutine TRLIST and, optionally, the nodal coordinates
! on logical unit LOUT. The numbers of boundary nodes,
! triangles, and arcs, and the constraint region triangle
! indexes, if any, are also printed.
! All parameters other than LOUT and PRNTX should be
! unaltered from their values on output from TRLIST.
! On input:
! NCC = Number of constraints.
! LCT = List of constraint triangle starting indexes
! (or dummy array of length 1 if NCC = 0).
! N = Number of nodes in the triangulation.
! 3 <= N <= 9999.
! X,Y = Arrays of length N containing the coordinates
! of the nodes in the triangulation -- not used
! unless PRNTX = TRUE.
! NROW = Number of rows (entries per triangle) re-
! served for the triangle list LTRI. The value
! must be 6 if only the vertex indexes and
! neighboring triangle indexes are stored, or 9
! if arc indexes are also stored.
! NT = Number of triangles in the triangulation.
! 1 <= NT <= 9999.
! LTRI = NROW by NT array whose J-th column contains
! the vertex nodal indexes (first three rows),
! neighboring triangle indexes (second three
! rows), and, if NROW = 9, arc indexes (last
! three rows) associated with triangle J for
! J = 1,...,NT.
! LOUT = Logical unit number for output. 0 <= LOUT
! <= 99. Output is printed on unit 6 if LOUT
! is outside its valid range on input.
! PRNTX = Logical variable with value TRUE if and only
! if X and Y are to be printed (to 6 decimal places).
! None of the parameters are altered by this routine.
! Modules required by TRLPRT: None
!***********************************************************
INTEGER :: i, k, lun, na, nb, nl
INTEGER, PARAMETER :: nmax = 9999, nlmax = 60
! Local parameters:
! I = DO-loop, nodal index, and row index for LTRI
! K = DO-loop and triangle index
! LUN = Logical unit number for output
! NA = Number of triangulation arcs
! NB = Number of boundary nodes
! NL = Number of lines printed on the current page
! NLMAX = Maximum number of print lines per page
! NMAX = Maximum value of N and NT (4-digit format)
lun = lout
IF (lun < 0 .OR. lun > 99) lun = 6
! Print a heading and test for invalid input.
WRITE (lun,100)
nl = 1
IF (n < 3 .OR. n > nmax .OR. (nrow /= 6 .AND. nrow /= 9) .OR. &
nt < 1 .OR. nt > nmax) THEN
! Print an error message and bypass the loops.
WRITE (lun,110) n, nrow, nt
GO TO 3
END IF
IF (prntx) THEN
! Print X and Y.
WRITE (lun,101)
nl = 6
DO i = 1,n
IF (nl >= nlmax) THEN
WRITE (lun,106)
nl = 0
END IF
WRITE (lun,102) i, x(i), y(i)
nl = nl + 1
END DO
END IF
! Print the triangulation LTRI.
IF (nl > nlmax/2) THEN
WRITE (lun,106)
nl = 0
END IF
IF (nrow == 6) THEN
WRITE (lun,103)
ELSE
WRITE (lun,104)
END IF
nl = nl + 5
DO k = 1,nt
IF (nl >= nlmax) THEN
WRITE (lun,106)
nl = 0
END IF
WRITE (lun,105) k, ltri(1:nrow,k)
nl = nl + 1
END DO
! Print NB, NA, and NT (boundary nodes, arcs, and triangles).
nb = 2*n - nt - 2
na = nt + n - 1
IF (nl > nlmax-6) WRITE (lun,106)
WRITE (lun,107) nb, na, nt
! Print NCC and LCT.
3 WRITE (lun,108) ncc
IF (ncc > 0) WRITE (lun,109) lct(1:ncc)
RETURN
! Print formats:
100 FORMAT (///t25, 'TRIPACK (TRLIST) Output')
101 FORMAT (//t17, 'Node X(Node) Y(Node)'//)
102 FORMAT (t17, i4, 2E17.6)
103 FORMAT (//' Triangle Vertices Neighbors'/ &
' KT N1 N2 N3 KT1 KT2 KT3'/)
104 FORMAT (//' Triangle Vertices Neighbors', t61,'Arcs'/ &
' KT N1 N2 N3 KT1 KT2 KT3 KA1 KA2 KA3'/)
105 FORMAT (' ', i4, ' ', 6(' ', i4), 3(' ', i5))
106 FORMAT (///)
107 FORMAT (/' NB = ', i4, ' Boundary Nodes NA = ', i5, &
' Arcs NT = ', i5, ' Triangles')
108 FORMAT (/' NCC =', i3, ' Constraint Curves')
109 FORMAT (t11, 14I5)
110 FORMAT (//t12, '*** Invalid Parameter: N =', i5, &
', NROW =', i5, ', NT =', i5, ' ***')
END SUBROUTINE trlprt
SUBROUTINE trmesh (n, x, y, list, lptr, lend, lnew, near, next, dist, ier)
INTEGER, INTENT(IN) :: n
REAL, INTENT(IN OUT) :: x(:)
REAL, INTENT(IN OUT) :: y(:)
INTEGER, INTENT(OUT) :: list(:)
INTEGER, INTENT(OUT) :: lptr(:)
INTEGER, INTENT(OUT) :: lend(:)
INTEGER, INTENT(OUT) :: lnew
INTEGER, INTENT(OUT) :: near(:)
INTEGER, INTENT(OUT) :: next(:)
REAL, INTENT(OUT) :: dist(:)
INTEGER, INTENT(OUT) :: ier
!***********************************************************
! From TRIPACK
! Robert J. Renka
! Dept. of Computer Science
! Univ. of North Texas
! renka@cs.unt.edu
! 06/28/98
! This subroutine creates a Delaunay triangulation of a set of N
! arbitrarily distributed points in the plane referred to as nodes.
! The Delaunay triangulation is defined as a set of triangles with the
! following five properties:
! 1) The triangle vertices are nodes.
! 2) No triangle contains a node other than its vertices.
! 3) The interiors of the triangles are pairwise disjoint.
! 4) The union of triangles is the convex hull of the set of nodes
! (the smallest convex set which contains the nodes).
! 5) The interior of the circumcircle of each triangle contains no node.
! The first four properties define a triangulation, and the last property
! results in a triangulation which is as close as possible to equiangular in
! a certain sense and which is uniquely defined unless four or more nodes lie
! on a common circle. This property makes the triangulation well-suited
! for solving closest point problems and for triangle-based interpolation.
! The triangulation can be generalized to a constrained Delaunay
! triangulation by a call to Subroutine ADDCST.
! This allows for user-specified boundaries defining a non-convex and/or
! multiply connected region.
! The algorithm for constructing the triangulation has expected time
! complexity O(N*log(N)) for most nodal distributions. Also, since the
! algorithm proceeds by adding nodes incrementally, the triangulation may be
! updated with the addition (or deletion) of a node very efficiently.
! The adjacency information representing the triangulation is stored as a
! linked list requiring approximately 13N storage locations.
! The following is a list of the software package modules
! which a user may wish to call directly:
! ADDCST - Generalizes the Delaunay triangulation to allow
! for user-specified constraints.
! ADDNOD - Updates the triangulation by appending or inserting a new node.
! AREAP - Computes the area bounded by a closed polygonal curve such as the
! boundary of the triangulation or of a constraint region.
! BNODES - Returns an array containing the indexes of the boundary nodes
! in counterclockwise order.
! Counts of boundary nodes, triangles, and arcs are also returned.
! CIRCUM - Computes the area, circumcenter, circumradius, and, optionally,
! the aspect ratio of a triangle defined by user-specified
! vertices.
! DELARC - Deletes a boundary arc from the triangulation.
! DELNOD - Updates the triangulation with the deletion of a node.
! EDGE - Forces a pair of nodes to be connected by an arc
! in the triangulation.
! GETNP - Determines the ordered sequence of L closest nodes to a given
! node, along with the associated distances. The distance
! between nodes is taken to be the length of the shortest
! connecting path which intersects no constraint region.
! INTSEC - Determines whether or not an arbitrary pair of
! line segments share a common point.
! JRAND - Generates a uniformly distributed pseudo-random integer.
! LEFT - Locates a point relative to a line.
! NEARND - Returns the index of the nearest node to an
! arbitrary point, along with its squared distance.
! STORE - Forces a value to be stored in main memory so
! that the precision of floating point numbers
! in memory locations rather than registers is computed.
! TRLIST - Converts the triangulation data structure to a triangle
! list more suitable for use in a finite element code.
! TRLPRT - Prints the triangle list created by Subroutine TRLIST.
! TRMESH - Creates a Delaunay triangulation of a set of nodes.
! TRMSHR - Creates a Delaunay triangulation (more efficiently than TRMESH)
! of a set of nodes lying at the vertices of a (possibly skewed)
! rectangular grid.
! TRPLOT - Creates a level-2 Encapsulated Postscript (EPS)
! file containing a triangulation plot.
! TRPRNT - Prints the triangulation data structure and,
! optionally, the nodal coordinates.
! On input:
! N = Number of nodes in the triangulation. N >= 3.
! X,Y = Arrays of length N containing the Cartesian coordinates of
! the nodes. (X(K),Y(K)) is referred to as node K, and K is
! referred to as a nodal index. The first three nodes must not
! be collinear.
! The above parameters are not altered by this routine.
! LIST,LPTR = Arrays of length at least 6N-12.
! LEND = Array of length at least N.
! NEAR,NEXT,DIST = Work space arrays of length at least N.
! The space is used to efficiently determine the
! nearest triangulation node to each unprocessed
! node for use by ADDNOD.
! On output:
! LIST = Set of nodal indexes which, along with LPTR, LEND, and LNEW,
! define the triangulation as a set of N adjacency lists
! -- counterclockwise-ordered sequences of neighboring nodes such
! that the first and last neighbors of a boundary node are
! boundary nodes (the first neighbor of an interior node is
! arbitrary). In order to distinguish between interior and
! boundary nodes, the last neighbor of each boundary node is
! represented by the negative of its index.
! LPTR = Set of pointers (LIST indexes) in one-to-one correspondence
! with the elements of LIST.
! LIST(LPTR(I)) indexes the node which follows LIST(I) in
! cyclical counterclockwise order (the first neighbor follows
! the last neighbor).
! LEND = Set of pointers to adjacency lists. LEND(K) points to the last
! neighbor of node K for K = 1,...,N.
! Thus, LIST(LEND(K)) < 0 if and only if K is a boundary node.
! LNEW = Pointer to the first empty location in LIST and LPTR
! (list length plus one). LIST, LPTR, LEND, and LNEW are not
! altered if IER < 0, and are incomplete if IER > 0.
! NEAR,NEXT,DIST = Garbage.
! IER = Error indicator:
! IER = 0 if no errors were encountered.
! IER = -1 if N < 3 on input.
! IER = -2 if the first three nodes are collinear.
! IER = -4 if an error flag was returned by a call to SWAP
! in ADDNOD. This is an internal error and should be
! reported to the programmer.
! IER = L if nodes L and M coincide for some M > L.
! The linked list represents a triangulation of nodes
! 1 to M-1 in this case.
! Modules required by TRMESH: ADDNOD, BDYADD, INSERT, INTADD, JRAND, LEFT,
! LSTPTR, STORE, SWAP, SWPTST, TRFIND
! Intrinsic function called by TRMESH: ABS
!***********************************************************
INTEGER :: i, i0, j, k, km1, lcc(1), lp, lpl, ncc, nexti, nn
REAL :: d, d1, d2, d3, eps
! Local parameters:
! D = Squared distance from node K to node I
! D1,D2,D3 = Squared distances from node K to nodes 1, 2, and 3, respectively
! EPS = Half the machine precision
! I,J = Nodal indexes
! I0 = Index of the node preceding I in a sequence of
! unprocessed nodes: I = NEXT(I0)
! K = Index of node to be added and DO-loop index: K > 3
! KM1 = K-1
! LCC(1) = Dummy array
! LP = LIST index (pointer) of a neighbor of K
! LPL = Pointer to the last neighbor of K
! NCC = Number of constraint curves
! NEXTI = NEXT(I)
! NN = Local copy of N
! SWTOL = Tolerance for function SWPTST
nn = n
IF (nn < 3) THEN
ier = -1
RETURN
END IF
! Compute a tolerance for function SWPTST: SWTOL = 10*(machine precision)
eps = 1.
1 eps = eps/2.
swtol = store(eps + 1.)
IF (swtol > 1.) GO TO 1
swtol = eps*20.
! Store the first triangle in the linked list.
IF ( .NOT. left(x(1), y(1), x(2), y(2), x(3), y(3)) ) THEN
! The initial triangle is (3,2,1) = (2,1,3) = (1,3,2).
list(1) = 3
lptr(1) = 2
list(2) = -2
lptr(2) = 1
lend(1) = 2
list(3) = 1
lptr(3) = 4
list(4) = -3
lptr(4) = 3
lend(2) = 4
list(5) = 2
lptr(5) = 6
list(6) = -1
lptr(6) = 5
lend(3) = 6
ELSE IF ( .NOT. left(x(2), y(2), x(1), y(1), x(3), y(3)) ) THEN
! The initial triangle is (1,2,3).
list(1) = 2
lptr(1) = 2
list(2) = -3
lptr(2) = 1
lend(1) = 2
list(3) = 3
lptr(3) = 4
list(4) = -1
lptr(4) = 3
lend(2) = 4
list(5) = 1
lptr(5) = 6
list(6) = -2
lptr(6) = 5
lend(3) = 6
ELSE
! The first three nodes are collinear.
ier = -2
RETURN
END IF
! Initialize LNEW and test for N = 3.
lnew = 7
IF (nn == 3) THEN
ier = 0
RETURN
END IF
! A nearest-node data structure (NEAR, NEXT, and DIST) is
! used to obtain an expected-time (N*log(N)) incremental
! algorithm by enabling constant search time for locating
! each new node in the triangulation.
! For each unprocessed node K, NEAR(K) is the index of the
! triangulation node closest to K (used as the starting
! point for the search in Subroutine TRFIND) and DIST(K)
! is an increasing function of the distance between nodes
! K and NEAR(K).
! Since it is necessary to efficiently find the subset of
! unprocessed nodes associated with each triangulation
! node J (those that have J as their NEAR entries), the
! subsets are stored in NEAR and NEXT as follows: for
! each node J in the triangulation, I = NEAR(J) is the
! first unprocessed node in J's set (with I = 0 if the
! set is empty), L = NEXT(I) (if I > 0) is the second,
! NEXT(L) (if L > 0) is the third, etc. The nodes in each
! set are initially ordered by increasing indexes (which
! maximizes efficiency) but that ordering is not main-
! tained as the data structure is updated.
! Initialize the data structure for the single triangle.
near(1) = 0
near(2) = 0
near(3) = 0
DO k = nn,4,-1
d1 = (x(k)-x(1))**2 + (y(k)-y(1))**2
d2 = (x(k)-x(2))**2 + (y(k)-y(2))**2
d3 = (x(k)-x(3))**2 + (y(k)-y(3))**2
IF (d1 <= d2 .AND. d1 <= d3) THEN
near(k) = 1
dist(k) = d1
next(k) = near(1)
near(1) = k
ELSE IF (d2 <= d1 .AND. d2 <= d3) THEN
near(k) = 2
dist(k) = d2
next(k) = near(2)
near(2) = k
ELSE
near(k) = 3
dist(k) = d3
next(k) = near(3)
near(3) = k
END IF
END DO
! Add the remaining nodes. Parameters for ADDNOD are as follows:
! K = Index of the node to be added.
! NEAR(K) = Index of the starting node for the search in TRFIND.
! NCC = Number of constraint curves.
! LCC = Dummy array (since NCC = 0).
! KM1 = Number of nodes in the triangulation.
ncc = 0
DO k = 4,nn
km1 = k-1
CALL addnod (k, x(k), y(k), near(k), ncc, lcc, km1, x, y, list, lptr, &
lend, lnew, ier)
IF (ier /= 0) RETURN
! Remove K from the set of unprocessed nodes associated with NEAR(K).
i = near(k)
IF (near(i) == k) THEN
near(i) = next(k)
ELSE
i = near(i)
3 i0 = i
i = next(i0)
IF (i /= k) GO TO 3
next(i0) = next(k)
END IF
near(k) = 0
! Loop on neighbors J of node K.
lpl = lend(k)
lp = lpl
4 lp = lptr(lp)
j = ABS(list(lp))
! Loop on elements I in the sequence of unprocessed nodes associated with J:
! K is a candidate for replacing J as the nearest triangulation node to I.
! The next value of I in the sequence, NEXT(I), must be saved before I
! is moved because it is altered by adding I to K's set.
i = near(j)
5 IF (i == 0) GO TO 6
nexti = next(i)
! Test for the distance from I to K less than the distance
! from I to J.
d = (x(k)-x(i))**2 + (y(k)-y(i))**2
IF (d < dist(i)) THEN
! Replace J by K as the nearest triangulation node to I:
! update NEAR(I) and DIST(I), and remove I from J's set
! of unprocessed nodes and add it to K's set.
near(i) = k
dist(i) = d
IF (i == near(j)) THEN
near(j) = nexti
ELSE
next(i0) = nexti
END IF
next(i) = near(k)
near(k) = i
ELSE
i0 = i
END IF
! Bottom of loop on I.
i = nexti
GO TO 5
! Bottom of loop on neighbors J.
6 IF (lp /= lpl) GO TO 4
END DO
RETURN
END SUBROUTINE trmesh
SUBROUTINE trmshr (n, nx, x, y, nit, list, lptr, lend, lnew, ier)
INTEGER, INTENT(IN) :: n
INTEGER, INTENT(IN) :: nx
REAL, INTENT(IN) :: x(:)
REAL, INTENT(IN) :: y(:)
INTEGER, INTENT(IN OUT) :: nit
INTEGER, INTENT(OUT) :: list(:)
INTEGER, INTENT(OUT) :: lptr(:)
INTEGER, INTENT(OUT) :: lend(:)
INTEGER, INTENT(OUT) :: lnew
INTEGER, INTENT(OUT) :: ier
!***********************************************************
! From TRIPACK
! Robert J. Renka
! Dept. of Computer Science
! Univ. of North Texas
! renka@cs.unt.edu
! 06/27/98
! This subroutine creates a Delaunay triangulation of a set of N nodes in
! the plane, where the nodes are the vertices of an NX by NY skewed
! rectangular grid with the natural ordering. Thus, N = NX*NY, and the nodes
! are ordered from left to right beginning at the top row so that adjacent
! nodes have indexes which differ by 1 in the x-direction and by NX in the
! y-direction. A skewed rectangular grid is defined as one in which each grid
! cell is a strictly convex quadrilateral (and is thus the convex hull of its
! four vertices). Equivalently, any transformation from a rectangle to a grid
! cell which is bilinear in both components has an invertible Jacobian.
! If the nodes are not distributed and ordered as defined above,
! Subroutine TRMESH must be called in place of this routine.
! Refer to Subroutine ADDCST for the treatment of constraints.
! The first phase of the algorithm consists of constructing a triangulation
! by choosing a diagonal arc in each grid cell. If NIT = 0, all diagonals
! connect lower left to upper right corners and no error checking or
! additional computation is performed. Otherwise, each diagonal arc is
! chosen to be locally optimal, and boundary arcs are added where necessary
! in order to cover the convex hull of the nodes. (This is the first
! iteration.) If NIT > 1 and no error was detected, the triangulation is then
! optimized by a sequence of up to NIT-1 iterations in which interior arcs of
! the triangulation are tested and swapped if appropriate. The algorithm
! terminates when an iteration results in no swaps and/or when the allowable
! number of iterations has been performed. NIT = 0 is sufficient to produce
! a Delaunay triangulation if the original grid is actually rectangular, and
! NIT = 1 is sufficient if it is close to rectangular. Note, however, that
! the ordering and distribution of nodes is not checked for validity in the
! case NIT = 0, and the triangulation will not be valid unless the rectangular
! grid covers the convex hull of the nodes.
! On input:
! N = Number of nodes in the grid. N = NX*NY for some NY >= 2.
! NX = Number of grid points in the x-direction. NX >= 2.
! X,Y = Arrays of length N containing coordinates of the nodes with the
! ordering and distribution defined in the header comments above.
! (X(K),Y(K)) is referred to as node K.
! The above parameters are not altered by this routine.
! NIT = Nonnegative integer specifying the maximum number of iterations
! to be employed. Refer to the header comments above.
! LIST,LPTR = Arrays of length at least 6N-12.
! LEND = Array of length at least N.
! On output:
! NIT = Number of iterations employed.
! LIST,LPTR,LEND,LNEW = Data structure defining the
! triangulation. Refer to Subroutine TRMESH.
! IER = Error indicator:
! IER = 0 if no errors were encountered.
! IER = K if the grid element with upper left
! corner at node K is not a strictly
! convex quadrilateral. The algorithm
! is terminated when the first such
! occurrence is detected. Note that
! this test is not performed if NIT = 0
! on input.
! IER = -1 if N, NX, or NIT is outside its valid range on input.
! IER = -2 if NIT > 1 on input, and the optimi-
! zation loop failed to converge within
! the allowable number of iterations.
! The triangulation is valid but not
! optimal in this case.
! Modules required by TRMSHR: INSERT, LEFT, LSTPTR, NBCNT,
! STORE, SWAP, SWPTST
! Intrinsic function called by TRMSHR: ABS
!***********************************************************
INTEGER :: i, iter, j, k, kp1, lp, lpf, lpk, lpl, lpp, &
m1, m2, m3, m4, maxit, n0, n1, n2, n3, n4, ni, nj, nm1, nn, nnb
LOGICAL :: tst
REAL :: eps
! Store local variables and test for errors in input parameters.
ni = nx
nj = n/ni
nn = ni*nj
maxit = nit
nit = 0
IF (n /= nn .OR. nj < 2 .OR. ni < 2 .OR. maxit < 0) THEN
ier = -1
RETURN
END IF
ier = 0
! Compute a tolerance for function SWPTST: SWTOL = 10*(machine precision)
eps = 1.
1 eps = eps/2.
swtol = store(eps + 1.)
IF (swtol > 1.) GO TO 1
swtol = eps*20.
! Loop on grid points (I,J) corresponding to nodes K = (J-1)*NI + I.
! TST = TRUE iff diagonals are to be chosen by the swap test. M1, M2, M3,
! and M4 are the slopes (-1, 0, or 1) of the diagonals in quadrants 1 to 4
! (counterclockwise beginning with the upper right)
! for a coordinate system with origin at node K.
tst = maxit > 0
m1 = 0
m4 = 0
lp = 0
kp1 = 1
DO j = 1,nj
DO i = 1,ni
m2 = m1
m3 = m4
k = kp1
kp1 = k + 1
lpf = lp + 1
IF (j == nj .AND. i /= ni) GO TO 2
IF (i /= 1) THEN
IF (j /= 1) THEN
! K is not in the top row, leftmost column, or bottom row (unless K is the
! lower right corner). Take the first neighbor to be the node above K.
lp = lp + 1
list(lp) = k - ni
lptr(lp) = lp + 1
IF (m2 <= 0) THEN
lp = lp + 1
list(lp) = k - 1 - ni
lptr(lp) = lp + 1
END IF
END IF
! K is not in the leftmost column. The next (or first)
! neighbor is to the left of K.
lp = lp + 1
list(lp) = k - 1
lptr(lp) = lp + 1
IF (j == nj) GO TO 3
IF (m3 >= 0) THEN
lp = lp + 1
list(lp) = k - 1 + ni
lptr(lp) = lp + 1
END IF
END IF
! K is not in the bottom row. The next (or first) neighbor is below K.
lp = lp + 1
list(lp) = k + ni
lptr(lp) = lp + 1
! Test for a negative diagonal in quadrant 4 unless K is in the rightmost
! column. The quadrilateral associated with the quadrant is tested for
! strict convexity unless NIT = 0 on input.
IF (i == ni) GO TO 3
m4 = 1
IF (.NOT. tst) GO TO 2
IF ( left(x(kp1),y(kp1),x(k+ni),y(k+ni),x(k),y(k)) &
.OR. left(x(k),y(k),x(kp1+ni),y(kp1+ni), x(k+ni),y(k+ni)) &
.OR. left(x(k+ni),y(k+ni),x(kp1),y(kp1), x(kp1+ni),y(kp1+ni)) &
.OR. left(x(kp1+ni),y(kp1+ni),x(k),y(k), &
x(kp1),y(kp1)) ) GO TO 12
IF ( swptst(kp1,k+ni,k,kp1+ni,x,y) ) GO TO 2
m4 = -1
lp = lp + 1
list(lp) = kp1 + ni
lptr(lp) = lp + 1
! The next (or first) neighbor is to the right of K.
2 lp = lp + 1
list(lp) = kp1
lptr(lp) = lp + 1
! Test for a positive diagonal in quadrant 1 (the neighbor of K-NI
! which follows K is not K+1) unless K is in the top row.
IF (j == 1) GO TO 3
IF (tst) THEN
m1 = -1
lpk = lstptr(lend(k-ni),k,list,lptr)
lpk = lptr(lpk)
IF (list(lpk) /= kp1) THEN
m1 = 1
lp = lp + 1
list(lp) = kp1 - ni
lptr(lp) = lp + 1
END IF
END IF
! If K is in the leftmost column (and not the top row) or in the bottom row
! (and not the rightmost column), then the next neighbor is the node
! above K.
IF (i /= 1 .AND. j /= nj) GO TO 4
lp = lp + 1
list(lp) = k - ni
lptr(lp) = lp + 1
IF (i == 1) GO TO 3
! K is on the bottom row (and not the leftmost or rightmost column).
IF (m2 <= 0) THEN
lp = lp + 1
list(lp) = k - 1 - ni
lptr(lp) = lp + 1
END IF
lp = lp + 1
list(lp) = k - 1
lptr(lp) = lp + 1
! K is a boundary node.
3 list(lp) = -list(lp)
! Bottom of loop. Store LEND and correct LPTR(LP).
! LPF and LP point to the first and last neighbors of K.
4 lend(k) = lp
lptr(lp) = lpf
END DO
END DO
! Store LNEW, and terminate the algorithm if NIT = 0 on input.
lnew = lp + 1
IF (maxit == 0) RETURN
! Add boundary arcs where necessary in order to cover the convex hull of the
! nodes. N1, N2, and N3 are consecutive boundary nodes in counterclockwise
! order, and N0 is the starting point for each loop around the boundary.
n0 = 1
n1 = n0
n2 = ni + 1
! TST is set to TRUE if an arc is added. The boundary
! loop is repeated until a traversal results in no added arcs.
7 tst = .false.
! Top of boundary loop. Set N3 to the first neighbor of
! N2, and test for N3 LEFT N1 -> N2.
8 lpl = lend(n2)
lp = lptr(lpl)
n3 = list(lp)
IF ( left(x(n1),y(n1),x(n2),y(n2),x(n3),y(n3)) ) n1 = n2
IF (n1 /= n2) THEN
! Add the boundary arc N1-N3. If N0 = N2, the starting
! point is changed to N3, since N2 will be removed from
! the boundary. N3 is inserted as the first neighbor of
! N1, N2 is changed to an interior node, and N1 is
! inserted as the last neighbor of N3.
tst = .true.
IF (n2 == n0) n0 = n3
lp = lend(n1)
CALL insert (n3,lp, list,lptr,lnew )
list(lpl) = -list(lpl)
lp = lend(n3)
list(lp) = n2
CALL insert (-n1,lp, list,lptr,lnew )
lend(n3) = lnew - 1
END IF
! Bottom of loops. Test for termination.
n2 = n3
IF (n1 /= n0) GO TO 8
IF (tst) GO TO 7
! Terminate the algorithm if NIT = 1 on input.
nit = 1
IF (maxit == 1) RETURN
! Optimize the triangulation by applying the swap test and appropriate swaps
! to the interior arcs. The loop is repeated until no swaps are performed
! or MAXIT iterations have been applied. ITER is the current iteration,
! and TST is set to TRUE if a swap occurs.
iter = 1
nm1 = nn - 1
9 iter = iter + 1
tst = .false.
! Loop on interior arcs N1-N2, where N2 > N1 and
! (N1,N2,N3) and (N2,N1,N4) are adjacent triangles.
! Top of loop on nodes N1.
loop11: DO n1 = 1,nm1
lpl = lend(n1)
n4 = list(lpl)
lpf = lptr(lpl)
n2 = list(lpf)
lp = lptr(lpf)
n3 = list(lp)
nnb = nbcnt(lpl,lptr)
! Top of loop on neighbors N2 of N1. NNB is the number of neighbors of N1.
DO i = 1,nnb
! Bypass the swap test if N1 is a boundary node and N2 is
! the first neighbor (N4 < 0), N2 < N1, or N1-N2 is a
! diagonal arc (already locally optimal) when ITER = 2.
IF ( n4 > 0 .AND. n2 > n1 .AND. &
(iter /= 2 .OR. ABS(n1+ni-n2) /= 1) ) THEN
IF (swptst(n3, n4, n1, n2, x, y) ) THEN
! Swap diagonal N1-N2 for N3-N4, set TST to TRUE, and set
! N2 to N4 (the neighbor preceding N3).
CALL swap (n3, n4, n1, n2, list, lptr, lend, lpp)
IF (lpp /= 0) THEN
tst = .true.
n2 = n4
END IF
END IF
END IF
! Bottom of neighbor loop.
IF (list(lpl) == -n3) CYCLE loop11
n4 = n2
n2 = n3
lp = lstptr(lpl,n2,list,lptr)
lp = lptr(lp)
n3 = ABS(list(lp))
END DO
END DO loop11
! Test for termination.
IF (tst .AND. iter < maxit) GO TO 9
nit = iter
IF (tst) ier = -2
RETURN
! Invalid grid cell encountered.
12 ier = k
RETURN
END SUBROUTINE trmshr
SUBROUTINE trplot (lun,pltsiz,wx1,wx2,wy1,wy2,ncc,lcc, &
n,x,y,list,lptr,lend,title, numbr, ier)
INTEGER, INTENT(IN) :: lun
REAL, INTENT(IN) :: pltsiz
REAL, INTENT(IN) :: wx1
REAL, INTENT(IN) :: wx2
REAL, INTENT(IN) :: wy1
REAL, INTENT(IN) :: wy2
INTEGER, INTENT(IN) :: ncc
INTEGER, INTENT(IN) :: lcc(:)
INTEGER, INTENT(IN) :: n
REAL, INTENT(IN) :: x(n)
REAL, INTENT(IN) :: y(n)
INTEGER, INTENT(IN OUT) :: list(:)
INTEGER, INTENT(IN) :: lptr(:)
INTEGER, INTENT(IN) :: lend(:)
CHARACTER (LEN=*), INTENT(IN) :: title
LOGICAL, INTENT(IN) :: numbr
INTEGER, INTENT(OUT) :: ier
!***********************************************************
! From TRIPACK
! Robert J. Renka
! Dept. of Computer Science
! Univ. of North Texas
! renka@cs.unt.edu
! 07/15/98
! This subroutine creates a level-2 Encapsulated Postscript (EPS) file
! containing a triangulation plot.
! On input:
! LUN = Logical unit number in the range 0 to 99.
! The unit should be opened with an appropriate file name before
! the call to this routine.
! PLTSIZ = Plot size in inches. The window is mapped, with aspect ratio
! preserved, to a rectangular viewport with maximum side-length
! equal to .88*PLTSIZ (leaving room for labels outside the
! viewport). The viewport is centered on the 8.5 by 11 inch
! page, and its boundary is drawn. 1.0 <= PLTSIZ <= 8.5.
! WX1,WX2,WY1,WY2 = Parameters defining a rectangular window against
! which the triangulation is clipped. (Only the
! portion of the triangulation that lies in the window
! is drawn.)
! (WX1,WY1) and (WX2,WY2) are the lower left and upper
! right corners, respectively. WX1 < WX2 and
! WY1 < WY2.
! NCC = Number of constraint curves. Refer to Subroutine ADDCST.
! NCC >= 0.
! LCC = Array of length NCC (or dummy parameter if
! NCC = 0) containing the index of the first
! node of constraint I in LCC(I). For I = 1 to
! NCC, LCC(I+1)-LCC(I) >= 3, where LCC(NCC+1) = N+1.
! N = Number of nodes in the triangulation. N >= 3.
! X,Y = Arrays of length N containing the coordinates of the nodes with
! non-constraint nodes in the first LCC(1)-1 locations.
! LIST,LPTR,LEND = Data structure defining the triangulation.
! Refer to Subroutine TRMESH.
! TITLE = Type CHARACTER variable or constant containing a string to be
! centered above the plot.
! The string must be enclosed in parentheses; i.e., the first
! and last characters must be '(' and ')', respectively, but
! these are not displayed. TITLE may have at most 80 characters
! including the parentheses.
! NUMBR = Option indicator: If NUMBR = TRUE, the
! nodal indexes are plotted next to the nodes.
! Input parameters are not altered by this routine.
! On output:
! IER = Error indicator:
! IER = 0 if no errors were encountered.
! IER = 1 if LUN, PLTSIZ, NCC, or N is outside its valid range.
! LCC is not tested for validity.
! IER = 2 if WX1 >= WX2 or WY1 >= WY2.
! IER = 3 if an error was encountered in writing to unit LUN.
! Various plotting options can be controlled by altering
! the data statement below.
! Modules required by TRPLOT: None
! Intrinsic functions called by TRPLOT: ABS, CHAR, NINT, REAL
!***********************************************************
INTEGER :: i, ifrst, ih, ilast, ipx1, ipx2, ipy1, ipy2, &
iw, lp, lpl, n0, n0bak, n0for, n1, nls
LOGICAL :: cnstr, pass1
REAL :: dx, dy, r, sfx, sfy, t, tx, ty, x0, y0
LOGICAL, PARAMETER :: annot = .TRUE.
REAL, PARAMETER :: dashl = 4.0, fsizn = 10.0, fsizt = 16.0
! Local parameters:
! ANNOT = Logical variable with value TRUE iff the plot
! is to be annotated with the values of WX1, WX2, WY1, and WY2
! CNSTR Logical variable used to flag constraint arcs:
! TRUE iff N0-N1 lies in a constraint region
! DASHL = Length (in points, at 72 points per inch) of dashes and spaces
! in a dashed line pattern used for drawing constraint arcs
! DX = Window width WX2-WX1
! DY = Window height WY2-WY1
! FSIZN = Font size in points for labeling nodes with
! their indexes if NUMBR = TRUE
! FSIZT = Font size in points for the title (and
! annotation if ANNOT = TRUE)
! I = Constraint index (1 to NCC)
! IFRST = Index of the first node in constraint I
! IH = Height of the viewport in points
! ILAST = Index of the last node in constraint I
! IPX1,IPY1 = X and y coordinates (in points) of the lower
! left corner of the bounding box or viewport
! IPX2,IPY2 = X and y coordinates (in points) of the upper
! right corner of the bounding box or viewport
! IW = Width of the viewport in points
! LP = LIST index (pointer)
! LPL = Pointer to the last neighbor of N0
! N0 = Nodal index and DO-loop index
! N0BAK = Predecessor of N0 in a constraint curve
! (sequence of adjacent constraint nodes)
! N0FOR = Successor to N0 in a constraint curve
! N1 = Index of a neighbor of N0
! NLS = Index of the last non-constraint node
! PASS1 = Logical variable used to flag the first pass
! through the constraint nodes
! R = Aspect ratio DX/DY
! SFX,SFY = Scale factors for mapping world coordinates
! (window coordinates in [WX1,WX2] X [WY1,WY2])
! to viewport coordinates in [IPX1,IPX2] X [IPY1,IPY2]
! T = Temporary variable
! TX,TY = Translation vector for mapping world coordinates to
! viewport coordinates
! X0,Y0 = X(N0),Y(N0) or label location
! Test for error 1, and set NLS to the last non-constraint node.
IF (lun < 0 .OR. lun > 99 .OR. pltsiz < 1.0 .OR. pltsiz > 8.5 .OR. &
ncc < 0 .OR. n < 3) GO TO 11
nls = n
IF (ncc > 0) nls = lcc(1)-1
! Compute the aspect ratio of the window.
dx = wx2 - wx1
dy = wy2 - wy1
IF (dx <= 0.0 .OR. dy <= 0.0) GO TO 12
r = dx/dy
! Compute the lower left (IPX1,IPY1) and upper right
! (IPX2,IPY2) corner coordinates of the bounding box.
! The coordinates, specified in default user space units
! (points, at 72 points/inch with origin at the lower
! left corner of the page), are chosen to preserve the
! aspect ratio R, and to center the plot on the 8.5 by 11
! inch page. The center of the page is (306,396), and
! T = PLTSIZ/2 in points.
t = 36.0*pltsiz
IF (r >= 1.0) THEN
ipx1 = 306 - nint(t)
ipx2 = 306 + nint(t)
ipy1 = 396 - nint(t/r)
ipy2 = 396 + nint(t/r)
ELSE
ipx1 = 306 - nint(t*r)
ipx2 = 306 + nint(t*r)
ipy1 = 396 - nint(t)
ipy2 = 396 + nint(t)
END IF
! Output header comments.
WRITE (lun,100,ERR=13) ipx1, ipy1, ipx2, ipy2
100 FORMAT ('%!PS-Adobe-3.0 EPSF-3.0'/ '%%BoundingBox:',4I4/ &
'%%Title: Triangulation'/ '%%Creator: TRIPACK'/ &
'%%EndComments')
! Set (IPX1,IPY1) and (IPX2,IPY2) to the corner coordinates
! of a viewport obtained by shrinking the bounding box by
! 12% in each dimension.
iw = nint(0.88*REAL(ipx2-ipx1))
ih = nint(0.88*REAL(ipy2-ipy1))
ipx1 = 306 - iw/2
ipx2 = 306 + iw/2
ipy1 = 396 - ih/2
ipy2 = 396 + ih/2
! Set the line thickness to 2 points, and draw the viewport boundary.
t = 2.0
WRITE (lun,110,ERR=13) t
WRITE (lun,120,ERR=13) ipx1, ipy1
WRITE (lun,130,ERR=13) ipx1, ipy2
WRITE (lun,130,ERR=13) ipx2, ipy2
WRITE (lun,130,ERR=13) ipx2, ipy1
WRITE (lun,140,ERR=13)
WRITE (lun,150,ERR=13)
110 FORMAT (f12.6,' setlinewidth')
120 FORMAT (2I4,' moveto')
130 FORMAT (2I4,' lineto')
140 FORMAT ('closepath')
150 FORMAT ('stroke')
! Set up a mapping from the window to the viewport.
sfx = REAL(iw)/dx
sfy = REAL(ih)/dy
tx = ipx1 - sfx*wx1
ty = ipy1 - sfy*wy1
WRITE (lun,160,ERR=13) tx, ty, sfx, sfy
160 FORMAT (2F12.6, ' translate'/ 2F12.6, ' scale')
! The line thickness (believe it or fucking not) must be
! changed to reflect the new scaling which is applied to
! all subsequent output. Set it to 1.0 point.
t = 2.0/(sfx+sfy)
WRITE (lun,110,ERR=13) t
! Save the current graphics state, and set the clip path to
! the boundary of the window.
WRITE (lun,170,ERR=13)
WRITE (lun,180,ERR=13) wx1, wy1
WRITE (lun,190,ERR=13) wx2, wy1
WRITE (lun,190,ERR=13) wx2, wy2
WRITE (lun,190,ERR=13) wx1, wy2
WRITE (lun,200,ERR=13)
170 FORMAT ('gsave')
180 FORMAT (2F12.6,' moveto')
190 FORMAT (2F12.6,' lineto')
200 FORMAT ('closepath clip newpath')
! Draw the edges N0->N1, where N1 > N0, beginning with a loop on
! non-constraint nodes N0. LPL points to the last neighbor of N0.
DO n0 = 1,nls
x0 = x(n0)
y0 = y(n0)
lpl = lend(n0)
lp = lpl
! Loop on neighbors N1 of N0.
2 lp = lptr(lp)
n1 = ABS(list(lp))
IF (n1 > n0) THEN
! Add the edge to the path.
WRITE (lun,210,ERR=13) x0, y0, x(n1), y(n1)
210 FORMAT (2F12.6,' moveto',2F12.6,' lineto')
END IF
IF (lp /= lpl) GO TO 2
END DO
! Loop through the constraint nodes twice. The non-
! constraint arcs incident on constraint nodes are
! drawn (with solid lines) on the first pass, and the
! constraint arcs (both boundary and interior, if any)
! are drawn (with dashed lines) on the second pass.
pass1 = .true.
! Loop on constraint nodes N0 with (N0BAK,N0,N0FOR) a sub-
! sequence of constraint I. The outer loop is on
! constraints I with first and last nodes IFRST and ILAST.
4 ifrst = n+1
DO i = ncc,1,-1
ilast = ifrst - 1
ifrst = lcc(i)
n0bak = ilast
DO n0 = ifrst,ilast
n0for = n0 + 1
IF (n0 == ilast) n0for = ifrst
lpl = lend(n0)
x0 = x(n0)
y0 = y(n0)
lp = lpl
! Loop on neighbors N1 of N0. CNSTR = TRUE iff N0-N1 is a
! constraint arc.
! Initialize CNSTR to TRUE iff the first neighbor of N0
! strictly follows N0FOR and precedes or coincides with
! N0BAK (in counterclockwise order).
5 lp = lptr(lp)
n1 = ABS(list(lp))
IF (n1 /= n0for .AND. n1 /= n0bak) GO TO 5
cnstr = n1 == n0bak
lp = lpl
! Loop on neighbors N1 of N0. Update CNSTR and test for
! N1 > N0.
6 lp = lptr(lp)
n1 = ABS(list(lp))
IF (n1 == n0for) cnstr = .true.
IF (n1 > n0) THEN
! Draw the edge iff (PASS1=TRUE and CNSTR=FALSE) or
! (PASS1=FALSE and CNSTR=TRUE); i.e., CNSTR and PASS1
! have opposite values.
IF (cnstr .NEQV. pass1) WRITE (lun,210,ERR=13) x0, y0, x(n1), y(n1)
END IF
IF (n1 == n0bak) cnstr = .false.
! Bottom of loops.
IF (lp /= lpl) GO TO 6
n0bak = n0
END DO
END DO
IF (pass1) THEN
! End of first pass: paint the path and change to dashed
! lines for subsequent drawing. Since the scale factors
! are applied to everything, the dash length must be
! specified in world coordinates.
pass1 = .false.
WRITE (lun,150,ERR=13)
t = dashl*2.0/(sfx+sfy)
WRITE (lun,220,ERR=13) t
220 FORMAT ('[',f12.6,'] 0 setdash')
GO TO 4
END IF
! Paint the path and restore the saved graphics state (with
! no clip path).
WRITE (lun,150,ERR=13)
WRITE (lun,230,ERR=13)
230 FORMAT ('grestore')
IF (numbr) THEN
! Nodes in the window are to be labeled with their indexes.
! Convert FSIZN from points to world coordinates, and
! output the commands to select a font and scale it.
t = fsizn*2.0/(sfx+sfy)
WRITE (lun,240,ERR=13) t
240 FORMAT ('/Helvetica findfont'/ f12.6,' scalefont setfont')
! Loop on nodes N0 with coordinates (X0,Y0).
DO n0 = 1,n
x0 = x(n0)
y0 = y(n0)
IF (x0 < wx1 .OR. x0 > wx2 .OR. y0 < wy1 .OR. y0 > wy2) CYCLE
! Move to (X0,Y0), and draw the label N0. The first char-
! acter will have its lower left corner about one
! character width to the right of the nodal position.
WRITE (lun,180,ERR=13) x0, y0
WRITE (lun,250,ERR=13) n0
250 FORMAT ('(',i3,') show')
END DO
END IF
! Convert FSIZT from points to world coordinates, and output
! the commands to select a font and scale it.
t = fsizt*2.0/(sfx+sfy)
WRITE (lun,240,ERR=13) t
! Display TITLE centered above the plot:
y0 = wy2 + 3.0*t
WRITE (lun,260,ERR=13) title, (wx1+wx2)/2.0, y0
260 FORMAT (a80/' stringwidth pop 2 div neg ',f12.6, ' add ',f12.6,' moveto')
WRITE (lun,270,ERR=13) title
270 FORMAT (a80/' show')
IF (annot) THEN
! Display the window extrema below the plot.
x0 = wx1
y0 = wy1 - 100.0/(sfx+sfy)
WRITE (lun,180,ERR=13) x0, y0
WRITE (lun,280,ERR=13) wx1, wx2
y0 = y0 - 2.0*t
WRITE (lun,290,ERR=13) x0, y0, wy1, wy2
280 FORMAT ('(Window: WX1 = ',e9.3,', WX2 = ',e9.3, ') show')
290 FORMAT ('(Window: ) stringwidth pop ',f12.6,' add', &
f12.6,' moveto'/ '( WY1 = ',e9.3,', WY2 = ',e9.3,') show')
END IF
! Paint the path and output the showpage command and
! end-of-file indicator.
WRITE (lun,300,ERR=13)
300 FORMAT ('stroke'/ 'showpage'/ '%%EOF')
! HP's interpreters require a one-byte End-of-PostScript-Job
! indicator (to eliminate a timeout error message):
! ASCII 4.
WRITE (lun,310,ERR=13) CHAR(4)
310 FORMAT (a1)
! No error encountered.
ier = 0
RETURN
! Invalid input parameter.
11 ier = 1
RETURN
! DX or DY is not positive.
12 ier = 2
RETURN
! Error writing to unit LUN.
13 ier = 3
RETURN
END SUBROUTINE trplot
SUBROUTINE trprnt (ncc, lcc, n, x, y, list, lptr, lend, lout, prntx)
INTEGER, INTENT(IN) :: ncc
INTEGER, INTENT(IN OUT) :: lcc(:)
INTEGER, INTENT(IN) :: n
REAL, INTENT(IN OUT) :: x(n)
REAL, INTENT(IN OUT) :: y(n)
INTEGER, INTENT(IN) :: list(:)
INTEGER, INTENT(IN) :: lptr(:)
INTEGER, INTENT(IN) :: lend(:)
INTEGER, INTENT(IN) :: lout
LOGICAL, INTENT(IN) :: prntx
!***********************************************************
! From TRIPACK
! Robert J. Renka
! Dept. of Computer Science
! Univ. of North Texas
! renka@cs.unt.edu
! 07/30/98
! Given a triangulation of a set of points in the plane,
! this subroutine prints the adjacency lists and, option-
! ally, the nodal coordinates on logical unit LOUT. The
! list of neighbors of a boundary node is followed by index
! 0. The numbers of boundary nodes, triangles, and arcs,
! and the constraint curve starting indexes, if any, are
! also printed.
! On input:
! NCC = Number of constraints.
! LCC = List of constraint curve starting indexes (or
! dummy array of length 1 if NCC = 0).
! N = Number of nodes in the triangulation.
! 3 <= N <= 9999.
! X,Y = Arrays of length N containing the coordinates
! of the nodes in the triangulation -- not used
! unless PRNTX = TRUE.
! LIST,LPTR,LEND = Data structure defining the trian-
! gulation. Refer to Subroutine
! TRMESH.
! LOUT = Logical unit number for output. 0 <= LOUT
! <= 99. Output is printed on unit 6 if LOUT
! is outside its valid range on input.
! PRNTX = Logical variable with value TRUE if and only
! if X and Y are to be printed (to 6 decimal places).
! None of the parameters are altered by this routine.
! Modules required by TRPRNT: None
!***********************************************************
INTEGER :: inc, k, lp, lpl, lun, na, nabor(100), nb, nd, nl, node, nn, nt
INTEGER, PARAMETER :: nmax = 9999, nlmax = 60
nn = n
lun = lout
IF (lun < 0 .OR. lun > 99) lun = 6
! Print a heading and test the range of N.
WRITE (lun,100) nn
IF (nn < 3 .OR. nn > nmax) THEN
! N is outside its valid range.
WRITE (lun,110)
GO TO 5
END IF
! Initialize NL (the number of lines printed on the current
! page) and NB (the number of boundary nodes encountered).
nl = 6
nb = 0
IF (.NOT. prntx) THEN
! Print LIST only. K is the number of neighbors of NODE
! which are stored in NABOR.
WRITE (lun,101)
DO node = 1,nn
lpl = lend(node)
lp = lpl
k = 0
1 k = k + 1
lp = lptr(lp)
nd = list(lp)
nabor(k) = nd
IF (lp /= lpl) GO TO 1
IF (nd <= 0) THEN
! NODE is a boundary node. Correct the sign of the last
! neighbor, add 0 to the end of the list, and increment NB.
nabor(k) = -nd
k = k + 1
nabor(k) = 0
nb = nb + 1
END IF
! Increment NL and print the list of neighbors.
inc = (k-1)/14 + 2
nl = nl + inc
IF (nl > nlmax) THEN
WRITE (lun,106)
nl = inc
END IF
WRITE (lun,103) node, nabor(1:k)
IF (k /= 14) WRITE (lun,105)
END DO
ELSE
! Print X, Y, and LIST.
WRITE (lun,102)
DO node = 1,nn
lpl = lend(node)
lp = lpl
k = 0
3 k = k + 1
lp = lptr(lp)
nd = list(lp)
nabor(k) = nd
IF (lp /= lpl) GO TO 3
IF (nd <= 0) THEN
! NODE is a boundary node.
nabor(k) = -nd
k = k + 1
nabor(k) = 0
nb = nb + 1
END IF
! Increment NL and print X, Y, and NABOR.
inc = (k-1)/8 + 2
nl = nl + inc
IF (nl > nlmax) THEN
WRITE (lun,106)
nl = inc
END IF
WRITE (lun,104) node, x(node), y(node), nabor(1:k)
IF (k /= 8) WRITE (lun,105)
END DO
END IF
! Print NB, NA, and NT (boundary nodes, arcs, and triangles).
nt = 2*nn - nb - 2
na = nt + nn - 1
IF (nl > nlmax-6) WRITE (lun,106)
WRITE (lun,107) nb, na, nt
! Print NCC and LCC.
5 WRITE (lun,108) ncc
IF (ncc > 0) WRITE (lun,109) lcc(1:ncc)
RETURN
! Print formats:
100 FORMAT (//t27, 'Adjacency Sets, N = ', i5//)
101 FORMAT (' Node', t38, 'Neighbours of Node'//)
102 FORMAT (' Node X(Node) Y(Node)', t53, 'Neighbours of Node'//)
103 FORMAT (' ', i4, ' ', 14I5 / (t11, 14I5))
104 FORMAT (' ', i4, 2g15.6, ' ', 8I5 / (t41, 8I5))
105 FORMAT (' ')
106 FORMAT (//)
107 FORMAT (/' NB = ', i4, ' Boundary Nodes NA = ', i5, &
' Arcs NT = ', i5, ' Triangles')
108 FORMAT (/' NCC =', i3, ' Constraint Curves')
109 FORMAT (t11, 14I5)
110 FORMAT (t12, '*** N is outside its valid', ' range ***')
END SUBROUTINE trprnt
FUNCTION frwrd(xa, ya, xb, yb, xc, yc) RESULT(fn_val)
REAL, INTENT(IN) :: xa, ya, xb, yb, xc, yc
LOGICAL :: fn_val
fn_val = (xb-xa)*(xc-xa) + (yb-ya)*(yc-ya) >= 0.
RETURN
END FUNCTION frwrd
END MODULE TRIPACK
PROGRAM Test_TriPack
! TRITEST: Portable Test Driver for TRIPACK
! 07/02/98
! This driver tests software package TRIPACK for constructing a constrained
! Delaunay triangulation of a set of points in the plane. All modules other
! than TRMSHR are tested unless an error is encountered, in which case the
! program terminates immediately.
! By default, tests are performed on a simple data set consisting of 12
! nodes whose convex hull covers the unit square. The data set includes a
! single constraint region consisting of four nodes forming a smaller square
! at the center of the unit square. However, by enabling the READ statements
! below (C# in the first two columns), testing may be performed on an
! arbitrary set of up to NMAX nodes with up to NCMAX constraint curves.
! (Refer to the PARAMETER statements below.) A data set consists of the
! following sequence of records:
! N = Number of nodes (format I4) -- 3 to NMAX.
! NCC = Number of constraint curves (format I4) -- 0 to NCMAX.
! (LCC(I), I = 1,NCC) = Indexes of the first node in each constraint curve
! (format I4). 1 <= LCC(1) and, for I > 1, LCC(I-1) + 3 <= LCC(I)
! <= N-2. (Each constraint curve has at least three nodes.)
! (X(I),Y(I), I = 1,N) = Nodal coordinates with non-constraint nodes
! followed by the NCC sequences of constraint nodes (format
! 2F13.8).
! The I/O units may be changed by altering LIN (input) and
! LOUT (output) in the DATA statement below.
! This driver must be linked to TRIPACK.
! Code converted using TO_F90 by Alan Miller
! Date: 2000-05-25 Time: 18:21:14
USE TriPack
IMPLICIT NONE
CHARACTER (LEN=80) :: title
INTEGER :: ier, io1, io2, k, ksum, lnew, lw, n0, na, nb, nn, nt
LOGICAL :: numbr, prntx
REAL :: a, armax, dsq, wx1, wx2, wy1, wy2
INTEGER, PARAMETER :: nmax=100, ncmax=5, ntmx=2*nmax, n6=6*nmax, &
lwk=2*nmax, nrow=9
! Array storage:
INTEGER :: lcc(ncmax), lct(ncmax), lend(nmax), list(n6), &
lptr(n6), ltri(nrow,ntmx), nodes(lwk), iwk(2,nmax)
REAL :: ds(nmax), x(nmax), y(nmax)
! Tolerance for TRMTST and NEARND: upper bound on squared distances.
REAL, PARAMETER :: tol = 1.0e-2
! Plot size for the triangulation plot.
REAL, PARAMETER :: pltsiz = 7.5
! Logical unit numbers for I/O:
INTEGER, PARAMETER :: lin = 1, lout = 2, lplt = 3
! Default data set:
INTEGER :: n = 12, ncc = 1
x(1:12) = (/ 0., 1., .5, .15, .85, .5, 0., 1., .35, .65, .65, .35 /)
y(1:12) = (/ 0., 0., .15, .5, .5, .85, 1., 1., .35, .35, .65, .65 /)
OPEN (lout, FILE='RES')
OPEN (lplt, FILE='RES.eps')
! Store a plot title. It must be enclosed in parentheses.
title = '(Triangulation created by TRITEST)'
! *** Read triangulation parameters -- N, NCC, LCC, X, Y.
!# OPEN (LIN,FILE='tritest.dat',STATUS='OLD')
!# READ (LIN,100,ERR=30) N, NCC
IF (n < 3 .OR. n > nmax .OR. ncc < 0 .OR. ncc > ncmax) GO TO 31
!# IF (NCC .GT. 0) READ (LIN,100,ERR=30)
!# . (LCC(K), K = 1,NCC)
!# READ (LIN,110,ERR=30) (X(K),Y(K), K = 1,N)
!#100 FORMAT (I4)
!#110 FORMAT (2F13.8)
lcc(1) = 9
! Print a heading.
WRITE (lout,400) n
! *** Create the Delaunay triangulation (TRMESH), and test for errors
! (refer to TRMTST below). NODES and DS are used as work space.
CALL trmesh (n,x,y, list,lptr,lend,lnew,nodes, nodes(n+1:),ds,ier)
IF (ier == -2) THEN
WRITE (lout,210)
STOP
ELSE IF (ier == -4) THEN
WRITE (lout,212)
STOP
ELSE IF (ier > 0) THEN
WRITE (lout,214)
STOP
END IF
CALL trmtst (n,x,y,list,lptr,lend,lnew,tol, lout, armax,ier)
WRITE (lout,410) armax
IF (ier > 0) STOP
! *** Add the constraint curves (ADDCST). Note that edges and triangles are
! not removed from constraint regions.
! ADDCST forces the inclusion of triangulation edges connecting the
! sequences of constraint nodes. If it is necessary to alter the
! triangulation, the empty circumcircle property is no longer satisfied.
lw = lwk
CALL addcst (ncc,lcc,n,x,y, lw,list,lptr, lend, ier)
IF (ier /= 0) THEN
WRITE (lout,220) ier
STOP
END IF
IF (lw == 0) WRITE (lout,430)
! *** Test TRPRNT, TRLIST, and TRLPRT, and TRPLOT.
prntx = .true.
CALL trprnt (ncc,lcc,n,x,y,list,lptr,lend,lout,prntx)
CALL trlist (ncc,lcc,n,list,lptr,lend,nrow, nt,ltri, lct,ier)
CALL trlprt (ncc,lct,n,x,y,nrow,nt,ltri,lout,prntx)
! Set the plot window [WX1,WX2] X [WY1,WY2] to the
! smallest rectangle that contains the nodes.
! NUMBR = TRUE iff nodal indexes are to be displayed.
wx1 = x(1)
wx2 = wx1
wy1 = y(1)
wy2 = wy1
DO k = 2,n
IF (x(k) < wx1) wx1 = x(k)
IF (x(k) > wx2) wx2 = x(k)
IF (y(k) < wy1) wy1 = y(k)
IF (y(k) > wy2) wy2 = y(k)
END DO
numbr = n <= 200
CALL trplot (lplt,pltsiz,wx1,wx2,wy1,wy2,ncc,lcc,n, &
x,y,list,lptr,lend,title,numbr, ier)
IF (ier == 0) THEN
WRITE (lout,470)
ELSE
WRITE (lout,270) ier
END IF
! *** Test BNODES and AREAP.
CALL bnodes (n,list,lptr,lend, nodes,nb,na,nt)
a = areap(x,y,nb,nodes)
WRITE (lout,420) nb, na, nt, a
! *** Test GETNP by ordering the nodes on distance from N0
! and verifying the ordering.
n0 = n/2
nodes(1) = n0
ds(1) = 0.
ksum = n0
DO k = 2,n
CALL getnp (ncc,lcc,n,x,y,list,lptr,lend, k, nodes,ds, ier)
IF (ier /= 0 .OR. ds(k) < ds(k-1)) THEN
WRITE (lout,230)
STOP
END IF
ksum = ksum + nodes(k)
END DO
! Test for all nodal indexes included in NODES.
IF (ksum /= (n*(n+1))/2) THEN
WRITE (lout,230)
STOP
END IF
! *** Test NEARND by verifying that the nearest node to K is
! node K for K = 1 to N.
DO k = 1,n
n0 = nearnd (x(k),y(k),1,n,x,y,list,lptr,lend, dsq)
IF (n0 /= k .OR. dsq > tol) THEN
WRITE (lout,240)
STOP
END IF
END DO
! *** Test DELARC by removing a boundary arc if possible.
! The first two nodes define a boundary arc
! in the default data set.
io1 = 1
io2 = 2
CALL delarc (n,io1,io2, list,lptr,lend,lnew, ier)
IF (ier == 1 .OR. ier == 4) THEN
WRITE (lout,250) ier
STOP
END IF
IF (ier /= 0) WRITE (lout,440)
! Recreate the triangulation without constraints.
CALL trmesh (n,x,y, list,lptr,lend,lnew,nodes, nodes(n+1:),ds,ier)
ncc = 0
! *** Test DELNOD by removing nodes 4 to N (in reverse order).
IF (n <= 3) THEN
WRITE (lout,450)
ELSE
nn = n
4 lw = lwk/2
CALL delnod (nn,ncc, lcc,nn,x,y,list,lptr,lend, lnew,lw,iwk, ier)
IF (ier /= 0) THEN
WRITE (lout,260) ier
STOP
END IF
IF (nn > 3) GO TO 4
END IF
! Successful test.
WRITE (lout,460)
STOP
! Error reading the data set.
!# 30 WRITE (*,200)
STOP
! Invalid value of N or NCC.
31 WRITE (*,205) n, ncc
STOP
! Error message formats:
!#200 FORMAT (//5X,'*** Input data set invalid ***'/)
205 FORMAT (//' *** N or NCC is outside its valid ', &
'range: N =', i5, ', NCC = ', i4, ' ***'/)
210 FORMAT (//' *** Error in TRMESH: the first three ', &
'nodes are collinear ***'/)
212 FORMAT (//' *** Error in TRMESH: invalid ', 'triangulation ***'/)
214 FORMAT (//' *** Error in TRMESH: duplicate nodes ', 'encountered ***'/)
220 FORMAT (//' *** Error in ADDCST: IER = ',i1, ' ***'/)
230 FORMAT (//' *** Error in GETNP ***'/)
240 FORMAT (//' *** Error in NEARND ***'/)
250 FORMAT (//' *** Error in DELARC: IER = ',i1, ' ***'/)
260 FORMAT (//' *** Error in DELNOD: IER = ',i1, ' ***'/)
270 FORMAT (//' *** Error in TRPLOT: IER = ',i1, ' ***'/)
! Informative message formats:
400 FORMAT (///t23, 'TRIPACK Test: N =', i5///)
410 FORMAT (' Maximum triangle aspect ratio = ', e10.3//)
420 FORMAT (/' Output from BNODES and AREAP'// &
' BNODES: ', i4, ' boundary nodes, ', i5, ' edges, ', i5, &
' triangles'/ &
' AREAP: area of convex hull = ', e15.8//)
430 FORMAT (' Subroutine EDGE not tested:'/ &
' No edges were swapped by ADDCST'//)
440 FORMAT (' Subroutine DELARC not tested:'/ &
' Nodes 1 and 2 do not form a ', 'removable boundary edge.'//)
450 FORMAT (' Subroutine DELNOD not tested:'/ &
' N cannot be reduced below 3'//)
460 FORMAT (' No triangulation errors encountered.'/)
470 FORMAT (/' A triangulation plot file was ', 'successfully created.'/)
CONTAINS
SUBROUTINE trmtst (n,x,y,list,lptr,lend,lnew,tol, lun, armax,ier)
INTEGER, INTENT(IN) :: n
REAL, INTENT(IN) :: x(:)
REAL, INTENT(IN) :: y(:)
INTEGER, INTENT(IN) :: list(:)
INTEGER, INTENT(IN) :: lptr(:)
INTEGER, INTENT(IN) :: lend(:)
INTEGER, INTENT(IN) :: lnew
REAL, INTENT(IN) :: tol
INTEGER, INTENT(IN) :: lun
REAL, INTENT(OUT) :: armax
INTEGER, INTENT(OUT) :: ier
!***********************************************************
! From TRPTEST
! Robert J. Renka
! Dept. of Computer Science
! Univ. of North Texas
! (817) 565-2767
! 09/01/91
! This subroutine tests the validity of the data structure representing a
! Delaunay triangulation created by subroutine TRMESH. The following
! properties are tested:
! 1) Each interior node has at least three neighbors, and
! each boundary node has at least two neighbors.
! 2) abs(LIST(LP)) is a valid nodal index in the range 1 to N and
! LIST(LP) > 0 unless LP = LEND(K) for some nodal index K.
! 3) Each pointer LEND(K) for K = 1 to N and LPTR(LP) for
! LP = 1 to LNEW-1 is a valid LIST index in the range 1 to LNEW-1.
! 4) N .GE. NB .GE. 3, NT = 2*N-NB-2, and NA = 3*N-NB-3 = (LNEW-1)/2,
! where NB, NT, and NA are the numbers of boundary nodes,
! triangles, and arcs, respectively.
! 5) Each circumcircle defined by the vertices of a triangle contains no
! nodes in its interior. This property distinguishes a Delaunay
! triangulation from an arbitrary triangulation of the nodes.
! Note that no test is made for the property that a triangulation covers
! the convex hull of the nodes.
! On input:
! N = Number of nodes. N >= 3.
! X,Y = Arrays of length N containing the nodal coordinates.
! LIST,LPTR,LEND = Data structure containing the triangulation.
! Refer to subroutine TRMESH.
! TOL = Nonnegative tolerance to allow for floating-point errors in the
! circumcircle test. An error situation is defined as
! (R**2 - D**2)/R**2 > TOL, where R is the radius of a
! circumcircle and D is the distance from the circumcenter to the
! nearest node. A reasonable value for TOL is 10*EPS, where EPS
! is the machine precision. The test is effectively bypassed by
! making TOL large. If TOL < 0, the tolerance is taken to be 0.
! LUN = Logical unit number for printing error messages.
! If LUN < 0 or LUN > 99, no messages are printed.
! Input parameters are not altered by this routine.
! On output:
! ARMAX = Maximum aspect ratio (radius of inscribed circle divided by
! circumradius) of a triangle in the triangulation unless
! IER > 0.
! IER = Error indicator:
! IER = -1 if one or more null triangles (area = 0) are present
! but no (other) errors were encountered. A null
! triangle is an error only if it occurs in the the
! interior.
! IER = 0 if no errors or null triangles were encountered.
! IER = 1 if a node has too few neighbors.
! IER = 2 if a LIST entry is outside its valid range.
! IER = 3 if a LPTR or LEND entry is outside its valid range.
! IER = 4 if the triangulation parameters (N, NB, NT, NA, and
! LNEW) are inconsistent (or N < 3 or LNEW is invalid).
! IER = 5 if a triangle contains a node interior to its
! circumcircle.
! Module required by TRMTST: CIRCUM
! Intrinsic function called by TRMTST: MAX, ABS
!***********************************************************
INTEGER :: k, lp, lpl, lpmax, lpn, n1, n2, n3, na, nb, &
nfail, nn, nnb, nt, null
LOGICAL :: ratio, rite
REAL :: ar, cr, cx, cy, rs, rtol, sa
! Store local variables, test for errors in input, and initialize counts.
nn = n
lpmax = lnew - 1
rtol = tol
IF (rtol < 0.) rtol = 0.
ratio = .true.
armax = 0.
rite = lun >= 0 .AND. lun <= 99
IF (nn < 3) GO TO 14
nb = 0
nt = 0
null = 0
nfail = 0
! Loop on triangles (N1,N2,N3) such that N2 and N3 index adjacent neighbors of
! N1 and are both larger than N1 (each triangle is associated with its
! smallest index).
! NNB is the neighbor count for N1.
DO n1 = 1,nn
nnb = 0
lpl = lend(n1)
IF (lpl < 1 .OR. lpl > lpmax) THEN
lp = lpl
GO TO 13
END IF
lp = lpl
! Loop on neighbors of N1.
1 lp = lptr(lp)
nnb = nnb + 1
IF (lp < 1 .OR. lp > lpmax) GO TO 13
n2 = list(lp)
IF (n2 < 0) THEN
IF (lp /= lpl) GO TO 12
IF (n2 == 0 .OR. -n2 > nn) GO TO 12
nb = nb + 1
GO TO 4
END IF
IF (n2 < 1 .OR. n2 > nn) GO TO 12
lpn = lptr(lp)
n3 = ABS(list(lpn))
IF (n2 < n1 .OR. n3 < n1) GO TO 4
nt = nt + 1
! Compute the coordinates of the circumcenter of (N1,N2,N3).
CALL circum (x(n1),y(n1),x(n2),y(n2),x(n3),y(n3), ratio, cx,cy,cr,sa,ar)
IF (sa == 0.) THEN
null = null + 1
GO TO 4
END IF
armax = MAX(armax,ar)
! Test for nodes within the circumcircle.
rs = cr*cr*(1.-rtol)
DO k = 1,nn
IF (k == n1 .OR. k == n2 .OR. k == n3) CYCLE
IF ((cx-x(k))**2 + (cy-y(k))**2 < rs) GO TO 3
END DO
GO TO 4
! Node K is interior to the circumcircle of (N1,N2,N3).
3 nfail = nfail + 1
! Bottom of loop on neighbors.
4 IF (lp /= lpl) GO TO 1
IF (nnb < 2 .OR. (nnb == 2 .AND. list(lpl) > 0)) GO TO 11
END DO
! Test parameters for consistency and check for NFAIL = 0.
na = lpmax/2
IF (nb < 3 .OR. nt /= 2*nn-nb-2 .OR. na /= 3*nn-nb-3) GO TO 14
IF (nfail /= 0) GO TO 15
! No errors were encountered.
ier = 0
IF (null == 0) RETURN
ier = -1
IF (rite) WRITE (lun,100) null
100 FORMAT (//' *** TRMTST -- ',i5,' NULL TRIANGLES ARE PRESENT'/ &
t20, '(NULL TRIANGLES ON THE BOUNDARY ARE UNAVOIDABLE) ***'//)
RETURN
! Node N1 has fewer than three neighbors.
11 ier = 1
IF (rite) WRITE (lun,110) n1, nnb
110 FORMAT (//' *** TRMTST -- NODE ',i5, ' HAS ONLY ',i5,' NEIGHBORS ***'/)
RETURN
! N2 = LIST(LP) is outside its valid range.
12 ier = 2
IF (rite) WRITE (lun,120) n2, lp, n1
120 FORMAT (//' *** TRMTST -- LIST(LP) =', i5, ', FOR LP =', i5, ','/ &
t20, 'IS NOT A VALID NEIGHBOR OF ', i5, ' ***'/)
RETURN
! LIST pointer LP is outside its valid range.
13 ier = 3
IF (rite) WRITE (lun,130) lp, lnew, n1
130 FORMAT (//' *** TRMTST -- LP =',i5,' IS NOT IN THE', &
' RANGE 1 TO LNEW-1 FOR LNEW = ',i5/ 19X,'LP POINTS TO A NEIGHBOR OF ',i5, &
' ***'/)
RETURN
! Inconsistent triangulation parameters encountered.
14 ier = 4
IF (rite) WRITE (lun,140) n, lnew, nb, nt, na
140 FORMAT (//' *** TRMTST -- INCONSISTENT PARAMETERS', &
' ***'/19X,'N = ',i5,' NODES',12X,'LNEW =',i5/ &
19X,'NB = ',i5,' BOUNDARY NODES'/ 19X,'NT = ',i5,' TRIANGLES'/ &
19X,'NA = ',i5,' ARCS'/)
RETURN
! Circumcircle test failure.
15 ier = 5
IF (rite) WRITE (lun,150) nfail
150 FORMAT (//' *** TRMTST -- ',i5,' CIRCUMCIRCLES ', &
'CONTAIN NODES IN THEIR INTERIORS ***'/)
RETURN
END SUBROUTINE trmtst
END PROGRAM Test_TriPack
!--------------------------------------------------------------------------
! The output file `RES' follows
TRIPACK Test: N = 12
Maximum triangle aspect ratio = 0.480E+00
Adjacency Sets, N = 12
Node X(Node) Y(Node) Neighbours of Node
1 0.00000 0.00000 2 3 9 4 7 0
2 1.00000 0.00000 8 5 10 3 1 0
3 0.500000 0.150000 10 9 1 2
4 0.150000 0.500000 7 1 9 12
5 0.850000 0.500000 8 11 10 2
6 0.500000 0.850000 8 7 12 11
7 0.00000 1.00000 1 4 12 6 8 0
8 1.00000 1.00000 7 6 11 5 2 0
9 0.350000 0.350000 10 11 12 4 1 3
10 0.650000 0.350000 2 5 11 9 3
11 0.650000 0.650000 12 9 10 5 8 6
12 0.350000 0.650000 9 11 6 7 4
NB = 4 Boundary Nodes NA = 29 Arcs NT = 18 Triangles
NCC = 1 Constraint Curves
9
TRIPACK (TRLIST) Output
Node X(Node) Y(Node)
1 0.000000E+00 0.000000E+00
2 0.100000E+01 0.000000E+00
3 0.500000E+00 0.150000E+00
4 0.150000E+00 0.500000E+00
5 0.850000E+00 0.500000E+00
6 0.500000E+00 0.850000E+00
7 0.000000E+00 0.100000E+01
8 0.100000E+01 0.100000E+01
9 0.350000E+00 0.350000E+00
10 0.650000E+00 0.350000E+00
11 0.650000E+00 0.650000E+00
12 0.350000E+00 0.650000E+00
Triangle Vertices Neighbors Arcs
KT N1 N2 N3 KT1 KT2 KT3 KA1 KA2 KA3
1 1 2 3 7 2 0 8 2 1
2 1 3 9 8 3 1 10 3 2
3 1 9 4 9 4 2 12 5 3
4 1 4 7 10 0 3 13 4 5
5 2 8 5 11 6 0 15 7 6
6 2 5 10 12 7 5 16 9 7
7 2 10 3 8 1 6 11 8 9
8 3 10 9 17 2 7 26 10 11
9 4 9 12 18 10 3 28 14 12
10 4 12 7 14 4 9 19 13 14
11 5 8 11 16 12 5 22 17 15
12 5 11 10 17 6 11 25 16 17
13 6 8 7 0 14 16 18 20 23
14 6 7 12 10 15 13 19 21 20
15 6 12 11 18 16 14 27 24 21
16 6 11 8 11 13 15 22 23 24
17 9 10 11 12 18 8 25 29 26
18 9 11 12 15 9 17 27 28 29
NB = 4 Boundary Nodes NA = 29 Arcs NT = 18 Triangles
NCC = 1 Constraint Curves
17
A triangulation plot file was successfully created.
Output from BNODES and AREAP
BNODES: 4 boundary nodes, 29 edges, 18 triangles
AREAP: area of convex hull = 0.10000000E+01
No triangulation errors encountered.
!--------------------------------------------------------------------------
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