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geompack2.f90
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geompack2.f90
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function angle ( xa, ya, xb, yb, xc, yc )
!*****************************************************************************80
!
!! ANGLE computes the interior angle at a vertex defined by 3 points.
!
! Discussion:
!
! ANGLE computes the interior angle, in radians, at vertex
! (XB,YB) of the chain formed by the directed edges from
! (XA,YA) to (XB,YB) to (XC,YC). The interior is to the
! left of the two directed edges.
!
! Modified:
!
! 17 July 1999
!
! Author:
!
! Original FORTRAN77 version by Barry Joe.
! FORTRAN90 version by John Burkardt.
!
! Reference:
!
! Barry Joe,
! GEOMPACK - a software package for the generation of meshes
! using geometric algorithms,
! Advances in Engineering Software,
! Volume 13, pages 325-331, 1991.
!
! Parameters:
!
! Input, real ( kind = 8 ) XA, YA, XB, YB, XC, YC, the coordinates of the
! vertices.
!
! Output, real ( kind = 8 ) ANGLE, the interior angle formed by
! the vertex, in radians, between 0 and 2*PI.
!
implicit none
real ( kind = 8 ) angle
real ( kind = 8 ), parameter :: pi = 3.141592653589793D+00
real ( kind = 8 ) t
real ( kind = 8 ) x1
real ( kind = 8 ) x2
real ( kind = 8 ) xa
real ( kind = 8 ) xb
real ( kind = 8 ) xc
real ( kind = 8 ) y1
real ( kind = 8 ) y2
real ( kind = 8 ) ya
real ( kind = 8 ) yb
real ( kind = 8 ) yc
x1 = xa - xb
y1 = ya - yb
x2 = xc - xb
y2 = yc - yb
t = sqrt ( ( x1 * x1 + y1 * y1 ) * ( x2 * x2 + y2 * y2 ) )
if ( t == 0.0D+00 ) then
angle = pi
return
end if
t = ( x1 * x2 + y1 * y2 ) / t
if ( t < -1.0D+00 ) then
t = -1.0D+00
else if ( 1.0D+00 < t ) then
t = 1.0D+00
end if
angle = acos ( t )
if ( x2 * y1 - y2 * x1 < 0.0D+00 ) then
angle = 2.0D+00 * pi - angle
end if
return
end
function areapg ( nvrt, xc, yc )
!*****************************************************************************80
!
!! AREAPG computes twice the signed area of a simple polygon.
!
! Modified:
!
! 13 July 1999
!
! Author:
!
! Original FORTRAN77 version by Barry Joe.
! FORTRAN90 version by John Burkardt.
!
! Reference:
!
! Barry Joe,
! GEOMPACK - a software package for the generation of meshes
! using geometric algorithms,
! Advances in Engineering Software,
! Volume 13, pages 325-331, 1991.
!
! Parameters:
!
! Input, integer ( kind = 4 ) NVRT, the number of vertices on the boundary of
! the polygon. N must be at least 3.
!
! Input, real ( kind = 8 ) XC(NVRT), YC(NVRT), the X and Y coordinates
! of the vertices.
!
! Output, real ( kind = 8 ) AREAPG, twice the signed area of the polygon,
! which will be positive if the vertices were listed in counter clockwise
! order, and negative otherwise.
!
implicit none
integer ( kind = 4 ) nvrt
real ( kind = 8 ) areapg
integer ( kind = 4 ) i
real ( kind = 8 ) sum2
real ( kind = 8 ) xc(nvrt)
real ( kind = 8 ) yc(nvrt)
sum2 = xc(1) * ( yc(2) - yc(nvrt) )
do i = 2, nvrt-1
sum2 = sum2 + xc(i) * ( yc(i+1) - yc(i-1) )
end do
sum2 = sum2 + xc(nvrt) * ( yc(1) - yc(nvrt-1) )
areapg = sum2
return
end
function areatr ( xa, ya, xb, yb, xc, yc )
!*****************************************************************************80
!
!! AREATR computes twice the signed area of a triangle.
!
! Modified:
!
! 12 July 1999
!
! Author:
!
! Original FORTRAN77 version by Barry Joe.
! FORTRAN90 version by John Burkardt.
!
! Reference:
!
! Barry Joe,
! GEOMPACK - a software package for the generation of meshes
! using geometric algorithms,
! Advances in Engineering Software,
! Volume 13, pages 325-331, 1991.
!
! Parameters:
!
! Input, real ( kind = 8 ) XA, YA, XB, YB, XC, YC, the coordinates of the
! vertices.
!
! Output, real ( kind = 8 ) AREATR, twice the signed area of the triangle.
! This will be positive if the vertices are listed in counter clockwise
! order.
!
implicit none
real ( kind = 8 ) areatr
real ( kind = 8 ) xa
real ( kind = 8 ) xb
real ( kind = 8 ) xc
real ( kind = 8 ) ya
real ( kind = 8 ) yb
real ( kind = 8 ) yc
areatr = ( xb - xa ) * ( yc - ya ) - ( xc - xa ) * ( yb - ya )
return
end
subroutine bedgmv ( nvc, npolg, nvert, maxvc, h, vcl, hvl, pvl, vstart, vnum, &
ierror )
!*****************************************************************************80
!
!! BEDGMV generates boundary edge mesh vertices.
!
! Purpose:
!
! Generate mesh vertices on boundary of convex polygons
! of decomposition with spacing determined by H array.
!
! Modified:
!
! 12 July 1999
!
! Author:
!
! Original FORTRAN77 version by Barry Joe.
! FORTRAN90 version by John Burkardt.
!
! Reference:
!
! Barry Joe,
! GEOMPACK - a software package for the generation of meshes
! using geometric algorithms,
! Advances in Engineering Software,
! Volume 13, pages 325-331, 1991.
!
! Parameters:
!
! Input/output, integer ( kind = 4 ) NVC, the number of coordinates or
! positions used in VCL array.
!
! Input, integer ( kind = 4 ) NPOLG, the number of polygons or positions used
! in HVL array.
!
! Input, integer ( kind = 4 ) NVERT, the number of vertices or positions
! used in PVL array.
!
! Input, integer ( kind = 4 ) MAXVC, the maximum size available for
! VCL array.
!
! Input, real ( kind = 8 ) H(1:NPOLG), the spacing of mesh vertices for
! convex polygons.
!
! Input/output, real ( kind = 8 ) VCL(1:2,1:NVC), the vertex coordinate list.
!
! Input, integer ( kind = 4 ) HVL(1:NPOLG, the head vertex list.
!
! Input, integer ( kind = 4 ) PVL(1:4,1:NVERT), the polygon vertex list.
!
! Output, integer ( kind = 4 ) VSTART(1:NVERT), the start location in VCL
! for mesh vertices on each edge in PVL if there are any, else 0.
!
! Output, integer ( kind = 4 ) VNUM(1:NVERT), the number of mesh vertices
! on interior of each edge in PVL; entry is negated if mesh vertices are
! listed in backward order in VCL.
!
! Output, integer ( kind = 4 ) IERROR, is set to 3 on error.
!
implicit none
integer ( kind = 4 ) maxvc
integer ( kind = 4 ) npolg
integer ( kind = 4 ) nvert
real ( kind = 8 ) dx
real ( kind = 8 ) dy
integer ( kind = 4 ), parameter :: edgv = 4
real ( kind = 8 ) h(npolg)
real ( kind = 8 ) hh
integer ( kind = 4 ) hvl(npolg)
integer ( kind = 4 ) i
integer ( kind = 4 ) ia
integer ( kind = 4 ) ierror
integer ( kind = 4 ) j
integer ( kind = 4 ) k
integer ( kind = 4 ) l
real ( kind = 8 ) leng
integer ( kind = 4 ), parameter :: loc = 1
integer ( kind = 4 ) m
integer ( kind = 4 ) nvc
integer ( kind = 4 ), parameter :: polg = 2
integer ( kind = 4 ) pvl(4,nvert)
integer ( kind = 4 ), parameter :: succ = 3
integer ( kind = 4 ) u
integer ( kind = 4 ) v
integer ( kind = 4 ) vstart(nvert)
integer ( kind = 4 ) vnum(nvert)
real ( kind = 8 ) vcl(2,maxvc)
real ( kind = 8 ) x
real ( kind = 8 ) y
ierror = 0
vstart(1:nvert) = -1
do k = 1, npolg
i = hvl(k)
do
j = pvl(succ,i)
if ( vstart(i) == -1 ) then
u = pvl(loc,i)
v = pvl(loc,j)
x = vcl(1,u)
y = vcl(2,u)
leng = sqrt ( ( vcl(1,v) - x )**2 + ( vcl(2,v) - y )**2 )
ia = pvl(edgv,i)
if ( ia <= 0 ) then
hh = h(k)
else
hh = sqrt ( h(k) * h(pvl(polg,ia)) )
end if
if ( hh == 0.0D+00 ) then
write ( *, '(a)' ) ' '
write ( *, '(a)' ) 'BEDGMV - Fatal error!'
write ( *, '(a)' ) ' HH = 0.'
stop
end if
l = int ( leng / hh )
if ( real ( l, kind = 8 ) / real ( 2 * l + 1, kind = 8 ) &
< ( leng / hh ) - real ( l, kind = 8 ) ) then
l = l + 1
end if
if ( l <= 1 ) then
vstart(i) = 0
vnum(i) = 0
else
dx = ( vcl(1,v) - x ) / real ( l, kind = 8 )
dy = ( vcl(2,v) - y ) / real ( l, kind = 8 )
l = l - 1
if ( maxvc < nvc + l ) then
write ( *, '(a)' ) ' '
write ( *, '(a)' ) 'BEDGMV - Fatal error!'
write ( *, '(a)' ) ' MAXVC < NVC + L.'
ierror = 3
return
end if
vstart(i) = nvc + 1
vnum(i) = l
do m = 1, l
x = x + dx
y = y + dy
nvc = nvc + 1
vcl(1,nvc) = x
vcl(2,nvc) = y
end do
end if
if ( 0 < ia ) then
vstart(ia) = vstart(i)
vnum(ia) = -vnum(i)
end if
end if
i = j
if ( i == hvl(k) ) then
exit
end if
end do
end do
return
end
subroutine bnsrt2 ( binexp, n, a, map, bin, iwk )
!*****************************************************************************80
!
!! BNSRT2 bin sorts N points in 2D into increasing bin order.
!
! Purpose:
!
! Use a bin sort to obtain the permutation of N 2D
! double precision points so that points are in increasing bin
! order, where the N points are assigned to about N**BINEXP bins.
!
! Modified:
!
! 12 July 1999
!
! Author:
!
! Original FORTRAN77 version by Barry Joe.
! FORTRAN90 version by John Burkardt.
!
! Reference:
!
! Barry Joe,
! GEOMPACK - a software package for the generation of meshes
! using geometric algorithms,
! Advances in Engineering Software,
! Volume 13, pages 325-331, 1991.
!
! Parameters:
!
! Input, integer ( kind = 4 ) BINEXP, the exponent for the number of bins.
!
! Input, integer ( kind = 4 ) N, the number of points.
!
! Input, real ( kind = 8 ) A(2,*), the points to be binned.
!
! Input/output, integer ( kind = 4 ) MAP(N); on input, the points of A with
! indices MAP(1), MAP(2), ..., MAP(N) are to be sorted. On output, MAP has
! been permuted so bin of MAP(1) <= bin of MAP(2) <= ... <= bin of MAP(N).
!
! Workspace, integer BIN(N), used for bin numbers and permutation of 1 to N.
!
! Workspace, integer IWK(N), used for copy of MAP array.
!
implicit none
integer ( kind = 4 ) n
real ( kind = 8 ) a(2,*)
integer ( kind = 4 ) bin(n)
real ( kind = 8 ) binexp
real ( kind = 8 ) dx
real ( kind = 8 ) dy
integer ( kind = 4 ) i
integer ( kind = 4 ) iwk(n)
integer ( kind = 4 ) j
integer ( kind = 4 ) k
integer ( kind = 4 ) l
integer ( kind = 4 ) map(n)
integer ( kind = 4 ) nside
real ( kind = 8 ) xmax
real ( kind = 8 ) xmin
real ( kind = 8 ) ymax
real ( kind = 8 ) ymin
nside = int ( real ( n, kind = 8 )**( binexp / 2.0D+00 ) + 0.5D+00 )
if ( nside <= 1 ) then
return
end if
xmin = a(1,map(1))
ymin = a(2,map(1))
xmax = xmin
ymax = ymin
do i = 2, n
j = map(i)
xmin = min ( xmin, a(1,j) )
xmax = max ( xmax, a(1,j) )
ymin = min ( ymin, a(2,j) )
ymax = max ( ymax, a(2,j) )
end do
dx = 1.0001D+00 * ( xmax - xmin ) / real ( nside, kind = 8 )
dy = 1.0001D+00 * ( ymax - ymin ) / real ( nside, kind = 8 )
if ( dx == 0.0D+00 ) then
dx = 1.0D+00
end if
if ( dy == 0.0D+00 ) then
dy = 1.0D+00
end if
do i = 1, n
j = map(i)
iwk(i) = j
map(i) = i
k = int ( ( a(1,j) - xmin ) / dx )
l = int ( ( a(2,j) - ymin ) / dy )
if ( mod ( k, 2 ) == 0 ) then
bin(i) = k * nside + l
else
bin(i) = ( k + 1 ) * nside - l - 1
end if
end do
call ihpsrt ( 1, n, 1, bin, map )
bin(1:n) = map(1:n)
do i = 1, n
map(i) = iwk(bin(i))
end do
return
end
function cmcirc ( x0, y0, x1, y1, x2, y2, x3, y3 )
!*****************************************************************************80
!
!! CMCIRC determines whether a point lies within a circle through 3 points.
!
! Modified:
!
! 12 July 1999
!
! Author:
!
! Original FORTRAN77 version by Barry Joe.
! FORTRAN90 version by John Burkardt.
!
! Reference:
!
! Barry Joe,
! GEOMPACK - a software package for the generation of meshes
! using geometric algorithms,
! Advances in Engineering Software,
! Volume 13, pages 325-331, 1991.
!
! Parameters:
!
! Input, real ( kind = 8 ) X0, Y0, the coordinates of the point to
! be tested.
!
! Input, real ( kind = 8 ) X1, Y1, X2, Y2, X3, Y3, the coordinates of
! three points that define a circle.
!
! Output, integer ( kind = 4 ) CMCIRC, reports the test results:
! 2, if the three vertices are collinear,
! 1, if (X0,Y0) is inside the circle,
! 0, if (X0,Y0) is on the circle,
! -1, if (X0,Y0) is outside the circle.
!
real ( kind = 8 ) a11
real ( kind = 8 ) a12
real ( kind = 8 ) a21
real ( kind = 8 ) a22
real ( kind = 8 ) b1
real ( kind = 8 ) b2
integer ( kind = 4 ) cmcirc
real ( kind = 8 ) det
real ( kind = 8 ) diff
real ( kind = 8 ) rsq
real ( kind = 8 ) tol
real ( kind = 8 ) tolabs
real ( kind = 8 ) xc
real ( kind = 8 ) yc
real ( kind = 8 ) x0
real ( kind = 8 ) x1
real ( kind = 8 ) x2
real ( kind = 8 ) x3
real ( kind = 8 ) y0
real ( kind = 8 ) y1
real ( kind = 8 ) y2
real ( kind = 8 ) y3
tol = 100.0D+00 * epsilon ( tol )
cmcirc = 2
a11 = x2 - x1
a12 = y2 - y1
a21 = x3 - x1
a22 = y3 - y1
tolabs = tol * max ( abs ( a11), abs ( a12), abs ( a21), abs ( a22) )
det = a11 * a22 - a21 * a12
if ( abs ( det ) <= tolabs ) then
return
end if
b1 = a11 * a11 + a12 * a12
b2 = a21 * a21 + a22 * a22
det = 2.0D+00 * det
xc = ( b1 * a22 - b2 * a12 ) / det
yc = ( b2 * a11 - b1 * a21 ) / det
rsq = xc * xc + yc * yc
diff = ( ( x0 - x1 - xc)**2 + ( y0 - y1 - yc )**2 ) - rsq
tolabs = tol * rsq
if ( diff < - tolabs ) then
cmcirc = 1
else if ( tolabs < diff ) then
cmcirc = -1
else
cmcirc = 0
end if
return
end
subroutine cvdec2 ( angspc, angtol, nvc, npolg, nvert, maxvc, maxhv, &
maxpv, maxiw, maxwk, vcl, regnum, hvl, pvl, iang, iwk, wk, ierror )
!*****************************************************************************80
!
!! CVDEC2 decomposes a polygonal region into convex polygons.
!
! Purpose:
!
! Decompose general polygonal region (which is decomposed
! into simple polygons on input) into convex polygons using
! vertex coordinate list, head vertex list, and polygon vertex
! list data structures.
!
! Modified:
!
! 12 July 1999
!
! Author:
!
! Original FORTRAN77 version by Barry Joe.
! FORTRAN90 version by John Burkardt.
!
! Reference:
!
! Barry Joe,
! GEOMPACK - a software package for the generation of meshes
! using geometric algorithms,
! Advances in Engineering Software,
! Volume 13, pages 325-331, 1991.
!
! Parameters:
!
! Input, real ( kind = 8 ) ANGSPC, the angle spacing parameter in radians
! used in controlling vertices to be considered as an endpoint of a
! separator.
!
! Input, real ( kind = 8 ) ANGTOL, the angle tolerance parameter in radians
! used in accepting separator(s).
!
! Input/output, integer ( kind = 4 ) NVC, the number of vertex coordinates
! or positions used in VCL.
!
! Input/output, integer ( kind = 4 ) NPOLG, the number of polygonal
! subregions or positions used in HVL array.
!
! Input/output, integer ( kind = 4 ) NVERT, the number of polygon vertices
! or positions used in PVL array.
!
! Input, integer ( kind = 4 ) MAXVC, the maximum size available for VCL
! array, should be greater than or equal to the number of vertex coordinates
! required for decomposition.
!
! Input, integer ( kind = 4 ) MAXHV, the maximum size available for HVL,
! REGNUM arrays, should be greater than or equal to the number of polygons
! required for decomposition.
!
! Input, integer ( kind = 4 ) MAXPV, the maximum size available for PVL,
! IANG arrays; should be greater than or equal to the number of polygon
! vertices required for decomposition.
!
! Input, integer ( kind = 4 ) MAXIW, the maximum size available for IWK
! array; should be about 3 times maximum number of vertices in any polygon.
!
! Input, integer ( kind = 4 ) MAXWK, the maximum size available for WK
! array; should be about 5 times maximum number of vertices in any polygon.
!
! Input/output, real ( kind = 8 ) VCL(1:2,1:NVC), the vertex coordinate list.
!
! Input/output, integer ( kind = 4 ) REGNUM(1:NPOLG), region numbers.
!
! Input/output, integer ( kind = 4 ) HVL(1:NPOLG), the head vertex list.
!
! Input/output, integer ( kind = 4 ) PVL(1:4,1:NVERT), real ( kind = 8 )
! IANG(1:NVERT), the polygon vertex list and interior angles; see routine
! DSPGDC for more details. Note that the data structures should be as
! output from routine SPDEC2.
!
! Workspace, integer IWK(1:MAXIW).
!
! Workspace, real ( kind = 8 ) WK(1:MAXWK).
!
! Output, integer ( kind = 4 ) IERROR, error flag. For abnormal return,
! IERROR is set to 3, 4, 5, 6, 7, 206, 207, 208, 209, 210, or 212.
!
integer ( kind = 4 ) maxhv
integer ( kind = 4 ) maxiw
integer ( kind = 4 ) maxpv
integer ( kind = 4 ) maxvc
integer ( kind = 4 ) maxwk
real ( kind = 8 ) angspc
real ( kind = 8 ) angtol
integer ( kind = 4 ) hvl(maxhv)
real ( kind = 8 ) iang(maxpv)
integer ( kind = 4 ) ierror
integer ( kind = 4 ) iwk(maxiw)
integer ( kind = 4 ) npolg
integer ( kind = 4 ) nvc
integer ( kind = 4 ) nvert
real ( kind = 8 ), parameter :: pi = 3.141592653589793D+00
real ( kind = 8 ) piptol
integer ( kind = 4 ) pvl(4,maxpv)
integer ( kind = 4 ) regnum(maxhv)
real ( kind = 8 ) tol
integer ( kind = 4 ) v
real ( kind = 8 ) vcl(2,maxvc)
integer ( kind = 4 ) w1
integer ( kind = 4 ) w2
real ( kind = 8 ) wk(maxwk)
ierror = 0
tol = 100.0D+00 * epsilon ( tol )
!
! For each reflex vertex, resolve it with one or two separators
! and update VCL, HVL, PVL, IANG.
!
piptol = pi + tol
v = 1
do
if ( nvert < v ) then
exit
end if
if ( piptol < iang(v) ) then
call resvrt ( v, angspc, angtol, nvc, nvert, maxvc, maxpv, maxiw, &
maxwk, vcl, pvl, iang, w1, w2, iwk, wk, ierror )
if ( ierror /= 0 ) then
return
end if
call insed2 ( v ,w1, npolg, nvert, maxhv, maxpv, vcl, regnum, hvl, &
pvl, iang, ierror )
if ( ierror /= 0 ) then
return
end if
if ( 0 < w2 ) then
call insed2 ( v, w2, npolg, nvert, maxhv, maxpv, vcl, regnum, hvl, &
pvl, iang, ierror )
end if
if ( ierror /= 0 ) then
return
end if
end if
v = v + 1
end do
return
end
subroutine cvdtri ( inter, ldv, nt, vcl, til, tedg, sptr, ierror )
!*****************************************************************************80
!
!! CVDTRI converts boundary triangles to Delaunay triangles.
!
! Purpose:
!
! Convert triangles in strip near boundary of polygon
! or inside polygon to Delaunay triangles.
!
! Modified:
!
! 12 July 1999
!
! Author:
!
! Original FORTRAN77 version by Barry Joe.
! FORTRAN90 version by John Burkardt.
!
! Reference:
!
! Barry Joe,
! GEOMPACK - a software package for the generation of meshes
! using geometric algorithms,
! Advances in Engineering Software,
! Volume 13, pages 325-331, 1991.
!
! Parameters:
!
! Input, logical INTER, is .TRUE. if and only if there is at least
! one interior mesh vertex.
!
! Input, integer ( kind = 4 ) LDV, the leading dimension of VCL in calling
! routine.
!
! Input, integer ( kind = 4 ) NT, the number of triangles in strip or
! polygon.
!
! Input, VCL(1:2,1:*), the vertex coordinate list.
!
! Input/output, integer ( kind = 4 ) TIL(1:3,1:NT), the triangle incidence
! list.
!
! Input/output, integer ( kind = 4 ) TEDG(1:3,1:NT) - TEDG(J,I) refers to
! edge with vertices TIL(J:J+1,I) and contains index of merge edge or
! a value greater than NT for edge of chains.
!
! Workspace, SPTR(1:NT) - SPTR(I) = -1 if merge edge I is not in LOP stack,
! else greater than or equal to 0 and pointer (index of SPTR) to next
! edge in stack (0 indicates bottom of stack).
!
! Output, integer ( kind = 4 ) IERROR, error flag. On abnormal return:
! IERROR is set to 231.
!
integer ( kind = 4 ) ldv
integer ( kind = 4 ) nt
integer ( kind = 4 ) e
integer ( kind = 4 ) ierror
integer ( kind = 4 ) ind(2)
logical inter
integer ( kind = 4 ) itr(2)
integer ( kind = 4 ) k
integer ( kind = 4 ) mxtr
logical sflag
integer ( kind = 4 ) sptr(nt)
integer ( kind = 4 ) tedg(3,nt)
integer ( kind = 4 ) til(3,nt)
integer ( kind = 4 ) top
real ( kind = 8 ) vcl(ldv,*)
ierror = 0
sflag = .true.
sptr(1:nt) = -1
do k = 1, nt
mxtr = k + 1
if ( k == nt ) then
if ( .not. inter ) then
return
end if
mxtr = nt
sflag = .false.
end if
top = k
sptr(k) = 0
do
e = top
top = sptr(e)
call fndtri ( e, mxtr, sflag, tedg, itr, ind, ierror )
if ( ierror /= 0 ) then
return
end if
call lop ( itr, ind, k, top, ldv, vcl, til, tedg, sptr )
if ( top <= 0 ) then
exit
end if
end do
end do
return
end
subroutine delaunay_print ( num_pts, xc, num_tri, nodtri, tnbr )
!*****************************************************************************80
!
!! DELAUNAY_PRINT prints out information defining a Delaunay triangulation.
!
! Modified:
!
! 08 July 2001
!
! Author:
!
! John Burkardt
!
! Parameters:
!
! Input, integer ( kind = 4 ) NUM_PTS, the number of points.
!
! Input, real ( kind = 8 ) XC(2,NUM_PTS), the point coordinates.
!
! Input, integer ( kind = 4 ) NUM_TRI, the number of triangles.
!
! Input, integer ( kind = 4 ) NODTRI(3,NUM_TRI), the nodes that make up
! the triangles.
!
! Input, integer ( kind = 4 ) TNBR(3,NUM_TRI), the triangle neighbors on
! each side.
!
integer ( kind = 4 ) num_pts
integer ( kind = 4 ) num_tri
integer ( kind = 4 ) i
integer ( kind = 4 ) i4_wrap
integer ( kind = 4 ) j
integer ( kind = 4 ) k
integer ( kind = 4 ) n1
integer ( kind = 4 ) n2
integer ( kind = 4 ) nodtri(3,num_tri)
integer ( kind = 4 ) s
integer ( kind = 4 ) t
integer ( kind = 4 ) tnbr(3,num_tri)
real ( kind = 8 ) xc(2,num_pts)
write ( *, '(a)' ) ' '
write ( *, '(a)' ) 'DELAUNAY_PRINT'
write ( *, '(a)' ) ' Information defining a Delaunay triangulation.'
write ( *, '(a)' ) ' '
write ( *, '(a,i6)' ) ' The number of points is ', num_pts
call r8mat_print ( num_pts, num_pts, 2, transpose ( xc ), &
' Point coordinates (transpose of internal array)' )
write ( *, '(a)' ) ' '
write ( *, '(a,i6)' ) ' The number of triangles is ', num_tri
write ( *, '(a)' ) ' '
write ( *, '(a)' ) ' Sets of three points are used as vertices of'
write ( *, '(a)' ) ' the triangles. For each triangle, the points'
write ( *, '(a)' ) ' are listed in counterclockwise order.'
call i4mat_print ( num_tri, num_tri, 3, transpose ( nodtri ), &
' Nodes that make up triangles (transpose of internal array)' )
write ( *, '(a)' ) ' '
write ( *, '(a)' ) ' On each side of a given triangle, there is either'
write ( *, '(a)' ) ' another triangle, or a piece of the convex hull.'
write ( *, '(a)' ) ' For each triangle, we list the indices of the three'
write ( *, '(a)' ) ' neighbors, or (if negative) the codes of the'
write ( *, '(a)' ) ' segments of the convex hull.'
call i4mat_print ( num_tri, num_tri, 3, transpose ( tnbr ), &
' Indices of neighboring triangles (transpose of internal array)' )
write ( *, '(a)' ) ' '
write ( *, '(a,i6)' ) ' The number of boundary points (and segments) is ', &
2 * num_pts - num_tri - 2
write ( *, '(a)' ) ' '
write ( *, '(a)' ) ' The segments that make up the convex hull can be'
write ( *, '(a)' ) ' determined from the negative entries of the triangle'
write ( *, '(a)' ) ' neighbor list.'
write ( *, '(a)' ) ' '
write ( *, '(a)' ) ' # Tri Side N1 N2'
write ( *, '(a)' ) ' '
k = 0
do i = 1, num_tri
do j = 1, 3
if ( tnbr(j,i) < 0 ) then
s = - tnbr(j,i)
t = s / 3
s = mod ( s, 3 ) + 1
k = k + 1
n1 = nodtri(s,t)
n2 = nodtri(i4_wrap(s+1,1,3),t)
write ( *, '(5i4)' ) k, t, s, n1, n2
end if
end do
end do
return
end
subroutine dhpsrt ( k, n, lda, a, map )
!*****************************************************************************80
!
!! DHPSRT sorts points into lexicographic order using heap sort
!
! Discussion:
!
! This routine uses heapsort to obtain the permutation of N K-dimensional
! points so that the points are in lexicographic increasing order.
!
! Author:
!
! Original FORTRAN77 version by Barry Joe.
! FORTRAN90 version by John Burkardt.
!
! Reference:
!
! Barry Joe,
! GEOMPACK - a software package for the generation of meshes
! using geometric algorithms,
! Advances in Engineering Software,
! Volume 13, pages 325-331, 1991.
!
! Modified:
!
! 19 February 2001
!
! Parameters:
!
! Input, integer ( kind = 4 ) K, the dimension of the points (for instance, 2
! for points in the plane).
!
! Input, integer ( kind = 4 ) N, the number of points.
!
! Input, integer ( kind = 4 ) LDA, the leading dimension of array A in the
! calling routine; LDA should be at least K.
!
! Input, real ( kind = 8 ) A(LDA,N); A(I,J) contains the I-th coordinate
! of point J.
!
! Input/output, integer ( kind = 4 ) MAP(N).
! On input, the points of A with indices MAP(1), MAP(2), ...,
! MAP(N) are to be sorted.
!