geomutilmodule Module Reference

Functions/Subroutines
logical function, public	between (x, a, b)
	Check if a value is between two other values (inclusive). More...
logical function, public	point_in_polygon (x, y, poly)
	Check if a point is within a polygon. More...
integer(i4b) function, public	get_node (ilay, irow, icol, nlay, nrow, ncol)
	Get node number, given layer, row, and column indices for a structured grid. If any argument is invalid return -1. More...
subroutine, public	get_ijk (nodenumber, nrow, ncol, nlay, irow, icol, ilay)
	Get row, column and layer indices from node number and grid dimensions. If nodenumber is invalid, irow, icol, and ilay are -1. More...
subroutine, public	get_jk (nodenumber, ncpl, nlay, icpl, ilay)
	Get layer index and within-layer node index from node number and grid dimensions. If nodenumber is invalid, icpl and ilay are -1. More...
pure real(dp) function, dimension(2), public	skew (v, s, invert)
	Skew a 2D vector along the x-axis. More...
subroutine, public	transform (xin, yin, zin, xout, yout, zout, xorigin, yorigin, zorigin, sinrot, cosrot, invert)
	Apply a 3D translation and optional 2D rotation to coordinates. More...
subroutine, public	compose (xorigin, yorigin, zorigin, sinrot, cosrot, xorigin_new, yorigin_new, zorigin_new, sinrot_new, cosrot_new, invert)
	Apply a 3D translation and 2D rotation to an existing transformation. More...
subroutine	defaults (xorigin, yorigin, zorigin, sinrot, cosrot, invert, translate, rotate, xorigin_opt, yorigin_opt, zorigin_opt, sinrot_opt, cosrot_opt, invert_opt)
	Process arguments and set defaults. Internal use only. More...
real(dp) function, public	area (xv, yv, cw)
	Calculate polygon area, with vertices given in CW or CCW order. More...
subroutine, public	shared_face (iverts1, iverts2, iface)
	Find the lateral face shared by two cells. More...
subroutine, public	clamp_bary (alpha, beta, gamma, pad)
	Clamp barycentric coordinates to the interior of a triangle, with optional padding some minimum distance from any face. More...

Function/Subroutine Documentation

area()

real(dp) function, public geomutilmodule::area	(	real(dp), dimension(:), intent(in)	xv,
		real(dp), dimension(:), intent(in)	yv,
		logical(lgp), intent(in), optional	cw
	)

Definition at line 374 of file GeomUtil.f90.

    ! dummy
    real(DP), dimension(:), intent(in) :: xv
    real(DP), dimension(:), intent(in) :: yv
    logical(LGP), intent(in), optional :: cw
    ! result
    real(DP) :: a
    integer(I4B) :: s
 
    if (present(cw)) then
      if (cw) then
        s = 1
      else
        s = -1
      end if
    else
      s = 1
    end if
 
    a = -dhalf * sum(xv(:) * cshift(yv(:), s) - cshift(xv(:), s) * yv(:))
 

between()

logical function, public geomutilmodule::between	(	real(dp), intent(in)	x,
		real(dp), intent(in)	a,
		real(dp), intent(in)	b
	)

Definition at line 16 of file GeomUtil.f90.

    real(DP), intent(in) :: x, a, b
    between = ((x >= a .and. x <= b) .or. (x <= a .and. x >= b))

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clamp_bary()

subroutine, public geomutilmodule::clamp_bary	(	real(dp), intent(inout)	alpha,
		real(dp), intent(inout)	beta,
		real(dp), intent(out)	gamma,
		real(dp), intent(in), optional	pad
	)

This routine requires 0 <= tol <= 1/3 and 1 = alpha + beta + gamma.

Definition at line 470 of file GeomUtil.f90.

    ! dummy
    real(DP), intent(inout) :: alpha
    real(DP), intent(inout) :: beta
    real(DP), intent(out) :: gamma
    real(DP), intent(in), optional :: pad
    ! local
    real(DP) :: lolimit
    real(DP) :: hilimit
    real(DP) :: delta
    real(DP) :: lpad
 
    if (present(pad)) then
      lpad = pad
      if (pad < dzero .or. pad > donethird) &
        call pstop(1, "pad must be between 0 and 1/3, inclusive")
    else
      lpad = dzero
    end if
 
    gamma = done - alpha - beta
    lolimit = lpad
    hilimit = done - dtwo * lpad
    ! Check alpha coordinate against lower limit
    if (alpha < lolimit) then
      ! Alpha is too low, so nudge alpha to lower limit; this is a move
      ! parallel to the "alpha axis," which also changes gamma
      alpha = lolimit
      gamma = done - alpha - beta
      ! Check beta coordinate against lower limit (which in this
      ! case is equivalent to checking gamma coordinate against
      ! upper limit)
      if (beta < lolimit) then
        ! Beta is too low (gamma is too high), so nudge beta to lower limit;
        ! this is a move parallel to the "beta axis," which also changes gamma
        beta = lolimit
        gamma = hilimit
        ! Check beta coordinate against upper limit (which in this
        ! case is equivalent to checking gamma coordinate against
        ! lower limit)
      else if (beta > hilimit) then
        ! Beta is too high (gamma is too low), so nudge beta to lower limit;
        ! this is a move parallel to the "beta axis," which also changes gamma
        beta = hilimit
        gamma = lolimit
      end if
    end if
    ! Check beta coordinate against lower limit. (If alpha coordinate
    ! was nudged to lower limit, beta and gamma coordinates have also
    ! been adjusted as necessary to place particle within subcell, and
    ! subsequent checks on beta and gamma will evaluate to false, and
    ! no further adjustments will be made.)
    if (beta < lolimit) then
      ! Beta is too low, so nudge beta to lower limit; this is a move
      ! parallel to the "beta axis," which also changes gamma
      beta = lolimit
      gamma = done - alpha - beta
      ! Check alpha coordinate against lower limit (which in this
      ! case is equivalent to checking gamma coordinate against
      ! upper limit)
      if (alpha < lolimit) then
        ! Alpha is too low (gamma is too high), so nudge alpha to lower limit;
        ! this is a move parallel to the "alpha axis," which also changes gamma
        alpha = lolimit
        gamma = hilimit
        ! Check alpha coordinate against upper limit (which in this
        ! case is equivalent to checking gamma coordinate against
        ! lower limit)
      else if (alpha > hilimit) then
        ! Alpha is too high (gamma is too low), so nudge alpha to lower limit;
        ! this is a move parallel to the "alpha axis," which also changes gamma
        alpha = hilimit
        gamma = lolimit
      end if
    end if
    ! Check gamma coordinate against lower limit.(If alpha and/or beta
    ! coordinate was nudged to lower limit, gamma coordinate has also
    ! been adjusted as necessary to place particle within subcell, and
    ! subsequent check on gamma will evaluate to false, and no further
    ! adjustment will be made.)
    if (gamma < lolimit) then
      ! Gamma is too low, so nudge gamma to lower limit; this is a move
      ! parallel to the "gamma axis," which also changes alpha and beta
      delta = dhalf * (lolimit - gamma)
      gamma = lpad
      alpha = alpha - delta
      beta = beta - delta
      ! Check beta coordinate against lower limit (which in this
      ! case is equivalent to checking alpha coordinate against
      ! upper limit)
      if (beta < lolimit) then
        ! Beta is too low (alpha is too high), so nudge beta to lower limit;
        ! this is a move parallel to the "gamma axis," which also changes alpha
        beta = lolimit
        alpha = done - beta - gamma
        ! Check beta coordinate against upper limit (which in this
        ! case is equivalent to checking gamma coordinate against
        ! lower limit)
      else if (beta > hilimit) then
        ! Beta is too high (alpha is too low), so nudge beta to lower limit;
        ! this is a move parallel to the "gamma axis," which also changes alpha
        beta = hilimit
        alpha = done - beta - gamma
      end if
    end if

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compose()

subroutine, public geomutilmodule::compose	(	real(dp)	xorigin,
		real(dp)	yorigin,
		real(dp)	zorigin,
		real(dp)	sinrot,
		real(dp)	cosrot,
		real(dp), optional	xorigin_new,
		real(dp), optional	yorigin_new,
		real(dp), optional	zorigin_new,
		real(dp), optional	sinrot_new,
		real(dp), optional	cosrot_new,
		logical(lgp), optional	invert
	)

Parameters

zorigin	origin coordinates (original)
cosrot	sine and cosine of rotation (original)
zorigin_new	origin coordinates (new)
cosrot_new	sine and cosine of rotation (new)
invert	whether to invert

Definition at line 238 of file GeomUtil.f90.

    ! -- dummy
    real(DP) :: xorigin, yorigin, zorigin !< origin coordinates (original)
    real(DP) :: sinrot, cosrot !< sine and cosine of rotation (original)
    real(DP), optional :: xorigin_new, yorigin_new, zorigin_new !< origin coordinates (new)
    real(DP), optional :: sinrot_new, cosrot_new !< sine and cosine of rotation (new)
    logical(LGP), optional :: invert !< whether to invert
    ! -- local
    logical(LGP) :: ltranslate, lrotate, linvert
    real(DP) :: xorigin_add, yorigin_add, zorigin_add
    real(DP) :: sinrot_add, cosrot_add
    real(DP) :: x0, y0, z0, s0, c0
 
    ! -- Process option arguments and set defaults and flags
    call defaults(xorigin_add, yorigin_add, zorigin_add, &
                  sinrot_add, cosrot_add, linvert, &
                  ltranslate, lrotate, &
                  xorigin_new, yorigin_new, zorigin_new, &
                  sinrot_new, cosrot_new, invert)
 
    ! -- Copy existing transformation into working copy
    x0 = xorigin
    y0 = yorigin
    z0 = zorigin
    s0 = sinrot
    c0 = cosrot
 
    ! -- Modify transformation
    if (.not. linvert) then
      ! -- Apply additional transformation to existing transformation
      if (ltranslate) then
        ! -- Calculate modified origin, XOrigin + R^T XOrigin_add, where
        ! -- XOrigin and XOrigin_add are the existing and additional origin
        ! -- vectors, respectively, and R^T is the transpose of the existing
        ! -- rotation matrix
        call transform(xorigin_add, yorigin_add, zorigin_add, &
                       xorigin, yorigin, zorigin, &
                       x0, y0, z0, s0, c0, .true.)
      end if
      if (lrotate) then
        ! -- Calculate modified rotation matrix (represented by sinrot
        ! -- and cosrot) as R_add R, where R and R_add are the existing
        ! -- and additional rotation matrices, respectively
        sinrot = cosrot_add * s0 + sinrot_add * c0
        cosrot = cosrot_add * c0 - sinrot_add * s0
      end if
    else
      ! -- Apply inverse of additional transformation to existing transformation.
      ! -- Calculate modified origin, R^T (XOrigin + R_add XOrigin_add), where
      ! -- XOrigin and XOrigin_add are the existing and additional origin
      ! -- vectors, respectively, R^T is the transpose of the existing rotation
      ! -- matrix, and R_add is the additional rotation matrix.
      if (lrotate) then
        if (ltranslate) then
          call transform(-xorigin_add, -yorigin_add, zorigin_add, &
                         x0, y0, z0, xorigin, yorigin, zorigin, &
                         -sinrot_add, cosrot_add, .true.)
        end if
        xorigin = c0 * x0 - s0 * y0
        yorigin = s0 * x0 + c0 * y0
        zorigin = z0
      else if (ltranslate) then
        xorigin = x0 - xorigin_add
        yorigin = y0 - yorigin_add
        zorigin = z0 - zorigin_add
      end if
      if (lrotate) then
        ! -- Calculate modified rotation matrix (represented by sinrot
        ! -- and cosrot) as R_add^T R, where R and R_add^T are the existing
        ! -- rotation matrix and the transpose of the additional rotation
        ! -- matrix, respectively
        sinrot = cosrot_add * s0 - sinrot_add * c0
        cosrot = cosrot_add * c0 + sinrot_add * s0
      end if
    end if

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defaults()

subroutine geomutilmodule::defaults ( real(dp)  xorigin, real(dp)  yorigin, real(dp)  zorigin, real(dp)  sinrot, real(dp)  cosrot, logical(lgp)  invert, logical(lgp)  translate, logical(lgp)  rotate, real(dp), optional  xorigin_opt, real(dp), optional  yorigin_opt, real(dp), optional  zorigin_opt, real(dp), optional  sinrot_opt, real(dp), optional  cosrot_opt, logical(lgp), optional  invert_opt  )

private

Definition at line 320 of file GeomUtil.f90.

    ! -- dummy
    real(DP) :: xorigin, yorigin, zorigin
    real(DP) :: sinrot, cosrot
    logical(LGP) :: invert, translate, rotate
    real(DP), optional :: xorigin_opt, yorigin_opt, zorigin_opt
    real(DP), optional :: sinrot_opt, cosrot_opt
    logical(LGP), optional :: invert_opt
 
    translate = .false.
    xorigin = dzero
    if (present(xorigin_opt)) then
      xorigin = xorigin_opt
      translate = .true.
    end if
    yorigin = dzero
    if (present(yorigin_opt)) then
      yorigin = yorigin_opt
      translate = .true.
    end if
    zorigin = dzero
    if (present(zorigin_opt)) then
      zorigin = zorigin_opt
      translate = .true.
    end if
    rotate = .false.
    sinrot = dzero
    cosrot = done
    if (present(sinrot_opt)) then
      sinrot = sinrot_opt
      if (present(cosrot_opt)) then
        cosrot = cosrot_opt
      else
        ! -- If sinrot_opt is specified but cosrot_opt is not,
        ! -- default to corresponding non-negative cosrot_add
        cosrot = dsqrt(done - sinrot * sinrot)
      end if
      rotate = .true.
    else if (present(cosrot_opt)) then
      cosrot = cosrot_opt
      ! -- cosrot_opt is specified but sinrot_opt is not, so
      ! -- default to corresponding non-negative sinrot_add
      sinrot = dsqrt(done - cosrot * cosrot)
      rotate = .true.
    end if
    invert = .false.
    if (present(invert_opt)) invert = invert_opt

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get_ijk()

subroutine, public geomutilmodule::get_ijk	(	integer(i4b), intent(in)	nodenumber,
		integer(i4b), intent(in)	nrow,
		integer(i4b), intent(in)	ncol,
		integer(i4b), intent(in)	nlay,
		integer(i4b), intent(out)	irow,
		integer(i4b), intent(out)	icol,
		integer(i4b), intent(out)	ilay
	)

Definition at line 99 of file GeomUtil.f90.

    ! -- dummy variables
    integer(I4B), intent(in) :: nodenumber
    integer(I4B), intent(in) :: nrow
    integer(I4B), intent(in) :: ncol
    integer(I4B), intent(in) :: nlay
    integer(I4B), intent(out) :: irow
    integer(I4B), intent(out) :: icol
    integer(I4B), intent(out) :: ilay
    ! -- local variables
    integer(I4B) :: nodes
    integer(I4B) :: ij
 
    nodes = nlay * nrow * ncol
    if (nodenumber < 1 .or. nodenumber > nodes) then
      irow = -1
      icol = -1
      ilay = -1
    else
      ilay = (nodenumber - 1) / (ncol * nrow) + 1
      ij = nodenumber - (ilay - 1) * ncol * nrow
      irow = (ij - 1) / ncol + 1
      icol = ij - (irow - 1) * ncol
    end if

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get_jk()

subroutine, public geomutilmodule::get_jk	(	integer(i4b), intent(in)	nodenumber,
		integer(i4b), intent(in)	ncpl,
		integer(i4b), intent(in)	nlay,
		integer(i4b), intent(out)	icpl,
		integer(i4b), intent(out)	ilay
	)

Definition at line 127 of file GeomUtil.f90.

    ! -- dummy variables
    integer(I4B), intent(in) :: nodenumber
    integer(I4B), intent(in) :: ncpl
    integer(I4B), intent(in) :: nlay
    integer(I4B), intent(out) :: icpl
    integer(I4B), intent(out) :: ilay
    ! -- local variables
    integer(I4B) :: nodes
 
    nodes = ncpl * nlay
    if (nodenumber < 1 .or. nodenumber > nodes) then
      icpl = -1
      ilay = -1
    else
      ilay = (nodenumber - 1) / ncpl + 1
      icpl = nodenumber - (ilay - 1) * ncpl
    end if

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get_node()

integer(i4b) function, public geomutilmodule::get_node	(	integer(i4b), intent(in)	ilay,
		integer(i4b), intent(in)	irow,
		integer(i4b), intent(in)	icol,
		integer(i4b), intent(in)	nlay,
		integer(i4b), intent(in)	nrow,
		integer(i4b), intent(in)	ncol
	)

Definition at line 82 of file GeomUtil.f90.

    integer(I4B), intent(in) :: ilay, irow, icol, nlay, nrow, ncol
    integer(I4B) :: get_node
 
    if (nlay > 0 .and. nrow > 0 .and. ncol > 0 .and. &
        ilay > 0 .and. ilay <= nlay .and. &
        irow > 0 .and. irow <= nrow .and. &
        icol > 0 .and. icol <= ncol) then
      get_node = &
        icol + ncol * (irow - 1) + (ilay - 1) * nrow * ncol
    else
      get_node = -1
    end if

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point_in_polygon()

logical function, public geomutilmodule::point_in_polygon	(	real(dp), intent(in)	x,
		real(dp), intent(in)	y,
		real(dp), dimension(:, :), intent(in), allocatable	poly
	)

Vertices and edge points are considered in the polygon. Adapted from https://stackoverflow.com/a/63436180/6514033,

Parameters

[in]	x	x point coordinate
[in]	y	y point coordinate
[in]	poly	polygon vertices (column-major indexing)

Definition at line 26 of file GeomUtil.f90.

    ! dummy
    real(DP), intent(in) :: x !< x point coordinate
    real(DP), intent(in) :: y !< y point coordinate
    real(DP), allocatable, intent(in) :: poly(:, :) !< polygon vertices (column-major indexing)
    ! local
    integer(I4B) :: i, ii, num_verts
    real(DP) :: xa, xb, ya, yb, c = 0.0_dp
 
    point_in_polygon = .false.
    num_verts = size(poly, 2)
    xa = poly(1, num_verts)
    ya = poly(2, num_verts)
 
    do i = 0, num_verts - 1
      ii = mod(i, num_verts) + 1
      xb = poly(1, ii)
      yb = poly(2, ii)
 
      if ((x == xa .and. y == ya) .or. &
          (x == xb .and. y == yb)) then
        ! on vertex
        point_in_polygon = .true.
        exit
      else if (ya == yb .and. &
               y == ya .and. &
               between(x, xa, xb)) then
        ! on horizontal edge
        point_in_polygon = .true.
        exit
      else if (between(y, ya, yb)) then
        if ((y == ya .and. yb >= ya) .or. &
            (y == yb .and. ya >= yb)) then
          xa = xb
          ya = yb
          cycle
        end if
        ! cross product
        c = (xa - x) * (yb - y) - (xb - x) * (ya - y)
        if (c == 0.0_dp) then
          ! on edge
          point_in_polygon = .true.
          exit
        else if ((ya < yb) .eqv. (c > 0)) then
          ! ray intersection
          point_in_polygon = .not. point_in_polygon
        end if
      end if
 
      xa = xb
      ya = yb
    end do

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shared_face()

subroutine, public geomutilmodule::shared_face	(	integer(i4b), dimension(:)	iverts1,
		integer(i4b), dimension(:)	iverts2,
		integer(i4b), intent(out)	iface
	)

Find the lateral (x-y plane) face shared by the given cells. The iface return argument will be 0 if they share no such face, otherwise the index of the shared face in cell 1's vertex array, where face N connects vertex N to vertex N + 1 going clockwise.

Note: assumes the cells are convex and share at most 2 vertices and that both vertex arrays are oriented clockwise.

Definition at line 407 of file GeomUtil.f90.

    integer(I4B), dimension(:) :: iverts1
    integer(I4B), dimension(:) :: iverts2
    integer(I4B), intent(out) :: iface
    integer(I4B) :: nv1
    integer(I4B) :: nv2
    integer(I4B) :: il1, iil1
    integer(I4B) :: il2, iil2
    logical(LGP) :: found
    logical(LGP) :: wrapped
 
    iface = 0
    found = .false.
    nv1 = size(iverts1)
    nv2 = size(iverts2)
    wrapped = iverts1(1) == iverts1(nv1)
 
    ! Find a vertex shared by the cells, then check the adjacent faces.
    ! If the cells share a face, it must be one of these. When looking
    ! forward in the 1st cell's vertices, look backwards in the 2nd's,
    ! and vice versa, since a clockwise face in cell 1 must correspond
    ! to a counter-clockwise face in cell 2.
    outerloop: do il1 = 1, nv1 - 1
      do il2 = 1, nv2 - 1
        if (iverts1(il1) == iverts2(il2)) then
 
          iil1 = il1 + 1
          if (il2 == 1) then
            iil2 = nv2
            if (wrapped) iil2 = iil2 - 1
          else
            iil2 = il2 - 1
          end if
          if (iverts1(iil1) == iverts2(iil2)) then
            found = .true.
            iface = il1
            exit outerloop
          end if
 
          iil2 = il2 + 1
          if (il1 == 1) then
            iil1 = nv1
            if (wrapped) iil1 = iil1 - 1
          else
            iil1 = il1 - 1
          end if
          if (iverts1(iil1) == iverts2(iil2)) then
            found = .true.
            iface = iil1
            exit outerloop
          end if
 
        end if
      end do
      if (found) exit
    end do outerloop

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skew()

pure real(dp) function, dimension(2), public geomutilmodule::skew	(	real(dp), dimension(2), intent(in)	v,
		real(dp), dimension(3), intent(in)	s,
		logical(lgp), intent(in), optional	invert
	)

Parameters

[in]	v	vector
[in]	s	skew matrix entries (top left, top right, bottom right)

Definition at line 148 of file GeomUtil.f90.

    ! -- dummy
    real(DP), intent(in) :: v(2) !< vector
    real(DP), intent(in) :: s(3) !< skew matrix entries (top left, top right, bottom right)
    logical(LGP), intent(in), optional :: invert
    real(DP) :: res(2)
    ! -- local
    logical(LGP) :: linvert
    real(DP) :: sxx, sxy, syy
 
    ! -- process optional arguments
    if (present(invert)) then
      linvert = invert
    else
      linvert = .false.
    end if
 
    sxx = s(1)
    sxy = s(2)
    syy = s(3)
    if (.not. linvert) then
      res(1) = sxx * v(1) + sxy * v(2)
      res(2) = syy * v(2)
    else
      res(2) = v(2) / syy
      res(1) = (v(1) - sxy * res(2)) / sxx
    end if

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transform()

subroutine, public geomutilmodule::transform	(	real(dp)	xin,
		real(dp)	yin,
		real(dp)	zin,
		real(dp)	xout,
		real(dp)	yout,
		real(dp)	zout,
		real(dp), optional	xorigin,
		real(dp), optional	yorigin,
		real(dp), optional	zorigin,
		real(dp), optional	sinrot,
		real(dp), optional	cosrot,
		logical(lgp), optional	invert
	)

Parameters

zin	input coordinates
zout	output coordinates
zorigin	origin coordinates
cosrot	sine and cosine of rotation
invert	whether to invert

Definition at line 178 of file GeomUtil.f90.

    ! -- dummy
    real(DP) :: xin, yin, zin !< input coordinates
    real(DP) :: xout, yout, zout !< output coordinates
    real(DP), optional :: xorigin, yorigin, zorigin !< origin coordinates
    real(DP), optional :: sinrot, cosrot !< sine and cosine of rotation
    logical(LGP), optional :: invert !< whether to invert
    ! -- local
    logical(LGP) :: ltranslate, lrotate, linvert
    real(DP) :: x, y
    real(DP) :: lxorigin, lyorigin, lzorigin
    real(DP) :: lsinrot, lcosrot
 
    ! -- Process option arguments and set defaults and flags
    call defaults(lxorigin, lyorigin, lzorigin, &
                  lsinrot, lcosrot, linvert, &
                  ltranslate, lrotate, &
                  xorigin, yorigin, zorigin, &
                  sinrot, cosrot, invert)
 
    ! -- Apply transformation or its inverse
    if (.not. linvert) then
      ! -- Apply transformation to coordinates
      if (ltranslate) then
        xout = xin - lxorigin
        yout = yin - lyorigin
        zout = zin - lzorigin
      else
        xout = lxorigin
        yout = lyorigin
        zout = lzorigin
      end if
      if (lrotate) then
        x = xout
        y = yout
        xout = x * lcosrot + y * lsinrot
        yout = -x * lsinrot + y * lcosrot
      end if
    else
      ! -- Apply inverse of transformation to coordinates
      if (lrotate) then
        x = xin * lcosrot - yin * lsinrot
        y = xin * lsinrot + yin * lcosrot
      else
        x = xin
        y = yin
      end if
      if (ltranslate) then
        xout = x + lxorigin
        yout = y + lyorigin
        zout = zin + lzorigin
      end if
    end if

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