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+! $Header$
+
+! Take a mask where the boundary has been been marked.
+! Return information about the normals in these locations.
+
+#include "cctk.h"
+#include "cctk_Parameters.h"
+
+#include "maskvalues.h"
+
+subroutine excision_findnormals (ierr, cctkgh, mask, &
+ dirx, diry, dirz, ni, nj, nk)
+
+ implicit none
+
+ DECLARE_CCTK_FUNCTIONS
+ DECLARE_CCTK_PARAMETERS
+
+ ! Arguments
+
+ ! out: zero for success, nonzero for error
+ integer :: ierr
+
+ ! in: pointer to Cactus GH
+ CCTK_POINTER :: cctkgh
+
+ ! in: array sizes for grid functions
+ ! (you can pass in cctk_lsh(:) for these)
+ integer :: ni,nj,nk
+
+ ! in: mask
+ CCTK_REAL :: mask(ni,nj,nk)
+
+ ! out: normal directions to use for interpolation
+ CCTK_REAL :: dirx(ni,nj,nk), diry(ni,nj,nk), dirz(ni,nj,nk)
+
+
+
+ ! distinguish between faces, edges, and corners.
+
+ ! look at the excised points, and distinguish the following cases,
+ ! in this order:
+
+ ! [trivial case]
+ ! 1: if (none)
+ ! case 0: interior
+ ! [box shape cases]
+ ! 2: if (only one corner)
+ ! case I: corner
+ ! 3: if (only points on one edge)
+ ! case II: edge
+ ! 4: if (only points on one face)
+ ! case III: face
+ ! [convex cases]
+ ! 5: if (only points on two adjacent faces)
+ ! case IIa: anti-edge
+ ! 6: if (one points on three adjacent faces)
+ ! case Ia: anti-corner
+ ! [illegal cases]
+ ! error
+
+ logical mask_interior (-1:+1,-1:+1,-1:+1, 1)
+ logical mask_corner (-1:+1,-1:+1,-1:+1, 8)
+ logical mask_edge (-1:+1,-1:+1,-1:+1, 12)
+ logical mask_face (-1:+1,-1:+1,-1:+1, 6)
+ logical mask_antiedge (-1:+1,-1:+1,-1:+1, 12)
+ logical mask_anticorner(-1:+1,-1:+1,-1:+1, 8)
+ integer dir_interior (3, 1), num_interior
+ integer dir_corner (3, 8), num_corner
+ integer dir_edge (3, 12), num_edge
+ integer dir_face (3, 6), num_face
+ integer dir_antiedge (3, 12), num_antiedge
+ integer dir_anticorner (3, 8), num_anticorner
+
+ logical msk(-1:+1,-1:+1,-1:+1)
+
+ integer di,dj,dk
+ integer i,j,k
+ integer n
+ integer dir(3)
+
+ character(1000) message
+
+
+
+ !
+ ! Create templates
+ !
+ num_interior = 0
+ num_corner = 0
+ num_edge = 0
+ num_face = 0
+ num_antiedge = 0
+ num_anticorner = 0
+
+ do dk=-1,+1
+ do dj=-1,+1
+ do di=-1,+1
+
+ select case (count( (/di,dj,dk/) /= 0 ))
+
+ case (0)
+ ! interior (or error, which is not explicitely checked)
+ num_interior = num_interior + 1
+ dir_interior(:,num_interior) = (/di,dj,dk/)
+ do k=-1,+1
+ do j=-1,+1
+ do i=-1,+1
+ mask_interior(i,j,k,num_interior) = &
+ any( (/di,dj,dk/)/=0 &
+ .and. (/i,j,k/)==(/di,dj,dk/) )
+ end do
+ end do
+ end do
+
+ case (1)
+ ! face (or anti-face, which is the same thing)
+ num_face = num_face + 1
+ dir_face(:,num_face) = (/di,dj,dk/)
+ do k=-1,+1
+ do j=-1,+1
+ do i=-1,+1
+ mask_face(i,j,k,num_face) = &
+ any( (/di,dj,dk/)/=0 &
+ .and. (/i,j,k/)==(/di,dj,dk/) )
+ end do
+ end do
+ end do
+
+ case (2)
+ ! edge or anti-edge
+ num_edge = num_edge + 1
+ dir_edge(:,num_edge) = (/di,dj,dk/)
+ do k=-1,+1
+ do j=-1,+1
+ do i=-1,+1
+ mask_edge(i,j,k,num_edge) = &
+ all( (/di,dj,dk/)==0 &
+ .or. (/i,j,k/)==(/di,dj,dk/) )
+ end do
+ end do
+ end do
+
+ num_antiedge = num_antiedge + 1
+ dir_antiedge(:,num_antiedge) = (/di,dj,dk/)
+ do k=-1,+1
+ do j=-1,+1
+ do i=-1,+1
+ mask_antiedge(i,j,k,num_antiedge) = &
+ any( (/di,dj,dk/)/=0 &
+ .and. (/i,j,k/)==(/di,dj,dk/) )
+ end do
+ end do
+ end do
+
+ case (3)
+ ! corner or anti-corner
+ num_corner = num_corner + 1
+ dir_corner(:,num_corner) = (/di,dj,dk/)
+ do k=-1,+1
+ do j=-1,+1
+ do i=-1,+1
+ mask_corner(i,j,k,num_corner) = &
+ all( (/di,dj,dk/)==0 &
+ .or. (/i,j,k/)==(/di,dj,dk/) )
+ end do
+ end do
+ end do
+
+ num_anticorner = num_anticorner + 1
+ dir_anticorner(:,num_anticorner) = (/di,dj,dk/)
+ do k=-1,+1
+ do j=-1,+1
+ do i=-1,+1
+ mask_anticorner(i,j,k,num_anticorner) = &
+ any( (/di,dj,dk/)/=0 &
+ .and. (/i,j,k/)==(/di,dj,dk/) )
+ end do
+ end do
+ end do
+
+ case default
+ call CCTK_WARN (0, "internal error")
+ end select
+
+ end do
+ end do
+ end do
+
+ ! sanity check
+ if ( num_interior /= 1 &
+ .or. num_corner /= 8 &
+ .or. num_edge /= 12 &
+ .or. num_face /= 6 &
+ .or. num_antiedge /= 12 &
+ .or. num_anticorner /= 8 ) then
+ call CCTK_WARN (0, "internal error")
+ end if
+
+
+
+ !
+ ! Calculate normal directions
+ !
+
+ dirx = 0
+ diry = 0
+ dirz = 0
+
+ do k=2,nk-1
+ do j=2,nj-1
+ do i=2,ni-1
+ if (mask(i,j,k)==MASK_BOUNDARY) then
+
+ ! make a snapshot
+ msk = mask(i-1:i+1,j-1:j+1,k-1:k+1) /= 0
+
+ ! for a template to match, all grid points have to be
+ ! either active, or set in the template.
+ search: do
+
+ ! 1: case 0: interior
+ do n=1,num_interior
+ if (all(msk .or. mask_interior(:,:,:,n))) then
+ dir = dir_interior(:,n)
+ exit search
+ end if
+ end do
+
+ ! 2: case I: corner
+ do n=1,num_corner
+ if (all(msk .or. mask_corner(:,:,:,n))) then
+ dir = dir_corner(:,n)
+ exit search
+ end if
+ end do
+
+ ! 3: case II: edge
+ do n=1,num_edge
+ if (all(msk .or. mask_edge(:,:,:,n))) then
+ dir = dir_edge(:,n)
+ exit search
+ end if
+ end do
+
+ ! 4: case III: face
+ do n=1,num_face
+ if (all(msk .or. mask_face(:,:,:,n))) then
+ dir = dir_face(:,n)
+ exit search
+ end if
+ end do
+
+ ! 5: case IIa: anti-edge
+ do n=1,num_antiedge
+ if (all(msk .or. mask_antiedge(:,:,:,n))) then
+ dir = dir_antiedge(:,n)
+ exit search
+ end if
+ end do
+
+ ! 6: case Ia: anticorner
+ do n=1,num_anticorner
+ if (all(msk .or. mask_anticorner(:,:,:,n))) then
+ dir = dir_anticorner(:,n)
+ exit search
+ end if
+ end do
+
+ ! error: unclassified
+ call CCTK_WARN (0, "Mask is not convex")
+
+ end do search
+
+ dir(:) = -dir(:)
+
+ dirx(i,j,k) = dir(1)
+ diry(i,j,k) = dir(2)
+ dirz(i,j,k) = dir(3)
+
+ end if
+
+ end do
+ end do
+ end do
+
+ ! Success
+ ierr = 0
+
+end subroutine excision_findnormals