/usr/share/octave/packages/msh-1.0.10/msh3m_structured_mesh.m is in octave-msh 1.0.10-1.
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##
## This file is part of:
## MSH - Meshing Software Package for Octave
##
## MSH is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 2 of the License, or
## (at your option) any later version.
##
## MSH is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
## GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with MSH; If not, see <http://www.gnu.org/licenses/>.
##
## author: Carlo de Falco <cdf _AT_ users.sourceforge.net>
## author: Massimiliano Culpo <culpo _AT_ users.sourceforge.net>
## -*- texinfo -*-
## @deftypefn {Function File} {[@var{mesh}]} = @
## msh3m_structured_mesh(@var{x},@var{y},@var{z},@var{region},@var{sides})
##
## Construct a structured tetrahedral 3D mesh on a parallelepipedal
## domain.
##
## @itemize @bullet
## @item @var{x}, @var{y} and @var{z} are the one dimensional mesh
## vector of the corresponding Cartesian axis.
## @item @var{region} is a number identifying the geometrical volume,
## while @var{sides} is a 6 components vector containing the numbers
## used to identify the geometrical face edges.
## @end itemize
##
## The returned value @var{mesh} is a PDE-tool like mesh structure
## composed of the following fields:
## @itemize @minus
## @item @var{p}: matrix with size 3 times number of mesh points.
## @itemize @bullet
## @item 1st row: x-coordinates of the points.
## @item 2nd row: y-coordinates of the points.
## @item 3rd row: z-coordinates of the points.
## @end itemize
## @item @var{e}: matrix with size 10 times number of mesh face edges.
## @itemize @bullet
## @item 1st row: number of the first vertex of the face edge.
## @item 2nd row: number of the second vertex of the face edge.
## @item 3rd row: number of the third vertex of the face edge.
## @item 4th row: set to 0, present for compatibility with MatLab PDE-tool.
## @item 5th row: set to 0, present for compatibility with MatLab PDE-tool.
## @item 6th row: set to 0, present for compatibility with MatLab PDE-tool.
## @item 7th row: set to 0, present for compatibility with MatLab PDE-tool.
## @item 8th row: number of the geometrical volume to the right of the
## face edge.
## @item 9th row: number of the geometrical volume to the left of the
## face edge.
## @item 10th row: number of the geometrical border containing the face
## edge.
## @end itemize
## @item @var{t}: matrix with size 5 times number of mesh elements.
## @itemize @bullet
## @item 1st row: number of the first vertex of the element.
## @item 2nd row: number of the second vertex of the element.
## @item 3rd row: number of the third vertex of the element.
## @item 4th row: number of the fourth vertex of the element.
## @item 5th row: number of the geometrical volume containing the element.
## @end itemize
## @end itemize
##
## @seealso{msh2m_structured_mesh, msh3m_gmsh, msh2m_mesh_along_spline,
## msh3m_join_structured_mesh, msh3m_submesh}
## @end deftypefn
function mesh = msh3m_structured_mesh (x, y, z, region, sides)
## Check input
if (nargin != 5) # Number of input parameters
print_usage ();
elseif !(isvector (x) && isnumeric (x) && ! isscalar (x)
&& isvector (y) && isnumeric (y) && ! isscalar (y)
&& isvector (z) && isnumeric (z) && ! isscalar (z))
error("msh3m_structured_mesh: X, Y, Z must be valid numeric vectors.");
elseif !isscalar(region)
error("msh3m_structured_mesh: REGION must be a valid scalar.");
elseif !(isvector(sides) && (length(sides) == 6))
error("msh3m_structured_mesh: SIDES must be a 6 components vector.");
endif
## Build mesh
## Sort point coordinates
x = sort (x);
y = sort (y);
z = sort (z);
## Compute # of points in each direction
nx = length (x);
ny = length (y);
nz = length (z);
## Generate vertices
[XX, YY, ZZ] = meshgrid (x, y, z);
p = [XX(:), YY(:), ZZ(:)]';
iiv (ny,nx,nz)=0;
iiv(:)=1:nx*ny*nz;
iiv(end,:,:)=[];
iiv(:,end,:)=[];
iiv(:,:,end)=[];
iiv=iiv(:)';
## Generate connections:
n1 = iiv; # bottom faces
n2 = iiv + 1;
n3 = iiv + ny;
n4 = iiv + ny + 1;
N1 = iiv + nx * ny; # top faces
N2 = N1 + 1;
N3 = N1 + ny;
N4 = N3 + 1;
t = [[n1; n3; n2; N2],...
[N1; N2; N3; n3],...
[N1; N2; n3; n1],...
[N2; n3; n2; n4],...
[N3; n3; N2; N4],...
[N4; n3; N2; n4]];
## Generate boundary face list
## left
T = t;
T(:) = p(1, t)' == x(1);
[~, order] = sort (T, 1);
ii = (find(sum(T,1)==3));
order(1,:) = [];
for jj=1:length (ii)
e1(:,jj) = t(order(:,ii(jj)),ii(jj));
endfor
e1(10,:) = sides(1);
## right
T(:) = p(1,t)' == x(end);
[~, order] = sort (T, 1);
ii = (find (sum (T, 1) == 3));
order(1,:) = [];
for jj=1:length (ii)
e2(:,jj) = t(order(:,ii(jj)),ii(jj));
end
e2(10,:) = sides(2);
## front
T(:) = p(2,t)' == y(1);
[~, order] = sort (T, 1);
ii = (find (sum (T, 1) == 3));
order(1,:) = [];
for jj=1:length (ii)
e3(:,jj) = t(order(:,ii(jj)),ii(jj));
endfor
e3(10,:) = sides(3);
## back
T(:) = p(2,t)' == y(end);
[~,order] = sort (T,1);
ii = (find (sum (T,1) == 3));
order(1,:) = [];
for jj=1:length (ii)
e4(:,jj) = t(order(:,ii(jj)),ii(jj));
endfor
e4(10,:) = sides(4);
## bottom
T = t;
T(:) = p(3,t)'==z(1);
[ignore,order] = sort(T,1);
ii = (find (sum (T,1)==3));
order(1,:) = [];
for jj=1:length(ii)
e5(:,jj) = t(order(:,ii(jj)),ii(jj));
endfor
e5(10,:) = sides(5);
## top
T = t;
T(:) = p(3,t)'==z(end);
[ignore,order] = sort(T,1);
ii = (find (sum (T,1) == 3));
order(1,:) = [];
for jj=1:length(ii)
e6(:,jj) = t(order(:,ii(jj)),ii(jj));
endfor
e6(10,:) = sides(6);
## Assemble structure
mesh.e = [e1,e2,e3,e4,e5,e6];
mesh.t = t;
mesh.e (9,:) = region;
mesh.t (5,:) = region;
mesh.p = p;
endfunction
%!test
% x = y = z = linspace (0,1,2)
% [mesh] = msh3m_structured_mesh (x, y, z, 1, 1:6)
% assert = (columns (mesh.p), 8)
% assert = (columns (mesh.t), 6)
% assert = (columns (mesh.e), 12)
%!test
%! x = y = z = linspace (0, 1, 3);
%! mesh = msh3m_structured_mesh (x, y, z, 1, 1:6);
%! assert (columns (mesh.p), 27)
%! assert (columns (mesh.t), 48)
%! assert (columns (mesh.e), 48)
%!test
%! x = y = z = linspace (0,1,4);
%! [mesh] = msh3m_structured_mesh (x, y, z, 1, 1:6);
%! assert (columns (mesh.p), 64)
%! assert (columns (mesh.t), 162)
%! assert (columns (mesh.e), 108)
%!test
%! x = y = z = linspace (0, 1, 1);
%! fail("mesh = msh3m_structured_mesh (x, y, z, 1, 1:6)", "msh3m_structured_mesh: X, Y, Z must be valid numeric vectors.");
%!test
%! x = y = z = eye (2);
%! fail("mesh = msh3m_structured_mesh (x, y, z, 1, 1:6)", "msh3m_structured_mesh: X, Y, Z must be valid numeric vectors.");
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