CubeMesh.m

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function Th=CubeMesh(N)
% function Th=CubeMesh(N)
% Initialization of a minimalist 3D Mesh structure for the cube domain
%
% Cube domain is `[0,1]\times[0,1]\times[0,1]` </br>
%  \image html images/CubeMesh.png "figure : CubeMesh function with N=3" 
%
% There are `(N+1)` vertices on each edges and `(N+1)\times(N+1)`vertices on
% each boundary faces.
%
% Parameters:
%  N: integer, number, minus one, of vertices on a edge 
%
% Return values:
%  Th: minimalist mesh structure
%
% Generated fields of Mesh:
%  nq: total number of vertices, also denoted by `\nq`.
%  q: Array of vertices coordinates, `3\times\nq` array. <br/>
%  `{\q}(\il,j)` is the
%  `\il`-th coordinate of the `j`-th vertex, `\il\in\{1,2,3\}` and
%  `j\in\ENS{1}{\nq}`
%  nme: total number of elements, also denoted by `\nme`.
%  me: Connectivity array, `4\times\nme` array. <br/>
%  `\me(\jl,k)` is the storage index of the
%  `\jl`-th  vertex of the `k`-th tetrahedron in the array `\q` of vertices coordinates, `\jl\in\{1,2,3,4\}` and
%       `k\in{\ENS{1}{\nme}}`.
%  volumes: Array of volumes, `1\times\nme array`. volumes(k) is the volume
%         of the k-th tetrahedron.
%
% See also
%  #ComputeVolumesOpt
% Copyright:
%   See \ref license

  L=1;
  h=L/N;t=0:h:L;
  if isOctave()
    assert(~isempty(ver('msh')),'package msh must be installed')
    mesh=msh3m_structured_mesh(t,t,t,1,1:6); % package msh
    me=mesh.t(1:4,:);
    q=mesh.p;
  else
    [x,y,z] = meshgrid(t,t,t);
    q=[x(:) y(:) z(:)];
    tri = delaunayn(q);
    me=tri';
    q=q';
  end
  
  nq=length(q);
  nme=length(me);
  
  V=ComputeVolumesOpt(me,q);
  Th=struct('q',q,'me',me, ...
            'nq',size(q,2), ...
            'nme',size(me,2),...
            'volumes',V);
            
%            'areas',ComputeAreaOpt(q,me),...
%            'lbe',EdgeLengthOpt(be,q));