/usr/share/octave/packages/msh-1.0.10/msh2m_equalize_mesh.m is in octave-msh 1.0.10-5.
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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}]} = @
## msh2m_equalize_mesh(@var{mesh})
##
## Apply a baricentric regularization to equalize the size of triangle
## edges, i.e. move each node to the center of mass of the patch of
## triangles to which it belongs.
##
## May be useful when distorting a mesh.
## Type @code{demo msh2m_equalize_mesh} to see some examples.
##
## @seealso{msh2m_displacement_smoothing}
##
## @end deftypefn
function [msh] = msh2m_equalize_mesh(msh)
## Check input
if nargin != 1 # Number of input parameters
error("msh2m_equalize_mesh: wrong number of input parameters.");
elseif !(isstruct(msh) && isfield(msh,"p") &&
isfield(msh,"t") && isfield(msh,"e"))
error("msh2m_equalize_mesh: first input is not a valid mesh structure.");
endif
## Apply regularization
nel= columns(msh.t);
x = msh.p(1,:)';
y = msh.p(2,:)';
dnodes = unique(msh.e(1:2,:)(:));
varnodes = setdiff([1:columns(msh.p)],dnodes);
Ax = spalloc(length(x),length(x),1);
Ay = spalloc(length(x),length(x),1);
ax = zeros(3,3,nel);
ay = zeros(3,3,nel);
for inode=1:3
giinode(inode,:)=msh.t(inode,:);
for jnode=1:3
ginode(inode,jnode,:)=msh.t(inode,:);
gjnode(inode,jnode,:)=msh.t(jnode,:);
endfor
endfor
for ii=1:3
for jj=ii+1:3
ax(ii,jj,:) = ax(jj,ii,:) = -ones(1,1,nel);
ay(ii,jj,:) = ay(jj,ii,:) = -ones(1,1,nel);
ax(ii,ii,:) -= ax(ii,jj,:);
ax(jj,jj,:) -= ax(ii,jj,:);
ay(ii,ii,:) -= ay(ii,jj,:);
ay(jj,jj,:) -= ay(ii,jj,:);
endfor
endfor
Ax = sparse(ginode(:),gjnode(:),ax(:));
Ay = sparse(ginode(:),gjnode(:),ay(:));
x(varnodes) = Ax(varnodes,varnodes) \ (-Ax(varnodes,dnodes)*x(dnodes));
y(varnodes) = Ay(varnodes,varnodes) \ (-Ay(varnodes,dnodes)*y(dnodes));
msh.p(1,:) = x';
msh.p(2,:) = y';
endfunction
%!demo
%! ### equalize a structured mesh without moving boundary nodes
%! msh = msh2m_structured_mesh(linspace(0,1,10),linspace(0,1,10),1,1:4,"random");
%! dnodes = msh2m_nodes_on_sides(msh,1:4);
%! varnodes = setdiff([1:columns(msh.p)],dnodes);
%! x = msh.p(1,:)';
%! y = msh.p(2,:)';
%! msh = msh2m_equalize_mesh(msh);
%! triplot(msh.t(1:3,:)',msh.p(1,:)',msh.p(2,:)');
%! pause(.01)
%!demo
%! ### distort a mesh on a square equalizing at each step
%! msh = msh2m_structured_mesh(linspace(0,1,10),linspace(0,1,10),1,1:4,"random");
%! dnodes = msh2m_nodes_on_sides(msh,1:4);
%! varnodes = setdiff([1:columns(msh.p)],dnodes);
%! x = msh.p(1,:)';
%! y = msh.p(2,:)';
%! dx = dy = zeros(columns(msh.p),1);
%! dytot = dxtot = -.7*sin(x(dnodes).*y(dnodes)*pi/2);
%! Nsteps = 10;
%! for ii=1:Nsteps
%! dx(dnodes) = dxtot;
%! dy(dnodes) = dytot;
%! [Ax,Ay] = msh2m_displacement_smoothing(msh,1);
%! dx(varnodes) = Ax(varnodes,varnodes) \ ...
%! (-Ax(varnodes,dnodes)*dx(dnodes));
%! dy(varnodes) = Ay(varnodes,varnodes) \ ...
%! (-Ay(varnodes,dnodes)*dy(dnodes));
%! msh.p(1,:) += dx'/Nsteps;
%! msh.p(2,:) += dy'/Nsteps;
%! triplot(msh.t(1:3,:)',msh.p(1,:)',msh.p(2,:)','r');
%! pause(.5)
%! x = msh.p(1,:)';
%! y = msh.p(2,:)';
%! msh = msh2m_equalize_mesh(msh);
%! hold on;triplot(msh.t(1:3,:)',msh.p(1,:)',msh.p(2,:)');hold off
%! pause(.5)
%! endfor
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