/usr/share/octave/packages/msh-1.0.10/msh2m_jiggle_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{newmsh}]} = @
## msh2m_jiggle_mesh(@var{msh},@var{steps})
##
## Equalize the size of triangle edges setting a spring of rest length
## @var{factor}*@var{area} along each edge of the mesh and solving for
## static equilibrium.
##
## The non-linear eqautions of the system obtained are solved via a
## non-linear Gauss-Seidel method. @var{step} is the number of steps of
## the method to be applied.
##
## May be useful when distorting a mesh, type @code{demo
## msh2m_jiggle_mesh} to see some examples.
##
## @seealso{msh2m_displacement_smoothing, msh2m_equalize_mesh}
##
## @end deftypefn
function [msh] = msh2m_jiggle_mesh(msh,steps)
## Check input
if nargin != 2 # Number of input parameters
error("msh2m_jiggle_mesh: wrong number of input parameters.");
elseif !(isstruct(msh) && isfield(msh,"p") &&
isfield(msh,"t") && isfield(msh,"e"))
error("msh2m_jiggle_mesh: first input is not a valid mesh structure.");
elseif !isscalar(steps)
error("msh2m_jiggle_mesh: second argument is not a valid scalar");
endif
## Solve for static equilibrium
nel= columns(msh.t);
nnodes = columns(msh.p);
x = msh.p(1,:)';
y = msh.p(2,:)';
dnodes = unique(msh.e(1:2,:)(:));
vnodes = setdiff(1:nnodes,dnodes);
## Find node neighbours
## FIXME: should this go into msh2m_topological_properties ?
sides = msh2m_topological_properties(msh,"sides");
for inode = 1:nnodes
neig{inode} = (sides(:, sides(1,:) == inode | sides(2,:) == inode))(:);
neig{inode} (neig{inode} == inode) = [];
endfor
for istep = 1:steps
for inode =vnodes
xx = x(neig{inode}) * ones(size(neig{inode}))';
lx = abs ( xx - xx' )(:);
mx = ( xx + xx' )(:)/2;
x(inode) = sum(mx.*lx)/sum(lx);
yy = y(neig{inode}) * ones(size(neig{inode}))';
ly = abs ( yy - yy' )(:);
my = (yy + yy')(:)/2;
y(inode) = sum(my.*ly)/sum(ly);
endfor
endfor
msh.p = [x';y'];
endfunction
%!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,"right");
%! 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 = -.4*sin(x(dnodes).*y(dnodes)*pi/2);
%! Nsteps = 30;
%! 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_jiggle_mesh(msh,10);
%! hold on;
%! triplot(msh.t(1:3,:)',msh.p(1,:)',msh.p(2,:)');
%! hold off;
%! pause(.5)
%! endfor
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