/usr/share/octave/packages/msh-1.0.10/msh2m_mesh_along_spline.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_mesh_along_spline(@var{xc},@var{yc},@var{Nnx},@var{Nny},@var{sigma})
##
## Generate a structured mesh in a thin layer of size @var{sigma}
## sitting on a natural Catmull-Rom type cubic spline with control
## points @var{xc}, @var{yc}.
##
## If @var{Nnx} and @var{Nny} are scalars, the mesh has @var{Nnx} nodes
## in the direction along the spline and @var{Nny} in the normal
## direction.
##
## If @var{Nnx} and @var{Nny} are vectors they indicate the curvilinear
## coordinates of the mesh nodes.
##
## The returned value @var{mesh} is a PDE-tool like mesh structure.
##
## Be aware that if @var{sigma} is not much smaller than the curvature
## of the line the resulting mesh may be invalid.
##
## @seealso{msh2m_structured_mesh, msh2m_gmsh, msh3m_structured_mesh}
## @end deftypefn
function msh2 = msh2m_mesh_along_spline(xc,yc,Nnx,Nny,sigma)
## Check input
## FIXME: input type not checked for the first 4 arguments
if (nargin != 5) # Number of input parameters
error("msh2m_mesh_along_spline: wrong number of input parameters.");
elseif (!isscalar(sigma))
error("msh2m_mesh_along_spline: sigma must be a valid scalar value.");
endif
## Construct mesh
s = [0:length(xc)-1];
xsPP = catmullrom ( s, xc );
ysPP = catmullrom ( s, yc );
if (length(Nnx)>1)
ss = Nnx(:).';
else
ss = linspace(0,s(end),Nnx);
endif
xs = ppval(xsPP,ss);
ys = ppval(ysPP,ss);
dxsPP = fnder(xsPP,1);
dysPP = fnder(ysPP,1);
nx = -ppval(dysPP,ss)';
ny = ppval(dxsPP,ss)';
nx = nx ./ sqrt(nx.^2+ny.^2);
ny = ny ./ sqrt(nx.^2+ny.^2);
if (length(Nny)>1)
ssy = Nny(:).';
else
ssy = linspace(0,1,Nny);
endif
msh2 = msh2m_structured_mesh([1:length(ss)], ssy, 1, 1:4);
jj = (msh2.p(1,:));
p(1,:) = xs(jj) + sigma*nx(jj)' .* msh2.p(2,:);
p(2,:) = ys(jj) + sigma*ny(jj)' .* msh2.p(2,:);
msh2.p = p;
endfunction
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