/usr/share/octave/packages/general-1.3.4/adresamp2.m is in octave-general 1.3.4-2.
This file is owned by root:root, with mode 0o644.
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##
## This program 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 3 of the License, or (at your option) any later
## version.
##
## This program 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
## this program; if not, see <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @deftypefn{Function File} {[@var{xs}, @var{ys}] =} adresamp2 (@var{x}, @var{y}, @var{n}, @var{eps})
## Perform an adaptive resampling of a planar curve.
## The arrays @var{x} and @var{y} specify x and y coordinates of the points of the curve.
## On return, the same curve is approximated by @var{xs}, @var{ys} that have length @var{n}
## and the angles between successive segments are approximately equal.
## @end deftypefn
## Author : Jaroslav Hajek <highegg@gmail.com>
function [xs, ys] = adresamp2 (x, y, n, eps)
if (! isvector (x) || ! size_equal (x, y) || ! isscalar (n) ...
|| ! isscalar (eps))
print_usage ();
endif
if (rows (x) == 1)
rowvec = true;
x = x.'; y = y.';
else
rowvec = false;
endif
# first differences
dx = diff (x); dy = diff (y);
# arc lengths
ds = hypot (dx, dy);
# derivatives
dx = dx ./ ds;
dy = dy ./ ds;
# second derivatives
d2x = deriv2 (dx, ds);
d2y = deriv2 (dy, ds);
# curvature
k = abs (d2x .* dy - d2y .* dx);
# curvature cut-off
if (eps > 0)
k = max (k, eps*max (k));
endif
# cumulative integrals
s = cumsum ([0; ds]);
t = cumsum ([0; ds .* k]);
# generate sample points
i = linspace (0, t(end), n);
if (! rowvec)
i = i.';
endif
# and resample
xs = interp1 (t, x, i);
ys = interp1 (t, y, i);
endfunction
# calculates second derivatives from first (non-uniform intervals), using local
# quadratic approximations.
function d2x = deriv2 (dx, dt)
n = length (dt);
if (n >= 2)
d2x = diff (dx) ./ (dt(1:n-1) + dt(2:n));
d2x = [2*d2x(1); d2x(1:n-2) + d2x(2:n-1); 2*d2x(n-1)];
else
d2x = zeros (n, 1);
endif
endfunction
%!demo
%! R = 2; r = 3; d = 1.5;
%! th = linspace (0, 2*pi, 1000);
%! x = (R-r) * cos (th) + d*sin ((R-r)/r * th);
%! y = (R-r) * sin (th) + d*cos ((R-r)/r * th);
%! x += 0.3*exp (-(th-0.8*pi).^2);
%! y += 0.4*exp (-(th-0.9*pi).^2);
%!
%! [xs, ys] = adresamp2 (x, y, 40);
%! plot (x, y, "-", xs, ys, "*");
%! title ("adaptive resampling")
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