Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / general-1.3.1 / adresamp2.m

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+## Copyright (C) 2009 VZLU Prague, a.s., Czech Republic
+##
+## 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")