Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / miscellaneous-1.1.0 / peano_curve.m

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+## Copyright (C) 2009 Javier Enciso <j4r.e4o@gmail.com>
+##
+## 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{x}, @var{y}} peano_curve (@var{n})
+## Creates an iteration of the Peano space-filling curve with @var{n} points. 
+## The argument @var{n} must be of the form @code{3^M}, where @var{m} is an 
+## integer greater than 0.
+## 
+## @example
+## n = 9;
+## [x, y] = peano_curve (n);
+## line (x, y, "linewidth", 4, "color", "red");
+## @end example
+## 
+## @end deftypefn
+
+function [x, y] = peano_curve (n)
+  
+  if (nargin != 1)
+    print_usage ();
+  endif
+  
+  check_power_of_three (n);
+  if (n == 3)
+    x = [0, 0, 0, 1, 1, 1, 2, 2, 2];
+    y = [0, 1, 2, 2, 1, 0, 0, 1, 2];
+  else
+    [x1, y1] = peano_curve (n/3);
+    x2 = n/3 - 1 - x1;
+    x3 = n/3 + x1;
+    x4 = n - n/3 - 1 - x1;
+    x5 = n - n/3 + x1;
+    x6 = n - 1 - x1;
+    y2 = n/3 + y1;
+    y3 = n - n/3 + y1;
+    y4 = n - 1 - y1;
+    y5 = n - n/3 - 1 - y1;
+    y6 = n/3 - 1 - y1;
+    x = [x1, x2, x1, x3, x4, x3, x5, x6, x5];
+    y = [y1, y2, y3, y4, y5, y6, y1, y2, y3];
+  endif
+  
+endfunction
+
+function check_power_of_three (n)
+  if (frac_part (log (n) / log (3)) != 0)
+    error ("peano_curve: input argument must be a power of 3.")
+  endif
+endfunction
+
+function d = frac_part (f)
+  d = f - floor (f);
+endfunction
+
+%!test
+%! n = 3;
+%! expect(1,:) = [0, 0, 0, 1, 1, 1, 2, 2, 2];
+%! expect(2,:) = [0, 1, 2, 2, 1, 0, 0, 1, 2];
+%! [get(1,:), get(2,:)] = peano_curve (n);
+%! if (any(size (expect) != size (get)))
+%!   error ("wrong size: expected %d,%d but got %d,%d", size (expect), size (get));
+%! elseif (any (any (expect!=get)))
+%!   error ("didn't get what was expected.");
+%! endif
+
+%!test
+%! n = 5;
+%!error peano_curve (n);
+
+%!demo
+%! clf
+%! n = 9;
+%! [x, y] = peano_curve (n);
+%! line (x, y, "linewidth", 4, "color", "red");
+%! % --------------------------------------------------------------------
+%! % the figure window shows an iteration of the Peano space-fillig curve 
+%! % with 9 points on each axis.
+
+%!demo
+%! clf
+%! n = 81;
+%! [x, y] = peano_curve (n);
+%! line (x, y, "linewidth", 2, "color", "red");
+%! % --------------------------------------------------------------------
+%! % the figure window shows an iteration of the Peano space-fillig curve 
+%! % with 81 points on each axis.