1 ## Copyright (C) 2009 Javier Enciso <j4r.e4o@gmail.com>
3 ## This program is free software; you can redistribute it and/or modify it under
4 ## the terms of the GNU General Public License as published by the Free Software
5 ## Foundation; either version 3 of the License, or (at your option) any later
8 ## This program is distributed in the hope that it will be useful, but WITHOUT
9 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
10 ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
13 ## You should have received a copy of the GNU General Public License along with
14 ## this program; if not, see <http://www.gnu.org/licenses/>.
17 ## @deftypefn {Function file} {@var{x}, @var{y}} peano_curve (@var{n})
18 ## Creates an iteration of the Peano space-filling curve with @var{n} points.
19 ## The argument @var{n} must be of the form @code{3^M}, where @var{m} is an
20 ## integer greater than 0.
24 ## [x, y] = peano_curve (n);
25 ## line (x, y, "linewidth", 4, "color", "red");
30 function [x, y] = peano_curve (n)
36 check_power_of_three (n);
38 x = [0, 0, 0, 1, 1, 1, 2, 2, 2];
39 y = [0, 1, 2, 2, 1, 0, 0, 1, 2];
41 [x1, y1] = peano_curve (n/3);
44 x4 = n - n/3 - 1 - x1;
50 y5 = n - n/3 - 1 - y1;
52 x = [x1, x2, x1, x3, x4, x3, x5, x6, x5];
53 y = [y1, y2, y3, y4, y5, y6, y1, y2, y3];
58 function check_power_of_three (n)
59 if (frac_part (log (n) / log (3)) != 0)
60 error ("peano_curve: input argument must be a power of 3.")
64 function d = frac_part (f)
70 %! expect(1,:) = [0, 0, 0, 1, 1, 1, 2, 2, 2];
71 %! expect(2,:) = [0, 1, 2, 2, 1, 0, 0, 1, 2];
72 %! [get(1,:), get(2,:)] = peano_curve (n);
73 %! if (any(size (expect) != size (get)))
74 %! error ("wrong size: expected %d,%d but got %d,%d", size (expect), size (get));
75 %! elseif (any (any (expect!=get)))
76 %! error ("didn't get what was expected.");
81 %!error peano_curve (n);
86 %! [x, y] = peano_curve (n);
87 %! line (x, y, "linewidth", 4, "color", "red");
88 %! % --------------------------------------------------------------------
89 %! % the figure window shows an iteration of the Peano space-fillig curve
90 %! % with 9 points on each axis.
95 %! [x, y] = peano_curve (n);
96 %! line (x, y, "linewidth", 2, "color", "red");
97 %! % --------------------------------------------------------------------
98 %! % the figure window shows an iteration of the Peano space-fillig curve
99 %! % with 81 points on each axis.