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1 ## Copyright (C) 1999, 2000, 2007 Kai Habel |
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2 ## |
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3 ## This file is part of Octave. |
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4 ## |
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5 ## Octave is free software; you can redistribute it and/or modify it |
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6 ## under the terms of the GNU General Public License as published by |
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7 ## the Free Software Foundation; either version 3 of the License, or (at |
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8 ## your option) any later version. |
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9 ## |
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10 ## Octave is distributed in the hope that it will be useful, but |
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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13 ## General Public License for more details. |
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14 ## |
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15 ## You should have received a copy of the GNU General Public License |
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16 ## along with Octave; see the file COPYING. If not, see |
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17 ## <http://www.gnu.org/licenses/>. |
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18 |
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19 ## -*- texinfo -*- |
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20 ## @deftypefn {Function File} {@var{tri}=} delaunay (@var{x}, @var{y}) |
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21 ## @deftypefnx {Function File} {@var{tri}=} delaunay (@var{x}, @var{y}, @var{opt}) |
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22 ## The return matrix of size [n, 3] contains a set triangles which are |
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23 ## described by the indices to the data point x and y vector. |
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24 ## The triangulation satisfies the Delaunay circumcircle criterion. |
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25 ## No other data point is in the circumcircle of the defining triangle. |
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26 ## |
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27 ## A third optional argument, which must be a string, contains extra options |
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28 ## passed to the underlying qhull command. See the documentation for the |
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29 ## Qhull library for details. |
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30 ## |
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31 ## @example |
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32 ## @group |
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33 ## x = rand (1, 10); |
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34 ## y = rand (size (x)); |
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35 ## T = delaunay (x, y); |
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36 ## X = [x(T(:,1)); x(T(:,2)); x(T(:,3)); x(T(:,1))]; |
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37 ## Y = [y(T(:,1)); y(T(:,2)); y(T(:,3)); y(T(:,1))]; |
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38 ## axis ([0,1,0,1]); |
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39 ## plot (X, Y, "b", x, y, "r*"); |
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40 ## @end group |
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41 ## @end example |
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42 ## @seealso{voronoi, delaunay3, delaunayn} |
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43 ## @end deftypefn |
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44 |
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45 ## Author: Kai Habel <kai.habel@gmx.de> |
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46 |
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47 function ret = delaunay (x, y, opt) |
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48 |
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49 if (nargin != 2 && nargin != 3) |
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50 print_usage (); |
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51 endif |
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52 |
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53 if (isvector (x) && isvector (y) && length (x) == length (y)) |
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54 if (nargin == 2) |
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55 tri = delaunayn ([x(:), y(:)]); |
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56 elseif (ischar (opt)) |
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57 tri = delaunayn ([x(:), y(:)], opt); |
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58 else |
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59 error ("delaunay: third argument must be a string"); |
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60 endif |
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61 else |
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62 error ("delaunay: first two input arguments must be vectors of same size"); |
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63 endif |
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64 |
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65 if (nargout == 0) |
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66 x = x(:).'; |
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67 y = y(:).'; |
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68 X = [x(tri(:,1)); x(tri(:,2)); x(tri(:,3)); x(tri(:,1))]; |
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69 Y = [y(tri(:,1)); y(tri(:,2)); y(tri(:,3)); y(tri(:,1))]; |
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70 plot(X, Y, 'b', x, y, 'r*'); |
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71 else |
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72 ret = tri; |
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73 endif |
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74 endfunction |
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75 |
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76 %!test |
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77 %! x = [-1, 0, 1, 0, 0]; |
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78 %! y = [0, 1, 0, -1, 0]; |
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79 %! assert (sortrows (sort (delaunay (x, y), 2)), [1,2,5;1,4,5;2,3,5;3,4,5]) |
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80 |
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81 %!demo |
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82 %! rand ('state', 1); |
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83 %! x = rand(1,10); |
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84 %! y = rand(size(x)); |
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85 %! T = delaunay(x,y); |
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86 %! X = [ x(T(:,1)); x(T(:,2)); x(T(:,3)); x(T(:,1)) ]; |
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87 %! Y = [ y(T(:,1)); y(T(:,2)); y(T(:,3)); y(T(:,1)) ]; |
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88 %! axis([0,1,0,1]); |
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89 %! plot(X,Y,'b',x,y,'r*'); |
