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annotate scripts/geometry/delaunayn.m @ 20830:b65888ec820e draft default tip gccjit

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dmalcom gcc jit import
author Stefan Mahr <dac922@gmx.de>
date Fri, 27 Feb 2015 16:59:36 +0100
parents 7503499a252b
children
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1 ## Copyright (C) 2007-2015 David Bateman
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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{T} =} delaunayn (@var{pts})
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21 ## @deftypefnx {Function File} {@var{T} =} delaunayn (@var{pts}, @var{options})
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22 ## Compute the Delaunay triangulation for an N-dimensional set of points.
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23 ##
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24 ## The Delaunay triangulation is a tessellation of the convex hull of a set of
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25 ## points such that no N-sphere defined by the N-triangles contains any other
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26 ## points from the set.
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27 ##
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28 ## The input matrix @var{pts} of size [n, dim] contains n points in a space of
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29 ## dimension dim. The return matrix @var{T} has size [m, dim+1]. Each row of
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30 ## @var{T} contains a set of indices back into the original set of points
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31 ## @var{pts} which describes a simplex of dimension dim. For example, a 2-D
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32 ## simplex is a triangle and 3-D simplex is a tetrahedron.
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33 ##
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34 ## An optional second argument, which must be a string or cell array of strings,
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35 ## contains options passed to the underlying qhull command.
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36 ## See the documentation for the Qhull library for details
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37 ## @url{http://www.qhull.org/html/qh-quick.htm#options}.
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38 ## The default options depend on the dimension of the input:
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39 ##
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40 ## @itemize
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41 ## @item 2-D and 3-D: @var{options} = @code{@{"Qt", "Qbb", "Qc", "Qz"@}}
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42 ##
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43 ## @item 4-D and higher: @var{options} = @code{@{"Qt", "Qbb", "Qc", "Qx"@}}
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44 ## @end itemize
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45 ##
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46 ## If @var{options} is not present or @code{[]} then the default arguments are
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47 ## used. Otherwise, @var{options} replaces the default argument list.
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48 ## To append user options to the defaults it is necessary to repeat the
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49 ## default arguments in @var{options}. Use a null string to pass no arguments.
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50 ##
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51 ## @seealso{delaunay, convhulln, voronoin, trimesh, tetramesh}
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52 ## @end deftypefn
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53
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54 function T = delaunayn (pts, varargin)
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55
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56 if (nargin < 1)
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57 print_usage ();
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58 endif
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59
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60 T = __delaunayn__ (pts, varargin{:});
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61
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62 if (isa (pts, "single"))
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63 tol = 1e3 * eps ("single");
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64 else
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65 tol = 1e3 * eps;
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66 endif
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67
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68 ## Try to remove the zero volume simplices. The volume of the i-th simplex is
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69 ## given by abs(det(pts(T(i,1:end-1),:)-pts(T(i,2:end),:)))/prod(1:n)
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70 ## (reference http://en.wikipedia.org/wiki/Simplex). Any simplex with a
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71 ## relative volume less than some arbitrary criteria is rejected. The
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72 ## criteria we use is the volume of the simplex corresponding to an
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73 ## orthogonal simplex is equal edge length all equal to the edge length of
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74 ## the original simplex. If the relative volume is 1e3*eps then the simplex
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75 ## is rejected. Note division of the two volumes means that the factor
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76 ## prod(1:n) is dropped.
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77 idx = [];
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78 [nt, n] = size (T);
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79 ## FIXME: Vectorize this for loop or convert delaunayn to .oct function
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80 for i = 1:nt
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81 X = pts(T(i,1:end-1),:) - pts(T(i,2:end),:);
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82 if (abs (det (X)) / sqrt (sumsq (X, 2)) < tol)
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83 idx(end+1) = i;
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84 endif
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85 endfor
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86 T(idx,:) = [];
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87
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88 endfunction
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89
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90
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91 %!testif HAVE_QHULL
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92 %! x = [-1, 0; 0, 1; 1, 0; 0, -1; 0, 0];
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93 %! assert (sortrows (sort (delaunayn (x), 2)), [1,2,5;1,4,5;2,3,5;3,4,5]);
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94
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95 ## Test 3-D input
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96 %!testif HAVE_QHULL
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97 %! x = [-1, -1, 1, 0, -1]; y = [-1, 1, 1, 0, -1]; z = [0, 0, 0, 1, 1];
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98 %! assert (sortrows (sort (delaunayn ([x(:) y(:) z(:)]), 2)), [1,2,3,4;1,2,4,5])
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99
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100 ## FIXME: Need tests for delaunayn
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101
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102 ## Input validation tests
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103 %!error delaunayn ()
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104