Mercurial > octave
annotate scripts/geometry/delaunayn.m @ 11563:3c6e8aaa9555
Grammarcheck m-files before 3.4 release.
| author | Rik <octave@nomad.inbox5.com> |
|---|---|
| date | Tue, 18 Jan 2011 20:55:01 -0800 |
| parents | fd0a3ac60b0e |
| children | c792872f8942 |
| rev | line source |
|---|---|
| 11523 | 1 ## Copyright (C) 2007-2011 David Bateman |
| 6823 | 2 ## |
| 3 ## This file is part of Octave. | |
| 4 ## | |
| 5 ## Octave is free software; you can redistribute it and/or modify it | |
| 6 ## under the terms of the GNU General Public License as published by | |
| 7016 | 7 ## the Free Software Foundation; either version 3 of the License, or (at |
| 8 ## your option) any later version. | |
| 6823 | 9 ## |
| 10 ## Octave is distributed in the hope that it will be useful, but | |
| 11 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
| 12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| 13 ## General Public License for more details. | |
| 14 ## | |
| 15 ## You should have received a copy of the GNU General Public License | |
| 7016 | 16 ## along with Octave; see the file COPYING. If not, see |
| 17 ## <http://www.gnu.org/licenses/>. | |
| 6823 | 18 |
| 19 ## -*- texinfo -*- | |
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20 ## @deftypefn {Function File} {@var{t} =} delaunayn (@var{p}) |
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21 ## @deftypefnx {Function File} {@var{t} =} delaunayn (@var{p}, @var{opt}) |
| 6823 | 22 ## Form the Delaunay triangulation for a set of points. |
| 23 ## The Delaunay triangulation is a tessellation of the convex hull of the | |
| 24 ## points such that no n-sphere defined by the n-triangles contains | |
| 6826 | 25 ## any other points from the set. |
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26 ## The input matrix @var{p} of size @code{[n, dim]} contains @math{n} |
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27 ## points in a space of dimension dim. The return matrix @var{t} has the |
| 6826 | 28 ## size @code{[m, dim+1]}. It contains for each row a set of indices to |
| 29 ## the points, which describes a simplex of dimension dim. For example, | |
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30 ## a 2-D simplex is a triangle and 3-D simplex is a tetrahedron. |
| 6823 | 31 ## |
| 32 ## Extra options for the underlying Qhull command can be specified by the | |
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33 ## second argument. This argument is a cell array of strings. The default |
| 6823 | 34 ## options depend on the dimension of the input: |
| 35 ## | |
| 36 ## @itemize | |
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37 ## @item 2D and 3D: @var{opt} = @code{@{"Qt", "Qbb", "Qc"@}} |
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38 ## |
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39 ## @item 4D and higher: @var{opt} = @code{@{"Qt", "Qbb", "Qc", "Qz"@}} |
| 6826 | 40 ## @end itemize |
| 6823 | 41 ## |
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42 ## If @var{opt} is [], then the default arguments are used. If @var{opt} |
| 6826 | 43 ## is @code{@{"@w{}"@}}, then none of the default arguments are used by Qhull. |
| 6823 | 44 ## See the Qhull documentation for the available options. |
| 45 ## | |
| 46 ## All options can also be specified as single string, for example | |
| 6826 | 47 ## @code{"Qt Qbb Qc Qz"}. |
| 6823 | 48 ## |
| 49 ## @end deftypefn | |
| 50 | |
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51 function t = delaunayn (p, varargin) |
| 6823 | 52 if (nargin < 1) |
| 6826 | 53 print_usage (); |
| 6823 | 54 endif |
| 55 | |
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56 t = __delaunayn__ (p, varargin{:}); |
| 6823 | 57 |
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58 if (isa (p, "single")) |
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59 myeps = eps ("single"); |
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60 else |
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61 myeps = eps; |
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62 endif |
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63 |
| 6823 | 64 ## Try to remove the zero volume simplices. The volume of the i-th simplex is |
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65 ## given by abs(det(p(t(i,1:end-1),:)-p(t(i,2:end),:)))/prod(1:n) |
| 6823 | 66 ## (reference http://en.wikipedia.org/wiki/Simplex). Any simplex with a |
| 67 ## relative volume less than some arbitrary criteria is rejected. The | |
| 68 ## criteria we use is the volume of the simplex corresponding to an | |
| 69 ## orthogonal simplex is equal edge length all equal to the edge length of | |
| 70 ## the original simplex. If the relative volume is 1e3*eps then the simplex | |
| 71 ## is rejected. Note division of the two volumes means that the factor | |
| 72 ## prod(1:n) is dropped. | |
| 73 idx = []; | |
| 6826 | 74 [nt, n] = size (t); |
| 75 for i = 1:nt | |
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Rik <octave@nomad.inbox5.com>
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76 X = p(t(i,1:end-1),:) - p(t(i,2:end),:); |
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77 if (abs (det (X)) / sqrt (sum (X .^ 2, 2)) < 1e3 * myeps) |
| 6823 | 78 idx = [idx, i]; |
| 79 endif | |
| 80 endfor | |
| 81 t(idx,:) = []; | |
| 82 endfunction |