Mercurial > octave
annotate scripts/geometry/delaunayn.m @ 10793:be55736a0783
Grammarcheck the documentation from m-files.
| author | Rik <octave@nomad.inbox5.com> |
|---|---|
| date | Sun, 18 Jul 2010 20:35:16 -0700 |
| parents | 16f53d29049f |
| children | 693e22af08ae |
| rev | line source |
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| 9245 | 1 ## Copyright (C) 2007, 2008, 2009 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}) |
| 6846 | 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. |
| 26 ## The input matrix @var{P} of size @code{[n, dim]} contains @var{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, | |
| 30 ## a 2d simplex is a triangle and 3d 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 ## @item 4D and higher: @var{opt} = @code{@{"Qt", "Qbb", "Qc", "Qz"@}} |
| 6826 | 39 ## @end itemize |
| 6823 | 40 ## |
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41 ## If @var{opt} is [], then the default arguments are used. If @var{opt} |
| 6826 | 42 ## is @code{@{"@w{}"@}}, then none of the default arguments are used by Qhull. |
| 6823 | 43 ## See the Qhull documentation for the available options. |
| 44 ## | |
| 45 ## All options can also be specified as single string, for example | |
| 6826 | 46 ## @code{"Qt Qbb Qc Qz"}. |
| 6823 | 47 ## |
| 48 ## @end deftypefn | |
| 49 | |
| 50 function t = delaunayn (x, varargin) | |
| 51 if (nargin < 1) | |
| 6826 | 52 print_usage (); |
| 6823 | 53 endif |
| 54 | |
| 7208 | 55 t = __delaunayn__ (x, varargin{:}); |
| 6823 | 56 |
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57 if (isa (x, "single")) |
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58 myeps = eps ("single"); |
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59 else |
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60 myeps = eps; |
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61 endif |
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62 |
| 6823 | 63 ## Try to remove the zero volume simplices. The volume of the i-th simplex is |
| 64 ## given by abs(det(x(t(i,1:end-1),:)-x(t(i,2:end),:)))/prod(1:n) | |
| 65 ## (reference http://en.wikipedia.org/wiki/Simplex). Any simplex with a | |
| 66 ## relative volume less than some arbitrary criteria is rejected. The | |
| 67 ## criteria we use is the volume of the simplex corresponding to an | |
| 68 ## orthogonal simplex is equal edge length all equal to the edge length of | |
| 69 ## the original simplex. If the relative volume is 1e3*eps then the simplex | |
| 70 ## is rejected. Note division of the two volumes means that the factor | |
| 71 ## prod(1:n) is dropped. | |
| 72 idx = []; | |
| 6826 | 73 [nt, n] = size (t); |
| 74 for i = 1:nt | |
| 6823 | 75 X = x(t(i,1:end-1),:) - x(t(i,2:end),:); |
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76 if (abs (det (X)) / sqrt (sum (X .^ 2, 2)) < 1e3 * myeps) |
| 6823 | 77 idx = [idx, i]; |
| 78 endif | |
| 79 endfor | |
| 80 t(idx,:) = []; | |
| 81 endfunction |