Mercurial > hg > octave-lyh
annotate scripts/geometry/tsearchn.m @ 13485:59d266f7ed89
Removed plotter tab.
| author | Jacob Dawid <jacob.dawid@googlemail.com> |
|---|---|
| date | Wed, 27 Apr 2011 14:21:28 +0200 |
| parents | d0b799dafede |
| children | 72c96de7a403 |
| rev | line source |
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| 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 -*- | |
| 6846 | 20 ## @deftypefn {Function File} {[@var{idx}, @var{p}] =} tsearchn (@var{x}, @var{t}, @var{xi}) |
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Grammarcheck files for 3.4.1 release.
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21 ## Search for the enclosing Delaunay convex hull. For @code{@var{t} = |
| 6823 | 22 ## delaunayn (@var{x})}, finds the index in @var{t} containing the |
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Grammar check TexInfo in all .m files
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23 ## points @var{xi}. For points outside the convex hull, @var{idx} is NaN. |
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Cleanup documentation for poly.texi, interp.texi, geometry.texi
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24 ## If requested @code{tsearchn} also returns the Barycentric coordinates @var{p} |
| 6823 | 25 ## of the enclosing triangles. |
| 26 ## @seealso{delaunay, delaunayn} | |
| 27 ## @end deftypefn | |
| 28 | |
| 29 function [idx, p] = tsearchn (x, t, xi) | |
| 30 if (nargin != 3) | |
| 31 print_usage (); | |
| 32 endif | |
| 33 | |
| 34 nt = size (t, 1); | |
| 35 [m, n] = size (x); | |
| 36 mi = size (xi, 1); | |
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37 idx = NaN (mi, 1); |
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38 p = NaN (mi, n + 1); |
| 6823 | 39 |
| 40 ni = [1:mi].'; | |
| 41 for i = 1 : nt | |
| 42 ## Only calculate the Barycentric coordinates for points that have not | |
| 43 ## already been found in a triangle. | |
| 44 b = cart2bary (x (t (i, :), :), xi(ni,:)); | |
| 45 | |
| 46 ## Our points xi are in the current triangle if | |
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all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
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47 ## (all(b >= 0) && all (b <= 1)). However as we impose that |
| 6823 | 48 ## sum(b,2) == 1 we only need to test all(b>=0). Note need to add |
| 49 ## a small margin for rounding errors | |
| 50 intri = all (b >= -1e-12, 2); | |
| 51 idx(ni(intri)) = i; | |
| 52 p(ni(intri),:) = b(intri, :); | |
| 53 ni(intri) = []; | |
| 54 endfor | |
| 55 endfunction | |
| 56 | |
| 57 function Beta = cart2bary (T, P) | |
| 58 ## Conversion of Cartesian to Barycentric coordinates. | |
| 59 ## Given a reference simplex in N dimensions represented by a | |
| 60 ## (N+1)-by-(N) matrix, and arbitrary point P in cartesion coordinates, | |
| 61 ## represented by a N-by-1 row vector can be written as | |
| 62 ## | |
| 63 ## P = Beta * T | |
| 64 ## | |
| 65 ## Where Beta is a N+1 vector of the barycentric coordinates. A criteria | |
| 66 ## on Beta is that | |
| 67 ## | |
| 68 ## sum (Beta) == 1 | |
| 69 ## | |
| 70 ## and therefore we can write the above as | |
| 71 ## | |
| 72 ## P - T(end, :) = Beta(1:end-1) * (T(1:end-1,:) - ones(N,1) * T(end,:)) | |
| 73 ## | |
| 74 ## and then we can solve for Beta as | |
| 75 ## | |
| 76 ## Beta(1:end-1) = (P - T(end,:)) / (T(1:end-1,:) - ones(N,1) * T(end,:)) | |
| 77 ## Beta(end) = sum(Beta) | |
| 78 ## | |
| 79 ## Note below is generalize for multiple values of P, one per row. | |
| 80 [M, N] = size (P); | |
| 81 Beta = (P - ones (M,1) * T(end,:)) / (T(1:end-1,:) - ones(N,1) * T(end,:)); | |
| 82 Beta (:,end+1) = 1 - sum(Beta, 2); | |
| 83 endfunction | |
| 84 | |
| 85 %!shared x, tri | |
| 86 %! x = [-1,-1;-1,1;1,-1]; | |
| 87 %! tri = [1, 2, 3]; | |
| 88 %!test | |
| 89 %! [idx, p] = tsearchn (x,tri,[-1,-1]); | |
| 90 %! assert (idx, 1) | |
| 91 %! assert (p, [1,0,0], 1e-12) | |
| 92 %!test | |
| 93 %! [idx, p] = tsearchn (x,tri,[-1,1]); | |
| 94 %! assert (idx, 1) | |
| 95 %! assert (p, [0,1,0], 1e-12) | |
| 96 %!test | |
| 97 %! [idx, p] = tsearchn (x,tri,[1,-1]); | |
| 98 %! assert (idx, 1) | |
| 99 %! assert (p, [0,0,1], 1e-12) | |
| 100 %!test | |
| 101 %! [idx, p] = tsearchn (x,tri,[-1/3,-1/3]); | |
| 102 %! assert (idx, 1) | |
| 103 %! assert (p, [1/3,1/3,1/3], 1e-12) | |
| 104 %!test | |
| 105 %! [idx, p] = tsearchn (x,tri,[1,1]); | |
| 106 %! assert (idx, NaN) | |
| 107 %! assert (p, [NaN, NaN, NaN]) |