annotate scripts/geometry/griddata.m @ 17281:bc924baa2c4e

doc: Add new @qcode macro for code samples which are quoted. Macro handles options ("on") or properties ("position") more elegantly than @code{"text"}. * doc/interpreter/macros.texi: Add new @qcode macro. * doc/interpreter/tips.txi: Add documentation about @qcode macro. * doc/interpreter/basics.txi, doc/interpreter/container.txi, doc/interpreter/emacs.txi, doc/interpreter/errors.txi, doc/interpreter/eval.txi, doc/interpreter/expr.txi, doc/interpreter/external.txi, doc/interpreter/func.txi, doc/interpreter/grammar.txi, doc/interpreter/image.txi, doc/interpreter/install.txi, doc/interpreter/interp.txi, doc/interpreter/io.txi, doc/interpreter/matrix.txi, doc/interpreter/numbers.txi, doc/interpreter/oop.txi, doc/interpreter/package.txi, doc/interpreter/plot.txi, doc/interpreter/quad.txi, doc/interpreter/sparse.txi, doc/interpreter/strings.txi, doc/interpreter/system.txi, doc/interpreter/vectorize.txi, libinterp/corefcn/balance.cc, libinterp/corefcn/bitfcns.cc, libinterp/corefcn/cellfun.cc, libinterp/corefcn/conv2.cc, libinterp/corefcn/data.cc, libinterp/corefcn/debug.cc, libinterp/corefcn/defaults.cc, libinterp/corefcn/dirfns.cc, libinterp/corefcn/dlmread.cc, libinterp/corefcn/error.cc, libinterp/corefcn/file-io.cc, libinterp/corefcn/find.cc, libinterp/corefcn/gammainc.cc, libinterp/corefcn/graphics.cc, libinterp/corefcn/help.cc, libinterp/corefcn/hex2num.cc, libinterp/corefcn/input.cc, libinterp/corefcn/load-path.cc, libinterp/corefcn/load-save.cc, libinterp/corefcn/ls-oct-ascii.cc, libinterp/corefcn/lu.cc, libinterp/corefcn/luinc.cc, libinterp/corefcn/matrix_type.cc, libinterp/corefcn/oct-hist.cc, libinterp/corefcn/pager.cc, libinterp/corefcn/pr-output.cc, libinterp/corefcn/pt-jit.cc, libinterp/corefcn/qz.cc, libinterp/corefcn/rand.cc, libinterp/corefcn/regexp.cc, libinterp/corefcn/schur.cc, libinterp/corefcn/sighandlers.cc, libinterp/corefcn/sparse.cc, libinterp/corefcn/spparms.cc, libinterp/corefcn/str2double.cc, libinterp/corefcn/svd.cc, libinterp/corefcn/symtab.cc, libinterp/corefcn/syscalls.cc, libinterp/corefcn/toplev.cc, libinterp/corefcn/tril.cc, libinterp/corefcn/typecast.cc, libinterp/corefcn/utils.cc, libinterp/corefcn/variables.cc, libinterp/dldfcn/__init_fltk__.cc, libinterp/dldfcn/chol.cc, libinterp/dldfcn/colamd.cc, libinterp/dldfcn/fftw.cc, libinterp/dldfcn/qr.cc, libinterp/dldfcn/symbfact.cc, libinterp/octave-value/ov-base.cc, libinterp/octave-value/ov-fcn-handle.cc, libinterp/octave-value/ov-fcn-inline.cc, libinterp/octave-value/ov-java.cc, libinterp/octave-value/ov-range.cc, libinterp/octave-value/ov-struct.cc, libinterp/octave-value/ov-usr-fcn.cc, libinterp/parse-tree/oct-parse.in.yy, libinterp/parse-tree/pt-binop.cc, libinterp/parse-tree/pt-eval.cc, libinterp/parse-tree/pt-mat.cc, scripts/@ftp/ftp.m, scripts/deprecated/java_convert_matrix.m, scripts/deprecated/java_debug.m, scripts/deprecated/java_unsigned_conversion.m, scripts/deprecated/shell_cmd.m, scripts/general/dblquad.m, scripts/general/display.m, scripts/general/genvarname.m, scripts/general/idivide.m, scripts/general/interp1.m, scripts/general/interp2.m, scripts/general/interp3.m, scripts/general/interpn.m, scripts/general/isa.m, scripts/general/profexplore.m, scripts/general/profile.m, scripts/general/quadgk.m, scripts/general/randi.m, scripts/general/structfun.m, scripts/general/subsindex.m, scripts/general/triplequad.m, scripts/geometry/griddata.m, scripts/geometry/griddata3.m, scripts/geometry/griddatan.m, scripts/geometry/voronoi.m, scripts/help/help.m, scripts/help/lookfor.m, scripts/image/cmpermute.m, scripts/image/colormap.m, scripts/image/image.m, scripts/image/imagesc.m, scripts/image/imfinfo.m, scripts/image/imformats.m, scripts/image/imread.m, scripts/image/imshow.m, scripts/image/imwrite.m, scripts/image/ind2gray.m, scripts/image/lines.m, scripts/image/rgb2ind.m, scripts/image/spinmap.m, scripts/io/dlmwrite.m, scripts/io/strread.m, scripts/io/textread.m, scripts/io/textscan.m, scripts/java/javaclasspath.m, scripts/java/usejava.m, scripts/miscellaneous/bzip2.m, scripts/miscellaneous/computer.m, scripts/miscellaneous/copyfile.m, scripts/miscellaneous/debug.m, scripts/miscellaneous/dos.m, scripts/miscellaneous/edit.m, scripts/miscellaneous/gzip.m, scripts/miscellaneous/license.m, scripts/miscellaneous/mkoctfile.m, scripts/miscellaneous/movefile.m, scripts/miscellaneous/parseparams.m, scripts/miscellaneous/unix.m, scripts/optimization/fminbnd.m, scripts/optimization/fminsearch.m, scripts/optimization/fminunc.m, scripts/optimization/fsolve.m, scripts/optimization/fzero.m, scripts/optimization/glpk.m, scripts/optimization/lsqnonneg.m, scripts/optimization/optimset.m, scripts/optimization/pqpnonneg.m, scripts/pkg/pkg.m, scripts/plot/allchild.m, scripts/plot/ancestor.m, scripts/plot/area.m, scripts/plot/axis.m, scripts/plot/bar.m, scripts/plot/barh.m, scripts/plot/box.m, scripts/plot/caxis.m, scripts/plot/cla.m, scripts/plot/clabel.m, scripts/plot/clf.m, scripts/plot/close.m, scripts/plot/colorbar.m, scripts/plot/daspect.m, scripts/plot/ezmesh.m, scripts/plot/ezmeshc.m, scripts/plot/ezsurf.m, scripts/plot/ezsurfc.m, scripts/plot/findall.m, scripts/plot/findobj.m, scripts/plot/gcbo.m, scripts/plot/gcf.m, scripts/plot/gco.m, scripts/plot/grid.m, scripts/plot/guihandles.m, scripts/plot/hdl2struct.m, scripts/plot/hidden.m, scripts/plot/hold.m, scripts/plot/isonormals.m, scripts/plot/isosurface.m, scripts/plot/legend.m, scripts/plot/mesh.m, scripts/plot/meshc.m, scripts/plot/meshz.m, scripts/plot/newplot.m, scripts/plot/orient.m, scripts/plot/pareto.m, scripts/plot/patch.m, scripts/plot/pbaspect.m, scripts/plot/pcolor.m, scripts/plot/plot.m, scripts/plot/print.m, scripts/plot/private/__add_default_menu__.m, scripts/plot/quiver.m, scripts/plot/quiver3.m, scripts/plot/refreshdata.m, scripts/plot/saveas.m, scripts/plot/scatter.m, scripts/plot/scatter3.m, scripts/plot/shading.m, scripts/plot/shrinkfaces.m, scripts/plot/slice.m, scripts/plot/stem.m, scripts/plot/stem3.m, scripts/plot/struct2hdl.m, scripts/plot/subplot.m, scripts/plot/surf.m, scripts/plot/surfc.m, scripts/plot/surfl.m, scripts/plot/tetramesh.m, scripts/plot/uigetfile.m, scripts/plot/uimenu.m, scripts/plot/uiputfile.m, scripts/plot/waterfall.m, scripts/plot/whitebg.m, scripts/plot/xlim.m, scripts/plot/ylim.m, scripts/plot/zlim.m, scripts/polynomial/conv.m, scripts/polynomial/polyout.m, scripts/polynomial/splinefit.m, scripts/set/ismember.m, scripts/set/powerset.m, scripts/set/setdiff.m, scripts/set/union.m, scripts/set/unique.m, scripts/signal/detrend.m, scripts/signal/filter2.m, scripts/signal/freqz.m, scripts/signal/periodogram.m, scripts/signal/spectral_adf.m, scripts/signal/spectral_xdf.m, scripts/sparse/eigs.m, scripts/sparse/svds.m, scripts/specfun/legendre.m, scripts/special-matrix/gallery.m, scripts/statistics/base/mean.m, scripts/statistics/base/moment.m, scripts/statistics/tests/cor_test.m, scripts/statistics/tests/kolmogorov_smirnov_test.m, scripts/statistics/tests/kolmogorov_smirnov_test_2.m, scripts/statistics/tests/kruskal_wallis_test.m, scripts/statistics/tests/prop_test_2.m, scripts/statistics/tests/sign_test.m, scripts/statistics/tests/t_test.m, scripts/statistics/tests/t_test_2.m, scripts/statistics/tests/t_test_regression.m, scripts/statistics/tests/u_test.m, scripts/statistics/tests/var_test.m, scripts/statistics/tests/welch_test.m, scripts/statistics/tests/wilcoxon_test.m, scripts/statistics/tests/z_test.m, scripts/statistics/tests/z_test_2.m, scripts/strings/base2dec.m, scripts/strings/index.m, scripts/strings/isstrprop.m, scripts/strings/mat2str.m, scripts/strings/regexptranslate.m, scripts/strings/rindex.m, scripts/strings/str2num.m, scripts/strings/strcat.m, scripts/strings/strjust.m, scripts/strings/strmatch.m, scripts/strings/validatestring.m, scripts/testfun/demo.m, scripts/testfun/example.m, scripts/testfun/test.m, scripts/time/addtodate.m, scripts/time/asctime.m, scripts/time/datestr.m, scripts/time/datetick.m, scripts/time/weekday.m, scripts/ui/errordlg.m, scripts/ui/helpdlg.m, scripts/ui/inputdlg.m, scripts/ui/listdlg.m, scripts/ui/msgbox.m, scripts/ui/questdlg.m, scripts/ui/warndlg.m: Use new @qcode macro.
author Rik <rik@octave.org>
date Mon, 19 Aug 2013 20:46:38 -0700
parents 5d3a684236b0
children d63878346099
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rev   line source
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1 ## Copyright (C) 1999-2012 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{zi} =} griddata (@var{x}, @var{y}, @var{z}, @var{xi}, @var{yi})
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21 ## @deftypefnx {Function File} {@var{zi} =} griddata (@var{x}, @var{y}, @var{z}, @var{xi}, @var{yi}, @var{method})
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22 ## @deftypefnx {Function File} {[@var{xi}, @var{yi}, @var{zi}] =} griddata (@dots{})
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23 ##
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24 ## Generate a regular mesh from irregular data using interpolation.
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25 ## The function is defined by @code{@var{z} = f (@var{x}, @var{y})}.
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26 ## Inputs @code{@var{x}, @var{y}, @var{z}} are vectors of the same length
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27 ## or @code{@var{x}, @var{y}} are vectors and @code{@var{z}} is matrix.
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28 ##
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29 ## The interpolation points are all @code{(@var{xi}, @var{yi})}. If
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30 ## @var{xi}, @var{yi} are vectors then they are made into a 2-D mesh.
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31 ##
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32 ## The interpolation method can be @qcode{"nearest"}, @qcode{"cubic"} or
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33 ## @qcode{"linear"}. If method is omitted it defaults to @qcode{"linear"}.
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34 ## @seealso{griddata3, griddatan, delaunay}
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35 ## @end deftypefn
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36
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37 ## Author: Kai Habel <kai.habel@gmx.de>
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38 ## Adapted-by: Alexander Barth <barth.alexander@gmail.com>
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39 ## xi and yi are not "meshgridded" if both are vectors
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40 ## of the same size (for compatibility)
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41
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42 function [rx, ry, rz] = griddata (x, y, z, xi, yi, method = "linear")
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43
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44 if (nargin < 5 || nargin > 7)
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45 print_usage ();
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46 endif
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47
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48 if (ischar (method))
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49 method = tolower (method);
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50 endif
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51
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52 ## Meshgrid if x and y are vectors but z is matrix
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53 if (isvector (x) && isvector (y) && all ([numel(y), numel(x)] == size (z)))
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54 [x, y] = meshgrid (x, y);
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55 endif
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56
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57 if (isvector (x) && isvector (y) && isvector (z))
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58 if (! isequal (length (x), length (y), length (z)))
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59 error ("griddata: X, Y, and Z must be vectors of the same length");
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60 endif
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61 elseif (! size_equal (x, y, z))
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62 error ("griddata: lengths of X, Y must match the columns and rows of Z");
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63 endif
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64
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65 ## Meshgrid xi and yi if they are a row and column vector.
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66 if (rows (xi) == 1 && columns (yi) == 1)
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67 [xi, yi] = meshgrid (xi, yi);
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68 elseif (isvector (xi) && isvector (yi))
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69 ## Otherwise, convert to column vectors
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70 xi = xi(:);
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71 yi = yi(:);
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72 endif
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73
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74 if (! size_equal (xi, yi))
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75 error ("griddata: XI and YI must be vectors or matrices of same size");
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76 endif
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77
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78 x = x(:);
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79 y = y(:);
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80 z = z(:);
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81
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82 ## Triangulate data.
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83 tri = delaunay (x, y);
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84 zi = NaN (size (xi));
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85
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86 if (strcmp (method, "cubic"))
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87 error ("griddata: cubic interpolation not yet implemented");
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88
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89 elseif (strcmp (method, "nearest"))
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90 ## Search index of nearest point.
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91 idx = dsearch (x, y, tri, xi, yi);
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92 valid = !isnan (idx);
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93 zi(valid) = z(idx(valid));
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94
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95 elseif (strcmp (method, "linear"))
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96 ## Search for every point the enclosing triangle.
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97 tri_list = tsearch (x, y, tri, xi(:), yi(:));
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98
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99 ## Only keep the points within triangles.
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100 valid = !isnan (tri_list);
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101 tri_list = tri_list(valid);
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102 nr_t = rows (tri_list);
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103
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104 tri = tri(tri_list,:);
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105
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106 ## Assign x,y,z for each point of triangle.
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107 x1 = x(tri(:,1));
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108 x2 = x(tri(:,2));
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109 x3 = x(tri(:,3));
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110
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111 y1 = y(tri(:,1));
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112 y2 = y(tri(:,2));
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113 y3 = y(tri(:,3));
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114
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115 z1 = z(tri(:,1));
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116 z2 = z(tri(:,2));
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117 z3 = z(tri(:,3));
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118
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119 ## Calculate norm vector.
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120 N = cross ([x2-x1, y2-y1, z2-z1], [x3-x1, y3-y1, z3-z1]);
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121 ## Normalize.
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122 N = diag (norm (N, "rows")) \ N;
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123
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124 ## Calculate D of plane equation
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125 ## Ax+By+Cz+D = 0;
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126 D = -(N(:,1) .* x1 + N(:,2) .* y1 + N(:,3) .* z1);
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127
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128 ## Calculate zi by solving plane equation for xi, yi.
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129 zi(valid) = -(N(:,1).*xi(:)(valid) + N(:,2).*yi(:)(valid) + D) ./ N(:,3);
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130
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131 else
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132 error ("griddata: unknown interpolation METHOD");
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133 endif
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134
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135 if (nargout == 3)
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136 rx = xi;
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137 ry = yi;
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138 rz = zi;
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139 elseif (nargout == 1)
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140 rx = zi;
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141 elseif (nargout == 0)
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142 mesh (xi, yi, zi);
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143 endif
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144
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145 endfunction
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146
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147
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148 %!demo
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149 %! clf;
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150 %! colormap ("default");
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151 %! x = 2*rand (100,1) - 1;
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152 %! y = 2*rand (size (x)) - 1;
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153 %! z = sin (2*(x.^2 + y.^2));
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154 %! [xx,yy] = meshgrid (linspace (-1,1,32));
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155 %! griddata (x,y,z,xx,yy);
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156 %! title ("nonuniform grid sampled at 100 points");
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157
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158 %!demo
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159 %! clf;
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160 %! colormap ("default");
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161 %! x = 2*rand (1000,1) - 1;
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162 %! y = 2*rand (size (x)) - 1;
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163 %! z = sin (2*(x.^2 + y.^2));
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164 %! [xx,yy] = meshgrid (linspace (-1,1,32));
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165 %! griddata (x,y,z,xx,yy);
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166 %! title ("nonuniform grid sampled at 1000 points");
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167
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168 %!demo
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169 %! clf;
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170 %! colormap ("default");
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171 %! x = 2*rand (1000,1) - 1;
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172 %! y = 2*rand (size (x)) - 1;
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173 %! z = sin (2*(x.^2 + y.^2));
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174 %! [xx,yy] = meshgrid (linspace (-1,1,32));
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175 %! griddata (x,y,z,xx,yy,"nearest");
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176 %! title ("nonuniform grid sampled at 1000 points with nearest neighbor");
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177
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178 %!testif HAVE_QHULL
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179 %! [xx,yy] = meshgrid (linspace (-1,1,32));
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180 %! x = xx(:);
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181 %! x = x + 10*(2*round (rand (size (x))) - 1) * eps;
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182 %! y = yy(:);
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183 %! y = y + 10*(2*round (rand (size (y))) - 1) * eps;
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184 %! z = sin (2*(x.^2 + y.^2));
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185 %! zz = griddata (x,y,z,xx,yy,"linear");
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186 %! zz2 = sin (2*(xx.^2 + yy.^2));
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187 %! zz2(isnan (zz)) = NaN;
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188 %! assert (zz, zz2, 100*eps);
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189
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190 %% Test input validation
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191 %!error griddata ()
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192 %!error griddata (1)
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193 %!error griddata (1,2)
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194 %!error griddata (1,2,3)
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195 %!error griddata (1,2,3,4)
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196 %!error griddata (1,2,3,4,5,6,7)
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197 %!error <vectors of the same length> griddata (1:3, 1:3, 1:4, 1:3, 1:3)
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198 %!error <vectors of the same length> griddata (1:3, 1:4, 1:3, 1:3, 1:3)
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199 %!error <vectors of the same length> griddata (1:4, 1:3, 1:3, 1:3, 1:3)
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Rik <octave@nomad.inbox5.com>
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200 %!error <the columns and rows of Z> griddata (1:4, 1:3, ones (4,4), 1:3, 1:3)
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201 %!error <the columns and rows of Z> griddata (1:4, 1:3, ones (3,5), 1:3, 1:3)
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Rik <octave@nomad.inbox5.com>
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202 %!error <matrices of same size> griddata (1:3, 1:3, 1:3, 1:4, 1:3)
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Rik <octave@nomad.inbox5.com>
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203 %!error <matrices of same size> griddata (1:3, 1:3, 1:3, 1:3, 1:4)
5736d93b22d0 griddata.m: Accept vectors in any orientation (Bug #33539)
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diff changeset
204