Mercurial > hg > octave-nkf
annotate scripts/geometry/griddata.m @ 10945:aa40bdbfa478
griddata.m: Allow x, y inputs to be vectors, and z a matrix.
| author | Ben Abbott <bpabbott@mac.com> |
|---|---|
| date | Mon, 06 Sep 2010 09:19:17 -0400 |
| parents | be55736a0783 |
| children | 1740012184f9 |
| rev | line source |
|---|---|
| 8920 | 1 ## Copyright (C) 1999, 2000, 2007, 2008, 2009 Kai Habel |
| 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{zi} =} griddata (@var{x}, @var{y}, @var{z}, @var{xi}, @var{yi}, @var{method}) |
| 6823 | 21 ## @deftypefnx {Function File} {[@var{xi}, @var{yi}, @var{zi}] =} griddata (@var{x}, @var{y}, @var{z}, @var{xi}, @var{yi}, @var{method}) |
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griddata.m: Allow x, y inputs to be vectors, and z a matrix.
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22 ## |
| 6823 | 23 ## Generate a regular mesh from irregular data using interpolation. |
| 24 ## The function is defined by @code{@var{z} = f (@var{x}, @var{y})}. | |
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25 ## Inputs @code{@var{x}, @var{y}, @var{z}} are vectors of the same length |
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26 ## or @code{@var{x}, @var{y}} are vectors and @code{@var{z}} is matrix. |
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27 ## |
| 6823 | 28 ## The interpolation points are all @code{(@var{xi}, @var{yi})}. If |
| 29 ## @var{xi}, @var{yi} are vectors then they are made into a 2D mesh. | |
| 30 ## | |
| 6826 | 31 ## The interpolation method can be @code{"nearest"}, @code{"cubic"} or |
| 32 ## @code{"linear"}. If method is omitted it defaults to @code{"linear"}. | |
| 6823 | 33 ## @seealso{delaunay} |
| 34 ## @end deftypefn | |
| 35 | |
| 10549 | 36 ## Author: Kai Habel <kai.habel@gmx.de> |
| 6823 | 37 ## Adapted-by: Alexander Barth <barth.alexander@gmail.com> |
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38 ## xi and yi are not "meshgridded" if both are vectors |
| 6823 | 39 ## of the same size (for compatibility) |
| 40 | |
| 6826 | 41 function [rx, ry, rz] = griddata (x, y, z, xi, yi, method) |
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42 |
| 6823 | 43 if (nargin == 5) |
| 6826 | 44 method = "linear"; |
| 6823 | 45 endif |
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46 if (nargin < 5 || nargin > 7) |
| 6826 | 47 print_usage (); |
| 6823 | 48 endif |
| 49 | |
| 6826 | 50 if (ischar (method)) |
| 51 method = tolower (method); | |
| 6823 | 52 endif |
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53 |
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54 if (isvector (x) && isvector (y) && all ([numel(y), numel(x)] == size (z))) |
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55 [x, y] = meshgrid (x, y); |
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56 elseif (! all (size (x) == size (y) & size (x) == size (z))) |
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57 if (isvector (z)) |
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58 error ("griddata: x, y, and z, be vectors of same length."); |
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59 else |
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60 error ("griddata: lengths of x, y must match the columns and rows of z."); |
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61 endif |
| 6823 | 62 endif |
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63 |
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64 ## Meshgrid xi and yi if they are a row and column vector. |
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65 if (rows (xi) == 1 && columns (yi) == 1) |
| 6826 | 66 [xi, yi] = meshgrid (xi, yi); |
| 6823 | 67 endif |
| 68 | |
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69 if (! size_equal (xi, yi)) |
| 6826 | 70 error ("griddata: xi and yi must be vectors or matrices of same size"); |
| 6823 | 71 endif |
| 72 | |
| 6826 | 73 [nr, nc] = size (xi); |
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74 |
| 9501 | 75 x = x(:); |
| 76 y = y(:); | |
| 77 z = z(:); | |
| 9495 | 78 |
| 8507 | 79 ## Triangulate data. |
| 6826 | 80 tri = delaunay (x, y); |
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81 zi = NaN (size (xi)); |
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82 |
| 6826 | 83 if (strcmp (method, "cubic")) |
| 8664 | 84 error ("griddata: cubic interpolation not yet implemented"); |
| 6823 | 85 |
| 6826 | 86 elseif (strcmp (method, "nearest")) |
| 8507 | 87 ## Search index of nearest point. |
| 6826 | 88 idx = dsearch (x, y, tri, xi, yi); |
| 89 valid = !isnan (idx); | |
| 6823 | 90 zi(valid) = z(idx(valid)); |
| 91 | |
| 6826 | 92 elseif (strcmp (method, "linear")) |
| 8507 | 93 ## Search for every point the enclosing triangle. |
| 94 tri_list = tsearch (x, y, tri, xi(:), yi(:)); | |
| 6823 | 95 |
| 8507 | 96 ## Only keep the points within triangles. |
| 9496 | 97 valid = !isnan (tri_list); |
| 98 tri_list = tri_list(valid); | |
| 6826 | 99 nr_t = rows (tri_list); |
| 6823 | 100 |
| 9496 | 101 tri = tri(tri_list,:); |
| 102 | |
| 8507 | 103 ## Assign x,y,z for each point of triangle. |
| 9496 | 104 x1 = x(tri(:,1)); |
| 105 x2 = x(tri(:,2)); | |
| 106 x3 = x(tri(:,3)); | |
| 6826 | 107 |
| 9496 | 108 y1 = y(tri(:,1)); |
| 109 y2 = y(tri(:,2)); | |
| 110 y3 = y(tri(:,3)); | |
| 6826 | 111 |
| 9496 | 112 z1 = z(tri(:,1)); |
| 113 z2 = z(tri(:,2)); | |
| 114 z3 = z(tri(:,3)); | |
| 6823 | 115 |
| 8507 | 116 ## Calculate norm vector. |
| 6826 | 117 N = cross ([x2-x1, y2-y1, z2-z1], [x3-x1, y3-y1, z3-z1]); |
| 9496 | 118 ## Normalize. |
| 119 N = diag (norm (N, "rows")) \ N; | |
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parents:
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120 |
| 8507 | 121 ## Calculate D of plane equation |
| 122 ## Ax+By+Cz+D = 0; | |
| 6823 | 123 D = -(N(:,1) .* x1 + N(:,2) .* y1 + N(:,3) .* z1); |
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124 |
| 8507 | 125 ## Calculate zi by solving plane equation for xi, yi. |
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126 zi(valid) = -(N(:,1).*xi(:)(valid) + N(:,2).*yi(:)(valid) + D) ./ N(:,3); |
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127 |
| 6823 | 128 else |
| 6826 | 129 error ("griddata: unknown interpolation method"); |
| 6823 | 130 endif |
| 131 | |
| 6826 | 132 if (nargout == 3) |
| 6823 | 133 rx = xi; |
| 134 ry = yi; | |
| 135 rz = zi; | |
| 6826 | 136 elseif (nargout == 1) |
| 6823 | 137 rx = zi; |
| 6826 | 138 elseif (nargout == 0) |
| 139 mesh (xi, yi, zi); | |
| 6823 | 140 endif |
| 141 endfunction | |
| 142 | |
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143 %!testif HAVE_QHULL |
| 6823 | 144 %! [xx,yy]=meshgrid(linspace(-1,1,32)); |
| 145 %! x = xx(:); | |
| 146 %! x = x + 10 * (2 * round(rand(size(x))) - 1) * eps; | |
| 147 %! y = yy(:); | |
| 148 %! y = y + 10 * (2 * round(rand(size(y))) - 1) * eps; | |
| 149 %! z = sin(2*(x.^2+y.^2)); | |
| 150 %! zz = griddata(x,y,z,xx,yy,'linear'); | |
| 151 %! zz2 = sin(2*(xx.^2+yy.^2)); | |
| 152 %! zz2(isnan(zz)) = NaN; | |
| 153 %! assert (zz, zz2, 100 * eps) | |
| 154 | |
| 155 %!demo | |
| 156 %! x=2*rand(100,1)-1; | |
| 157 %! y=2*rand(size(x))-1; | |
| 158 %! z=sin(2*(x.^2+y.^2)); | |
| 159 %! [xx,yy]=meshgrid(linspace(-1,1,32)); | |
| 160 %! griddata(x,y,z,xx,yy); | |
| 161 %! title('nonuniform grid sampled at 100 points'); | |
| 162 | |
| 163 %!demo | |
| 164 %! x=2*rand(1000,1)-1; | |
| 165 %! y=2*rand(size(x))-1; | |
| 166 %! z=sin(2*(x.^2+y.^2)); | |
| 167 %! [xx,yy]=meshgrid(linspace(-1,1,32)); | |
| 168 %! griddata(x,y,z,xx,yy); | |
| 169 %! title('nonuniform grid sampled at 1000 points'); | |
| 170 | |
| 171 %!demo | |
| 172 %! x=2*rand(1000,1)-1; | |
| 173 %! y=2*rand(size(x))-1; | |
| 174 %! z=sin(2*(x.^2+y.^2)); | |
| 175 %! [xx,yy]=meshgrid(linspace(-1,1,32)); | |
| 176 %! griddata(x,y,z,xx,yy,'nearest'); | |
| 177 %! title('nonuniform grid sampled at 1000 points with nearest neighbor'); |