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scripts/geometry/griddatan.m

changeset 10289: 4b124317dc38
parent:ec0a13863eb7
author: John W. Eaton <jwe@octave.org>
date: Tue Feb 09 20:58:55 2010 -0500 (69 minutes ago)
permissions: -rw-r--r--
description: base_properties::set_children: account for hidden children 
     1## Copyright (C) 2007, 2008 David Bateman

     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

     7## the Free Software Foundation; either version 3 of the License, or (at

     8## your option) any later version.

     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

    16## along with Octave; see the file COPYING.  If not, see

    17## <http://www.gnu.org/licenses/>.

    18

    19## -*- texinfo -*-

    20## @deftypefn {Function File} {@var{yi} =} griddatan (@var{x}, @var{y}, @var{xi}, @var{method}, @var{options})

    21## 

    22## Generate a regular mesh from irregular data using interpolation.

    23## The function is defined by @code{@var{y} = f (@var{x})}.

    24## The interpolation points are all @var{xi}.  

    25##

    26## The interpolation method can be @code{"nearest"} or @code{"linear"}.

    27## If method is omitted it defaults to @code{"linear"}.

    28## @seealso{griddata, delaunayn}

    29## @end deftypefn

    30

    31## Author: David Bateman <dbateman@free.fr>

    32

    33function yi = griddatan (x, y, xi, method, varargin)

    34

    35  if (nargin == 3)

    36    method = "linear";

    37  endif

    38  if (nargin < 3) 

    39    print_usage ();

    40  endif

    41

    42  if (ischar (method))

    43    method = tolower (method);

    44  endif

    45

    46  [m, n] = size (x);

    47  [mi, ni] = size (xi);

    48  

    49  if (n != ni || size (y, 1) != m || size (y, 2) != 1)

    50    error ("griddatan: dimensional mismatch");

    51  endif

    52

    53  ## triangulate data

    54  ## tri = delaunayn(x, varargin{:});

    55  tri = delaunayn (x);

    56

    57  yi = nan (mi, 1);

    58  

    59  if (strcmp (method, "nearest"))

    60    ## search index of nearest point

    61    idx = dsearchn (x, tri, xi);

    62    valid = !isnan (idx);

    63    yi(valid) = y(idx(valid));

    64

    65  elseif (strcmp (method, "linear"))

    66    ## search for every point the enclosing triangle

    67    [tri_list, bary_list] = tsearchn (x, tri, xi);

    68

    69    ## only keep the points within triangles.

    70    valid = !isnan (tri_list);

    71    tri_list = tri_list(!isnan (tri_list));

    72    bary_list = bary_list(!isnan (tri_list), :);

    73    nr_t = rows (tri_list);

    74

    75    ## assign x,y for each point of simplex

    76    xt =  reshape (x(tri(tri_list,:),:), [nr_t, n+1, n]);

    77    yt = y(tri(tri_list,:));

    78

    79    ## Use barycentric coordinate of point to calculate yi

    80    yi(valid) = sum (y(tri(tri_list,:)) .* bary_list, 2);

    81

    82  else

    83    error ("griddatan: unknown interpolation method");

    84  endif

    85

    86endfunction

    87

    88%!testif HAVE_QHULL

    89%! [xx,yy] = meshgrid(linspace(-1,1,32));

    90%! xi = [xx(:), yy(:)];

    91%! x = (2 * rand(100,2) - 1);

    92%! x = [x;1,1;1,-1;-1,-1;-1,1];

    93%! y = sin(2*(sum(x.^2,2)));

    94%! zz = griddatan(x,y,xi,'linear');

    95%! zz2 = griddata(x(:,1),x(:,2),y,xi(:,1),xi(:,2),'linear');

    96%! assert (zz, zz2, 1e-10)

    97

    98%!testif HAVE_QHULL

    99%! [xx,yy] = meshgrid(linspace(-1,1,32));

   100%! xi = [xx(:), yy(:)];

   101%! x = (2 * rand(100,2) - 1);

   102%! x = [x;1,1;1,-1;-1,-1;-1,1];

   103%! y = sin(2*(sum(x.^2,2)));

   104%! zz = griddatan(x,y,xi,'nearest');

   105%! zz2 = griddata(x(:,1),x(:,2),y,xi(:,1),xi(:,2),'nearest');

   106%! assert (zz, zz2, 1e-10)