scripts/geometry/griddata.m

## Copyright (C) 1999, 2000, 2007, 2008, 2009 Kai Habel
##
## This file is part of Octave.
##
## Octave is free software; you can redistribute it and/or modify it
## under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 3 of the License, or (at
## your option) any later version.
##
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## WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
## General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with Octave; see the file COPYING.  If not, see
## <http://www.gnu.org/licenses/>.

## -*- texinfo -*-
## @deftypefn {Function File} {@var{zi} =} griddata (@var{x}, @var{y}, @var{z}, @var{xi}, @var{yi}, @var{method})
## @deftypefnx {Function File} {[@var{xi}, @var{yi}, @var{zi}] =} griddata (@var{x}, @var{y}, @var{z}, @var{xi}, @var{yi}, @var{method})
## 
## Generate a regular mesh from irregular data using interpolation.
## The function is defined by @code{@var{z} = f (@var{x}, @var{y})}.
## The interpolation points are all @code{(@var{xi}, @var{yi})}.  If
## @var{xi}, @var{yi} are vectors then they are made into a 2D mesh.
##
## The interpolation method can be @code{"nearest"}, @code{"cubic"} or
## @code{"linear"}.  If method is omitted it defaults to @code{"linear"}.
## @seealso{delaunay}
## @end deftypefn

## Author:	Kai Habel <kai.habel@gmx.de>
## Adapted-by:  Alexander Barth <barth.alexander@gmail.com>
##              xi and yi are not "meshgridded" if both are vectors 
##              of the same size (for compatibility)

function [rx, ry, rz] = griddata (x, y, z, xi, yi, method)
	
  if (nargin == 5)
    method = "linear";
  endif
  if (nargin < 5 || nargin > 7) 
    print_usage ();
  endif

  if (ischar (method))
    method = tolower (method);
  endif
  if (! all (size (x) == size (y) & size (x) == size (z)))
    error ("griddata: x, y, and z must be vectors of same length");
  endif
  
  ## Meshgrid xi and yi if they are a row and column vector.
  if (rows (xi) == 1 && columns (yi) == 1)
    [xi, yi] = meshgrid (xi, yi);
  endif

  if (! size_equal (xi, yi))
    error ("griddata: xi and yi must be vectors or matrices of same size");
  endif

  [nr, nc] = size (xi);
  
  x = x(:);
  y = y(:);
  z = z(:);

  ## Triangulate data.
  tri = delaunay (x, y);
  zi = nan (size (xi));
  
  if (strcmp (method, "cubic"))
    error ("griddata: cubic interpolation not yet implemented");

  elseif (strcmp (method, "nearest"))
    ## Search index of nearest point.
    idx = dsearch (x, y, tri, xi, yi);
    valid = !isnan (idx);
    zi(valid) = z(idx(valid));

  elseif (strcmp (method, "linear"))
    ## Search for every point the enclosing triangle.
    tri_list = tsearch (x, y, tri, xi(:), yi(:));

    ## Only keep the points within triangles.
    valid = !isnan (tri_list);
    tri_list = tri_list(valid);
    nr_t = rows (tri_list);

    tri = tri(tri_list,:);

    ## Assign x,y,z for each point of triangle.
    x1 = x(tri(:,1));
    x2 = x(tri(:,2));
    x3 = x(tri(:,3));

    y1 = y(tri(:,1));
    y2 = y(tri(:,2));
    y3 = y(tri(:,3));

    z1 = z(tri(:,1));
    z2 = z(tri(:,2));
    z3 = z(tri(:,3));

    ## Calculate norm vector.
    N = cross ([x2-x1, y2-y1, z2-z1], [x3-x1, y3-y1, z3-z1]);
    ## Normalize.
    N = diag (norm (N, "rows")) \ N;
    
    ## Calculate D of plane equation
    ## Ax+By+Cz+D = 0;
    D = -(N(:,1) .* x1 + N(:,2) .* y1 + N(:,3) .* z1);
    
    ## Calculate zi by solving plane equation for xi, yi.
    zi(valid) = -(N(:,1).*xi(:)(valid) + N(:,2).*yi(:)(valid) + D) ./ N(:,3);
    
  else
    error ("griddata: unknown interpolation method");
  endif

  if (nargout == 3)
    rx = xi;
    ry = yi;
    rz = zi;
  elseif (nargout == 1)
    rx = zi;
  elseif (nargout == 0)
    mesh (xi, yi, zi);
  endif
endfunction

%!testif HAVE_QHULL
%! [xx,yy]=meshgrid(linspace(-1,1,32));
%! x = xx(:);
%! x = x + 10 * (2 * round(rand(size(x))) - 1) * eps;
%! y = yy(:);
%! y = y + 10 * (2 * round(rand(size(y))) - 1) * eps;
%! z = sin(2*(x.^2+y.^2));
%! zz = griddata(x,y,z,xx,yy,'linear');
%! zz2 = sin(2*(xx.^2+yy.^2));
%! zz2(isnan(zz)) = NaN;
%! assert (zz, zz2, 100 * eps)

%!demo
%! x=2*rand(100,1)-1;
%! y=2*rand(size(x))-1;
%! z=sin(2*(x.^2+y.^2));
%! [xx,yy]=meshgrid(linspace(-1,1,32));
%! griddata(x,y,z,xx,yy);
%! title('nonuniform grid sampled at 100 points');

%!demo
%! x=2*rand(1000,1)-1;
%! y=2*rand(size(x))-1;
%! z=sin(2*(x.^2+y.^2));
%! [xx,yy]=meshgrid(linspace(-1,1,32));
%! griddata(x,y,z,xx,yy);
%! title('nonuniform grid sampled at 1000 points');

%!demo
%! x=2*rand(1000,1)-1;
%! y=2*rand(size(x))-1;
%! z=sin(2*(x.^2+y.^2));
%! [xx,yy]=meshgrid(linspace(-1,1,32));
%! griddata(x,y,z,xx,yy,'nearest');
%! title('nonuniform grid sampled at 1000 points with nearest neighbor');