--- /dev/null
+## Copyright (C) 1999-2012 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.
+##
+## Octave is distributed in the hope that it will be useful, but
+## 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})}.
+## Inputs @code{@var{x}, @var{y}, @var{z}} are vectors of the same length
+## or @code{@var{x}, @var{y}} are vectors and @code{@var{z}} is matrix.
+##
+## The interpolation points are all @code{(@var{xi}, @var{yi})}. If
+## @var{xi}, @var{yi} are vectors then they are made into a 2-D 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 (isvector (x) && isvector (y) && all ([numel(y), numel(x)] == size (z)))
+ [x, y] = meshgrid (x, y);
+ elseif (! all (size (x) == size (y) & size (x) == size (z)))
+ if (isvector (z))
+ error ("griddata: X, Y, and Z, be vectors of same length");
+ else
+ error ("griddata: lengths of X, Y must match the columns and rows of Z");
+ endif
+ 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');
git://git.creatis.insa-lyon.fr / CreaPhase.git / blobdiff