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## -*- texinfo -*-
## @deftypefn  {} {@var{vi} =} griddata3 (@var{x}, @var{y}, @var{z}, @var{v}, @var{xi}, @var{yi}, @var{zi})
## @deftypefnx {} {@var{vi} =} griddata3 (@var{x}, @var{y}, @var{z}, @var{v}, @var{xi}, @var{yi}, @var{zi}, @var{method})
## @deftypefnx {} {@var{vi} =} griddata3 (@var{x}, @var{y}, @var{z}, @var{v}, @var{xi}, @var{yi}, @var{zi}, @var{method}, @var{options})
##
## Interpolate irregular 3-D source data at specified points.
##
## The inputs @var{x}, @var{y}, and @var{z} define the points where the
## function @code{@var{v} = f (@var{x}, @var{y}, @var{z})} is evaluated.  The
## inputs @var{x}, @var{y}, @var{z} are either vectors of the same length, or
## if they are of unequal length, then they are expanded to a 3-D grid with
## @code{meshgrid}.  The size of the input @var{v} must match the size of the
## original data, either as a vector or a matrix.
##
## The interpolation points are specified by @var{xi}, @var{yi}, @var{zi}.
##
## The optional input interpolation @var{method} can be @qcode{"nearest"} or
## @qcode{"linear"}.  When the method is @qcode{"nearest"}, the output @var{vi}
## will be the closest point in the original data (@var{x}, @var{y}, @var{z})
## to the query point (@var{xi}, @var{yi}, @var{zi}).  When the method is
## @qcode{"linear"}, the output @var{vi} will be a linear interpolation between
## the two closest points in the original source data in each dimension.
## If @var{method} is omitted or empty, it defaults to @qcode{"linear"}.
##
## The optional argument @var{options} is passed directly to Qhull when
## computing the Delaunay triangulation used for interpolation.  See
## @code{delaunayn} for information on the defaults and how to pass different
## values.
##
## Programming Notes: If the input is complex the real and imaginary parts
## are interpolated separately.  Interpolation is based on a Delaunay
## triangulation and any query values outside the convex hull of the input
## points will return @code{NaN}.
## @seealso{griddata, griddatan, delaunayn}
## @end deftypefn

function vi = griddata3 (x, y, z, v, xi, yi, zi, method = "linear", varargin)

  if (nargin < 7)
    print_usage ();
  endif

  if (isvector (x) && isvector (y) && isvector (z) && isvector (v))
    if (! isequal (length (x), length (y), length (z), length (v)))
      error ("griddata: X, Y, Z, and V must be vectors of the same length");
    endif
  elseif (! size_equal (x, y, z, v))
    error ("griddata: X, Y, Z, and V must have equal sizes");
  endif

  ## meshgrid xi, yi and zi if they are vectors unless
  ## they are vectors of the same length.
  if (isvector (xi) && isvector (yi) && isvector (zi))
    if (! isequal (length (xi), length (yi), length (zi)))
      [xi, yi, zi] = meshgrid (xi, yi, zi);
    else
      ## Otherwise, convert to column vectors
      xi = xi(:);
      yi = yi(:);
      zi = zi(:);
    endif
  endif

  if (! size_equal (xi, yi, zi))
    error ("griddata3: XI, YI, and ZI must be vectors or matrices of the same size");
  endif

  vi = griddatan ([x(:), y(:), z(:)], v(:), [xi(:), yi(:), zi(:)], method, ...
                  varargin{:});
  vi = reshape (vi, size (xi));

endfunction


%!testif HAVE_QHULL
%! old_state = rand ("state");
%! restore_state = onCleanup (@() rand ("state", old_state));
%! rand ("state", 0);
%! x = 2 * rand (1000, 1) - 1;
%! y = 2 * rand (1000, 1) - 1;
%! z = 2 * rand (1000, 1) - 1;
%! v = x.^2 + y.^2 + z.^2;
%! [xi, yi, zi] = meshgrid (-0.8:0.2:0.8);
%! vi = griddata3 (x, y, z, v, xi, yi, zi, "linear");
%! vv = vi - xi.^2 - yi.^2 - zi.^2;
%! assert (max (abs (vv(:))), 0, 0.1);

%!testif HAVE_QHULL
%! old_state = rand ("state");
%! restore_state = onCleanup (@() rand ("state", old_state));
%! rand ("state", 0);
%! x = 2 * rand (1000, 1) - 1;
%! y = 2 * rand (1000, 1) - 1;
%! z = 2 * rand (1000, 1) - 1;
%! v = x.^2 + y.^2 + z.^2;
%! [xi, yi, zi] = meshgrid (-0.8:0.2:0.8);
%! vi = griddata3 (x, y, z, v, xi, yi, zi, "nearest");
%! vv = vi - xi.^2 - yi.^2 - zi.^2;
%! assert (max (abs (vv(:))), 0.385, 0.1);

## FIXME: Ideally, there should be BIST tests for input validation.
## However, this function is deprecated in Matlab and it probably isn't worth
## the coding time to work on a function that will be removed soon.
