--- a/NEWS	Tue Mar 10 07:51:55 2020 -0400
+++ b/NEWS	Sun Feb 16 21:37:13 2020 -0500
@@ -41,6 +41,8 @@
 
 ### Matlab compatibility
 
+- The function `griddata` now accepts 3-D inputs by passing data
+directly to `griddata3`.
 
 ### Alphabetical list of new functions added in Octave 7
 

--- a/scripts/geometry/griddata.m	Tue Mar 10 07:51:55 2020 -0400
+++ b/scripts/geometry/griddata.m	Sun Feb 16 21:37:13 2020 -0500
@@ -27,123 +27,158 @@
 ## @deftypefn  {} {@var{zi} =} griddata (@var{x}, @var{y}, @var{z}, @var{xi}, @var{yi})
 ## @deftypefnx {} {@var{zi} =} griddata (@var{x}, @var{y}, @var{z}, @var{xi}, @var{yi}, @var{method})
 ## @deftypefnx {} {[@var{xi}, @var{yi}, @var{zi}] =} griddata (@dots{})
-##
-## Generate a regular mesh from irregular data using interpolation.
+## @deftypefnx {} {@var{vi} =} griddata (@var{x}, @var{y}, @var{z}, @var{v}, @var{xi}, @var{yi}, @var{zi})
+## @deftypefnx {} {@var{vi} =} griddata (@var{x}, @var{y}, @var{z}, @var{v}, @var{xi}, @var{yi}, @var{zi}, @var{method})
+## @deftypefnx {} {@var{vi} =} griddata (@var{x}, @var{y}, @var{z}, @var{v}, @var{xi}, @var{yi}, @var{zi}, @var{method}, @var{options})
 ##
-## The function is defined by @code{@var{z} = f (@var{x}, @var{y})}.  Inputs
+## Generate a regular mesh from irregular data using 2-D or 3-D interpolation.
+##
+## For 2-D 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.
+## @code{@var{x}, @var{y}} are vectors and @code{@var{z}} is a 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 @qcode{"nearest"}, @qcode{"cubic"} or
-## @qcode{"linear"}.  If method is omitted it defaults to @qcode{"linear"}.
+## For 3-D interpolation, the function is defined by
+## @code{@var{v} = f (@var{x}, @var{y}, @var{z})}, and the interpolation points
+## are specified by @var{xi}, @var{yi}, @var{zi}.
+##
+## For both 2-D and 3-D cases, the interpolation method can be
+## @qcode{"nearest"} or @qcode{"linear"}.  If method is omitted it defaults
+## to @qcode{"linear"}.
+##
+## For 3-D interpolation, 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.
 ## @seealso{griddata3, griddatan, delaunay}
 ## @end deftypefn
 
 ## Algorithm: 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 = "linear")
+function [rx, ry, rz] = griddata (x, y, z, varargin)
 
-  if (nargin < 5 || nargin > 7)
+  if (nargin < 5)
     print_usage ();
   endif
 
-  if (ischar (method))
-    method = tolower (method);
-  endif
-
-  ## Meshgrid if x and y are vectors but z is matrix
-  if (isvector (x) && isvector (y) && all ([numel(y), numel(x)] == size (z)))
-    [x, y] = meshgrid (x, y);
-  endif
-
-  if (isvector (x) && isvector (y) && isvector (z))
-    if (! isequal (length (x), length (y), length (z)))
-      error ("griddata: X, Y, and Z must be vectors of the same length");
-    endif
-  elseif (! size_equal (x, y, z))
-    error ("griddata: lengths of X, Y must match the columns and rows of Z");
-  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);
-  elseif (isvector (xi) && isvector (yi))
-    ## Otherwise, convert to column vectors
-    xi = xi(:);
-    yi = yi(:);
-  endif
-
-  if (! size_equal (xi, yi))
-    error ("griddata: XI and YI must be vectors or matrices of same size");
-  endif
-
-  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");
+  if (nargin > 6)
+    ## Current 2D implementation has nargin max = 6, since no triangulation
+    ## options are passed to the 2D algorithm. 3D algorithm requires nargin >=7
 
-  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);
+    if (nargout > 1)
+      error ("griddata: only one output argument valid for 3D interpolation");
+    endif
+    rx = griddata3 (x, y, z, varargin{:});
 
   else
-    error ("griddata: unknown interpolation METHOD");
-  endif
+    ## for nargin 5 or 6, assign varargin terms to variables for 2D algorithm
+    xi = varargin{1};
+    yi = varargin{2};
+
+    if (nargin == 6)
+      if (! ischar (varargin{3}))
+        error ("griddata: unknown interpolation METHOD");
+      endif
+      method = tolower (varargin{3});
+    else
+      method = "linear";
+    endif
+
+    ## Meshgrid if x and y are vectors but z is matrix
+    if (isvector (x) && isvector (y) && all ([numel(y), numel(x)] == size (z)))
+      [x, y] = meshgrid (x, y);
+    endif
+
+    if (isvector (x) && isvector (y) && isvector (z))
+      if (! isequal (length (x), length (y), length (z)))
+        error ("griddata: X, Y, and Z must be vectors of the same length");
+      endif
+    elseif (! size_equal (x, y, z))
+      error ("griddata: lengths of X, Y must match the columns and rows of Z");
+    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);
+    elseif (isvector (xi) && isvector (yi))
+      ## Otherwise, convert to column vectors
+      xi = xi(:);
+      yi = yi(:);
+    endif
+
+    if (! size_equal (xi, yi))
+      error ("griddata: XI and YI must be vectors or matrices of same size");
+    endif
+
+    x = x(:);
+    y = y(:);
+    z = z(:);
+
+    ## Triangulate data.
+    tri = delaunay (x, y);
+    zi = NaN (size (xi));
+
+    if (any (strcmp (method, {"cubic", "natural", "v4"})))
+      ## FIXME: implement missing interpolation methods.
+      error ('griddata: "%s" interpolation not yet implemented', method);
 
-  if (nargout > 1)
-    rx = xi;
-    ry = yi;
-    rz = zi;
-  else
-    rx = zi;
+    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: "%s"', method);
+    endif
+
+    if (nargout > 1)
+      rx = xi;
+      ry = yi;
+      rz = zi;
+    else
+      rx = zi;
+    endif
+
   endif
 
 endfunction
@@ -155,10 +190,10 @@
 %! 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));
+%! [xx,yy] = meshgrid (linspace (-1, 1, 32));
 %! zz = griddata (x,y,z,xx,yy);
 %! mesh (xx, yy, zz);
-%! title ("nonuniform grid sampled at 100 points");
+%! title ("non-uniform grid sampled at 100 points");
 
 %!demo
 %! clf;
@@ -166,10 +201,11 @@
 %! 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));
+%! [xx,yy] = meshgrid (linspace (-1, 1, 32));
 %! zz = griddata (x,y,z,xx,yy);
 %! mesh (xx, yy, zz);
-%! title ("nonuniform grid sampled at 1000 points");
+%! title ({"non-uniform grid sampled at 1,000 points",
+%!         'method = "linear"'});
 
 %!demo
 %! clf;
@@ -177,19 +213,20 @@
 %! 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));
+%! [xx,yy] = meshgrid (linspace (-1, 1, 32));
 %! zz = griddata (x,y,z,xx,yy,"nearest");
 %! mesh (xx, yy, zz);
-%! title ("nonuniform grid sampled at 1000 points with nearest neighbor");
+%! title ({"non-uniform grid sampled at 1,000 points",
+%!         'method = "nearest neighbor"'});
 
 %!testif HAVE_QHULL
-%! [xx,yy] = meshgrid (linspace (-1,1,32));
+%! [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");
+%! zz = griddata (x,y,z,xx,yy, "linear");
 %! zz2 = sin (2*(xx.^2 + yy.^2));
 %! zz2(isnan (zz)) = NaN;
 %! assert (zz, zz2, 100*eps);
@@ -200,11 +237,16 @@
 %!error griddata (1,2)
 %!error griddata (1,2,3)
 %!error griddata (1,2,3,4)
-%!error griddata (1,2,3,4,5,6,7)
+%!error <only one output argument> [xi,yi] = griddata (1,2,3,4,5,6,7)
+%!error <unknown interpolation METHOD> griddata (1,2,3,4,5, {"linear"})
+%!error <vectors of the same length> griddata (1:4, 1:3, 1:3, 1:3, 1:3)
+%!error <vectors of the same length> griddata (1:3, 1:4, 1:3, 1:3, 1:3)
 %!error <vectors of the same length> griddata (1:3, 1:3, 1:4, 1:3, 1:3)
-%!error <vectors of the same length> griddata (1:3, 1:4, 1:3, 1:3, 1:3)
-%!error <vectors of the same length> griddata (1:4, 1:3, 1:3, 1:3, 1:3)
 %!error <the columns and rows of Z> griddata (1:4, 1:3, ones (4,4), 1:3, 1:3)
 %!error <the columns and rows of Z> griddata (1:4, 1:3, ones (3,5), 1:3, 1:3)
-%!error <matrices of same size> griddata (1:3, 1:3, 1:3, 1:4, 1:3)
-%!error <matrices of same size> griddata (1:3, 1:3, 1:3, 1:3, 1:4)
+%!error <XI and YI .* matrices of same size> griddata (1:3, 1:3, 1:3, 1:4, 1:3)
+%!error <XI and YI .* matrices of same size> griddata (1:3, 1:3, 1:3, 1:3, 1:4)
+%!error <"cubic" .* not yet implemented> griddata (1,2,3,4,5, "cubic")
+%!error <"natural" .* not yet implemented> griddata (1,2,3,4,5, "natural")
+%!error <"v4" .* not yet implemented> griddata (1,2,3,4,5, "v4")
+%!error <unknown interpolation METHOD: "foobar"> griddata (1,2,3,4,5, "foobar")