--- a/NEWS	Tue Aug 09 15:40:32 2016 +0100
+++ b/NEWS	Mon Jul 18 19:49:39 2016 +0200
@@ -123,6 +123,7 @@
       padecoef
       psi
       rad2deg
+      reducevolume
       uibuttongroup
 
  ** Deprecated functions.

--- a/doc/interpreter/plot.txi	Tue Aug 09 15:40:32 2016 +0100
+++ b/doc/interpreter/plot.txi	Mon Jul 18 19:49:39 2016 +0200
@@ -386,6 +386,8 @@
 
 @DOCSTRING(smooth3)
 
+@DOCSTRING(reducevolume)
+
 @DOCSTRING(shrinkfaces)
 
 @DOCSTRING(diffuse)

--- a/scripts/help/__unimplemented__.m	Tue Aug 09 15:40:32 2016 +0100
+++ b/scripts/help/__unimplemented__.m	Mon Jul 18 19:49:39 2016 +0200
@@ -787,7 +787,6 @@
   "rbbox",
   "readtable",
   "reducepatch",
-  "reducevolume",
   "remove",
   "removecats",
   "renamecats",

--- a/scripts/plot/draw/isosurface.m	Tue Aug 09 15:40:32 2016 +0100
+++ b/scripts/plot/draw/isosurface.m	Mon Jul 18 19:49:39 2016 +0200
@@ -133,7 +133,7 @@
 ## light ("Position", [1 1 5]);
 ## @end smallexample
 ##
-## @seealso{isonormals, isocolors, smooth3}
+## @seealso{isonormals, isocolors, smooth3, reducevolume}
 ## @end deftypefn
 
 ## Author: Martin Helm <martin@mhelm.de>

--- a/scripts/plot/draw/module.mk	Tue Aug 09 15:40:32 2016 +0100
+++ b/scripts/plot/draw/module.mk	Mon Jul 18 19:49:39 2016 +0200
@@ -72,6 +72,7 @@
   scripts/plot/draw/quiver3.m \
   scripts/plot/draw/quiver.m \
   scripts/plot/draw/rectangle.m \
+  scripts/plot/draw/reducevolume.m \
   scripts/plot/draw/ribbon.m \
   scripts/plot/draw/rose.m \
   scripts/plot/draw/scatter3.m \

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/scripts/plot/draw/reducevolume.m	Mon Jul 18 19:49:39 2016 +0200
@@ -0,0 +1,286 @@
+## Copyright (C) 2016 Markus Muetzel
+##
+## 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  {} {[@var{nx}, @var{ny}, @var{nz}, @var{nv}] =} reducevolume (@var{v}, @var{r})
+## @deftypefnx {} {[@var{nx}, @var{ny}, @var{nz}, @var{nv}] =} reducevolume (@var{x}, @var{y}, @var{z}, @var{v}, @var{r})
+## @deftypefnx {} {@var{nv} =} reducevolume (@dots{})
+##
+## Reduce the volume of the dataset in @var{v} according to the values in
+## @var{r}.
+##
+## @var{v} is a matrix that is non-singleton in the first 3 dimensions.
+##
+## @var{r} can either be a vector of 3 elements representing the reduction
+## factors in the x-, y-, and z-directions or a scalar, in which case the same
+## reduction factor is used in all three dimensions.
+##
+## @code{reducevolume} reduces the number of elements of @var{v} by taking
+## only every @var{r}-th element in the respective dimension.
+##
+## Optionally, @var{x}, @var{y}, and @var{z} can be supplied to represent the
+## set of coordinates of @var{v}.  They can either be matrices of the same size
+## as @var{v} or vectors with sizes according to the dimensions of @var{v}, in
+## which case they are expanded to matrices (@pxref{XREFmeshgrid,,meshgrid}).
+##
+## If @code{reducevolume} is called with two arguments then @var{x}, @var{y},
+## and @var{z} are assumed to match the respective indices of @var{v}.
+##
+## The reduced matrix is returned in @var{nv}.
+##
+## Optionally, the reduced set of coordinates are returned in @var{nx},
+## @var{ny}, and @var{nz}, respectively.
+##
+## Examples:
+##
+## @example
+## @group
+## @var{v} = reshape (1:6*8*4, [6 8 4]);
+## @var{nv} = reducevolume (@var{v}, [4 3 2]);
+## @end group
+## @end example
+##
+## @example
+## @group
+## @var{v} = reshape (1:6*8*4, [6 8 4]);
+## @var{x} = 1:3:24;  @var{y} = -14:5:11;  @var{z} = linspace (16, 18, 4);
+## [@var{nx}, @var{ny}, @var{nz}, @var{nv}] = reducevolume (@var{x}, @var{y}, @var{z}, @var{v}, [4 3 2]);
+## @end group
+## @end example
+##
+## @seealso{isosurface, isonormals}
+## @end deftypefn
+
+## Author: mmuetzel
+
+function [nx, ny, nz, nv] = reducevolume (varargin)
+
+  if (nargin < 2 || nargin > 5)
+    print_usage ();
+  endif
+
+  [x, y, z, v, r] = __get_check_reducevolume_args__ (nargout, varargin{:});
+
+  [nx, ny, nz, nv] = __reducevolume__ (x, y, z, v, r);
+
+  if (nargout <= 1)
+    nx = nv;
+  endif
+
+endfunction
+
+function [x, y, z, v, r] = __get_check_reducevolume_args__ (naout, varargin)
+
+  x = y = z = [];
+
+  switch (nargin)
+    case 3
+      v = varargin{1};
+      r = varargin{2};
+
+    case 6
+      if (naout == 4)
+        x = varargin{1};
+        y = varargin{2};
+        z = varargin{3};
+      endif
+      v = varargin{4};
+      r = varargin{5};
+
+    otherwise
+      error ("reducevolume: incorrect number of arguments");
+
+  endswitch
+
+  ## Check reduction values R
+  if (isscalar (r))
+    r = [r, r, r];
+  elseif (numel (r) != 3)
+    error (["reducevolume: reduction value R must be a scalar or " ...
+            "a vector of length 3"]);
+  endif
+
+  if (any (r < 1 | r != fix (r)))
+    error ("reducevolume: reduction values R must be positive integers");
+  endif
+
+  ## Check dimensions of data
+  if (ndims (v) < 3)
+    error ("reducevolume: data V must have at least 3 dimensions");
+  endif
+
+  v_sz = size (v);
+  if (any (v_sz(1:3) < 2))
+    error ("reducevolume: data must be a non-singleton 3-dimensional matrix");
+  endif
+
+  if (naout == 4)
+    if (isempty (x))
+      x = 1:size (v, 2);
+    endif
+    if (isempty (y))
+      y = 1:size (v, 1);
+    endif
+    if (isempty (z))
+      z = 1:size (v, 3);
+    endif
+
+    ## check x
+    if (isvector (x) && length (x) == v_sz(2))
+      x = repmat (x(:)', [v_sz(1) 1 v_sz(3)]);
+    elseif (! size_equal (v, x))
+      error ("reducevolume: X must match the size of data V");
+    endif
+
+    ## check y
+    if (isvector (y) && length (y) == v_sz(1))
+      y = repmat (y(:), [1 v_sz(2) v_sz(3)]);
+    elseif (! size_equal (v, y))
+      error ("reducevolume: Y must match the size of data V");
+    endif
+
+    ## check z
+    if (isvector (z) && length (z) == v_sz(3))
+      z = repmat (reshape (z(:), [1 1 length(z)]), ...
+                  [v_sz(1) v_sz(2) 1]);
+    elseif (! size_equal (v, z))
+      error ("reducevolume: Z must match the size of data V");
+    endif
+
+  endif
+
+endfunction
+
+function [nx, ny, nz, nv] = __reducevolume__ (x, y, z, v, r)
+
+  v_sz = size (v);
+  nv = v(1:r(2):end, 1:r(1):end, 1:r(3):end, :);
+  nv_sz = size (nv);
+  if (length (nv_sz) < 3 || min (nv_sz) < 2)
+    error ("reducevolume: reduction value R is too high");
+  endif
+  if (length (v_sz) > 3)
+    nv = reshape (nv, [nv_sz(1:3) v_sz(4:end)]);
+  endif
+
+  if (isempty (x))
+    nx = ny = nz = [];
+  else
+    nx = x(1:r(2):end, 1:r(1):end, 1:r(3):end);
+    ny = y(1:r(2):end, 1:r(1):end, 1:r(3):end);
+    nz = z(1:r(2):end, 1:r(1):end, 1:r(3):end);
+  endif
+
+endfunction
+
+
+%!shared v, x, y, z, xx, yy, zz
+%! v = reshape (1:6*8*4, [6 8 4]);
+%! x = 1:3:22;  y = -14:5:11;  z = linspace (16, 18, 4);
+%! [xx, yy, zz] = meshgrid (x, y, z);
+
+## two inputs, one output
+%!test
+%! nv = reducevolume (v, [4 3 2]);
+%! nv_expected = [1 25; 4 28];  nv_expected(:,:,2) = [97 121; 100 124]; 
+%! assert (nv, nv_expected);
+
+## two inputs, four outputs
+%!test
+%! [nx, ny, nz, nv] = reducevolume (v, [4 3 2]);
+%! nx_expected(1:2,1,1:2) = 1;  nx_expected(:,2,:) = 5;
+%! ny_expected(1,1:2,1:2) = 1;  ny_expected(2,:,:) = 4;
+%! nz_expected(1:2,1:2,1) = 1;  nz_expected(:,:,2) = 3;
+%! nv_expected = [1 25; 4 28];  nv_expected(:,:,2) = [97 121; 100 124]; 
+%! assert (nx, nx_expected);
+%! assert (ny, ny_expected);
+%! assert (nz, nz_expected);
+%! assert (nv, nv_expected);
+
+## five inputs, one output
+%!test
+%! nv = reducevolume (x, y, z, v, [4 3 2]);
+%! nv_expected = [1 25; 4 28];  nv_expected(:,:,2) = [97 121; 100 124]; 
+%! assert (nv, nv_expected);
+
+## five inputs, four outputs (coordinates are vectors)
+%!test
+%! [nx, ny, nz, nv] = reducevolume (x, y, z, v, [4 3 2]);
+%! nx_expected(1:2,1,1:2) = x(1); nx_expected(:,2,:) = x(5);
+%! ny_expected(1,1:2,1:2) = y(1); ny_expected(2,:,:) = y(4);
+%! nz_expected(1:2,1:2,1) = z(1); nz_expected(:,:,2) = z(3);
+%! nv_expected = [1 25; 4 28]; nv_expected(:,:,2) = [97 121; 100 124]; 
+%! assert (nx, nx_expected);
+%! assert (ny, ny_expected);
+%! assert (nz, nz_expected);
+%! assert (nv, nv_expected);
+
+## five inputs, four outputs (coordinates are matrices)
+%!test
+%! [nx, ny, nz, nv] = reducevolume (xx, yy, zz, v, [4 3 2]);
+%! nx_expected(1:2,1,1:2) = x(1); nx_expected(:,2,:) = x(5);
+%! ny_expected(1,1:2,1:2) = y(1); ny_expected(2,:,:) = y(4);
+%! nz_expected(1:2,1:2,1) = z(1); nz_expected(:,:,2) = z(3);
+%! nv_expected = [1 25; 4 28]; nv_expected(:,:,2) = [97 121; 100 124]; 
+%! assert (nx, nx_expected);
+%! assert (ny, ny_expected);
+%! assert (nz, nz_expected);
+%! assert (nv, nv_expected);
+
+## five inputs, four outputs (coordinates are matrices, R is scalar)
+%!test
+%! [nx, ny, nz, nv] = reducevolume (xx, yy, zz, v, 3);
+%! nx_expected(1:2,1,1:2) = x(1); nx_expected(:,2,:) = x(4);
+%! nx_expected(:,3,:) = x(7);
+%! ny_expected(1,1:3,1:2) = y(1); ny_expected(2,:,:) = y(4);
+%! nz_expected(1:2,1:3,1) = z(1); nz_expected(:,:,2) = z(4);
+%! nv_expected = [1 19 37; 4 22 40];
+%! nv_expected(:,:,2) = [145 163 181; 148 166 184]; 
+%! assert (nx, nx_expected);
+%! assert (ny, ny_expected);
+%! assert (nz, nz_expected);
+%! assert (nv, nv_expected);
+
+## Test for each error
+%!test
+%!error reducevolume ()
+%!error reducevolume (1)
+%!error reducevolume (1,2,3,4,5,6)
+%!error <incorrect number of arguments> reducevolume (1, 2, 3)
+%!error <R must be a scalar or a vector of length 3> reducevolume (v, [])
+%!error <R must be a scalar or a vector of length 3> reducevolume (v, [1 2])
+%!error <reduction values R must be positive integers> reducevolume (v, 0)
+%!error <reduction values R must be positive integers> reducevolume (v, 1.5)
+%!error <data V must have at least 3 dimensions>
+%! v = reshape(1:6*8, [6 8]);
+%! [nv] = reducevolume (v, [4 3 2]);
+%!error <data must be a non-singleton 3-dimensional matrix>
+%! v = reshape(1:6*8, [6 1 8]);
+%! nv = reducevolume (v, [4 3 2]);
+%!error <X must match the size of data V>
+%! x = 1:2:24;
+%! [nx, ny, nz, nv] = reducevolume (x, y, z, v, [4 3 2]);
+%!error <Y must match the size of data V>
+%! y = -14:6:11;
+%! [nx, ny, nz, nv] = reducevolume (x, y, z, v, [4 3 2]);
+%!error <Z must match the size of data V>
+%! z = linspace (16, 18, 5);
+%! [nx, ny, nz, nv] = reducevolume (x, y, z, v, [4 3 2]);
+%!error <reduction value R is too high> [nv] = reducevolume (v, 5)
+%!error <reduction value R is too high> [nv] = reducevolume (v, [4 7 2])
+