--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/scripts/plot/draw/private/__interp_cube__.m	Fri Oct 04 17:09:08 2013 -0700
@@ -0,0 +1,185 @@
+## Copyright (C) 2009-2012 Martin Helm
+##
+## 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/>.
+##
+## Author: Martin Helm <martin@mhelm.de>
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {[@var{vxyz}, @var{idx}, @var{frac}] =} __interp_cube__ (@var{x}, @var{y}, @var{z}, @var{val}, @var{v})
+## Undocumented internal function.
+## @end deftypefn
+
+function [Vxyz, idx, frac] = __interp_cube__ (x, y, z, val, v, req = "values" )
+  if (ismatrix (x) && ndims (x) == 3 && ismatrix (y) && ndims (y) == 3
+       && ismatrix (z) && ndims (z) == 3 && size_equal (x, y, z, val))
+    x = squeeze (x(1,:,1))(:);
+    y = squeeze (y(:,1,1))(:);
+    z = squeeze (z(1,1,:))(:);
+  elseif (isvector (x) && isvector (y) && isvector (z))
+    x = x(:);
+    y = y(:);
+    z = z(:);
+  else
+    error ("__interp_cube__: X, Y, Z have wrong dimensions");
+  endif
+  if (size (val) != [length(x), length(y), length(z)])
+    error ("__interp_cube__: VAL has wrong dimensions");
+  endif
+  if (columns (v) != 3)
+    error ( "V has to be Nx3 matrix");
+  endif
+  ##if (!ischar (req))
+  ## error ('__interp_cube__: Invalid request parameter use "values", "normals" or "normals8"');
+  ##endif
+  if (isempty (v))
+    Vxyz = idx = frac = [];
+    return;
+  endif
+
+  switch (req)
+    case "normals"
+      [idx, frac] = cube_idx (x, y, z, v);
+
+      dx = x(2:end) - x(1:end-1);
+      dy = y(2:end) - y(1:end-1);
+      dz = z(2:end) - z(1:end-1);
+      dx = 0.5 .* [dx;dx(end)](idx(:,2));
+      dy = 0.5 .* [dy;dy(end)](idx(:,1));
+      dz = 0.5 .* [dz;dz(end)](idx(:,3));
+
+      p000 = [v(:, 1) - dx, v(:, 2) - dy, v(:, 3) - dz];
+      p100 = [v(:, 1) + dx, v(:, 2) - dy, v(:, 3) - dz];
+      p010 = [v(:, 1) - dx, v(:, 2) + dy, v(:, 3) - dz];
+      p001 = [v(:, 1) - dx, v(:, 2) - dy, v(:, 3) + dz];
+      p011 = [v(:, 1) - dx, v(:, 2) + dy, v(:, 3) + dz];
+      p101 = [v(:, 1) + dx, v(:, 2) - dy, v(:, 3) + dz];
+      p110 = [v(:, 1) + dx, v(:, 2) + dy, v(:, 3) - dz];
+      p111 = [v(:, 1) + dx, v(:, 2) + dy, v(:, 3) + dz];
+
+      v000 = interp_cube_trilin (x, y, z, val, p000);
+      v100 = interp_cube_trilin (x, y, z, val, p100);
+      v010 = interp_cube_trilin (x, y, z, val, p010);
+      v001 = interp_cube_trilin (x, y, z, val, p001);
+      v011 = interp_cube_trilin (x, y, z, val, p011);
+      v101 = interp_cube_trilin (x, y, z, val, p101);
+      v110 = interp_cube_trilin (x, y, z, val, p110);
+      v111 = interp_cube_trilin (x, y, z, val, p111);
+
+      Dx = -v000 .+ v100 .- v010 .- v001 .- v011 .+ v101 .+ v110 .+ v111;
+      Dy = -v000 .- v100 .+ v010 .- v001 .+ v011 .- v101 .+ v110 .+ v111;
+      Dz = -v000 .- v100 .- v010 .+ v001 .+ v011 .+ v101 .- v110 .+ v111;
+      Vxyz = 0.5 .* [Dx./dx, Dy./dy, Dz./dz];
+    case "normals8"
+      [idx, frac] = cube_idx (x, y, z, v);
+
+      dx = x(2:end) - x(1:end-1);
+      dy = y(2:end) - y(1:end-1);
+      dz = z(2:end) - z(1:end-1);
+      dx = [dx;dx(end)](idx(:,2));
+      dy = [dy;dy(end)](idx(:,1));
+      dz = [dz;dz(end)](idx(:,3));
+      [Dx, Dy, Dz, idx, frac] = interp_cube_trilin_grad (x, y, z, val, v);
+      Vxyz = [Dx./dx, Dy./dy, Dz./dz];
+    case "values"
+      [Vxyz, idx, frac] = interp_cube_trilin (x, y, z, val, v);
+   otherwise
+     error ('__interp_cube__: Invalid request type "%s", use "values", "normals" or "normals8"', req);
+  endswitch
+endfunction
+
+function [Vxyz, idx, frac] = interp_cube_trilin (x, y, z, val, v)
+  [idx, frac] = cube_idx (x(:), y(:), z(:), v);
+  sval = size (val);
+  i000 = sub2ind (sval, idx(:, 1), idx(:, 2), idx(:, 3));
+  i100 = sub2ind (sval, idx(:, 1)+1, idx(:, 2), idx(:, 3));
+  i010 = sub2ind (sval, idx(:, 1), idx(:, 2)+1, idx(:, 3));
+  i001 = sub2ind (sval, idx(:, 1), idx(:, 2), idx(:, 3)+1);
+  i101 = sub2ind (sval, idx(:, 1)+1, idx(:, 2), idx(:, 3)+1);
+  i011 = sub2ind (sval, idx(:, 1), idx(:, 2)+1, idx(:, 3)+1);
+  i110 = sub2ind (sval, idx(:, 1)+1, idx(:, 2)+1, idx(:, 3));
+  i111 = sub2ind (sval, idx(:, 1)+1, idx(:, 2)+1, idx(:, 3)+1 );
+  Bx = frac(:, 1);
+  By = frac(:, 2);
+  Bz = frac(:, 3);
+  Vxyz = ...
+    val( i000 ) .* (1 .- Bx) .* (1 .- By) .* (1 .- Bz) .+ ...
+    val( i100 ) .* Bx .* (1 .- By) .* (1 .- Bz) .+ ...
+    val( i010 ) .* (1 .- Bx) .* By .* (1 .- Bz) .+ ...
+    val( i001 ) .* (1 .- Bx) .* (1 .- By) .* Bz .+ ...
+    val( i011 ) .* (1 .- Bx) .* By .* Bz .+ ...
+    val( i101 ) .* Bx .* (1 .- By) .* Bz .+ ...
+    val( i110 ) .* Bx .* By .* (1 .- Bz) .+ ...
+    val( i111 ) .* Bx .* By .* Bz;
+endfunction
+
+function [Dx, Dy, Dz, idx, frac] = interp_cube_trilin_grad (x, y, z, val, v)
+  [idx, frac] = cube_idx (x(:), y(:), z(:), v);
+  sval = size (val);
+  i000 = sub2ind (sval, idx(:, 1), idx(:, 2), idx(:, 3));
+  i100 = sub2ind (sval, idx(:, 1)+1, idx(:, 2), idx(:, 3));
+  i010 = sub2ind (sval, idx(:, 1), idx(:, 2)+1, idx(:, 3));
+  i001 = sub2ind (sval, idx(:, 1), idx(:, 2), idx(:, 3)+1);
+  i101 = sub2ind (sval, idx(:, 1)+1, idx(:, 2), idx(:, 3)+1);
+  i011 = sub2ind (sval, idx(:, 1), idx(:, 2)+1, idx(:, 3)+1);
+  i110 = sub2ind (sval, idx(:, 1)+1, idx(:, 2)+1, idx(:, 3));
+  i111 = sub2ind (sval, idx(:, 1)+1, idx(:, 2)+1, idx(:, 3)+1 );
+  Bx = frac(:, 1);
+  By = frac(:, 2);
+  Bz = frac(:, 3);
+  Dx = ...
+    val( i000 ) .* -1 .* (1 .- By) .* (1 .- Bz) .+ ...
+    val( i100 ) .* (1 .- By) .* (1 .- Bz) .+ ...
+    val( i010 ) .* -1 .* By .* (1 .- Bz) .+ ...
+    val( i001 ) .* -1 .* (1 .- By) .* Bz .+ ...
+    val( i011 ) .* -1 .* By .* Bz .+ ...
+    val( i101 ) .* (1 .- By) .* Bz .+ ...
+    val( i110 ) .* By .* (1 .- Bz) .+ ...
+    val( i111 ) .* By .* Bz;
+  Dy = ...
+    val( i000 ) .* (1 .- Bx) .* -1 .* (1 .- Bz) .+ ...
+    val( i100 ) .* Bx .* -1 .* (1 .- Bz) .+ ...
+    val( i010 ) .* (1 .- Bx) .* (1 .- Bz) .+ ...
+    val( i001 ) .* (1 .- Bx) .* -1 .* Bz .+ ...
+    val( i011 ) .* (1 .- Bx) .* Bz .+ ...
+    val( i101 ) .* Bx .* -1 .* Bz .+ ...
+    val( i110 ) .* Bx .* (1 .- Bz) .+ ...
+    val( i111 ) .* Bx .* Bz;
+  Dz = ...
+    val( i000 ) .* (1 .- Bx) .* (1 .- By) .* -1 .+ ...
+    val( i100 ) .* Bx .* (1 .- By) .* -1 .+ ...
+    val( i010 ) .* (1 .- Bx) .* By .* -1 .+ ...
+    val( i001 ) .* (1 .- Bx) .* (1 .- By) .+ ...
+    val( i011 ) .* (1 .- Bx) .* By + ...
+    val( i101 ) .* Bx .* (1 .- By) .+ ...
+    val( i110 ) .* Bx .* By .* -1 .+ ...
+    val( i111 ) .* Bx .* By;
+endfunction
+
+function [idx, frac] = cube_idx (x, y, z, v)
+  idx = zeros (size (v));
+  frac = zeros (size (v));
+  idx(:, 2) = lookup (x(2:end-1), v(:, 1)) + 1;
+  frac(:, 2) = (v(:, 1) - x(idx(:, 2)) )...
+      ./ (x(idx(:, 2)+1) - x(idx(:, 2)));
+  idx(:, 1) = lookup (y(2:end-1), v(:, 2)) + 1;
+  frac(:, 1) = (v(:, 2) - y(idx(:, 1))) ...
+      ./ (y(idx(:, 1)+1) - y(idx(:, 1)));
+  idx(:, 3) = lookup (z(2:end-1), v(:, 3)) + 1;
+  frac(:, 3) = (v(:, 3) - z(idx(:, 3))) ...
+      ./ (z(idx(:, 3)+1) - z(idx(:, 3)));
+endfunction
+