function ret = smooth3(data, filt, sz, arg)
%SMOOTH3  Smooth 3D data.
%   W = SMOOTH3(V) smoothes input data V. The smoothed data is returned
%       in W.
%   
%   W = SMOOTH3(V, 'filter') Filter can be 'gaussian' or 'box' (default)
%       and determines the convolution kernel.
%   
%   W = SMOOTH3(V, 'filter', SIZE) sets the size of the convolution
%   kernel (default is [3 3 3]). If SIZE is a scalar, the size is 
%   interpreted as [SIZE SIZE SIZE].
%   
%   W = SMOOTH3(V, 'filter', SIZE, ARG) sets an attribute of the
%   convolution kernel. When filter is 'gaussian', ARG is the standard
%   deviation (default is .65).
%
%   Example:
%      data = rand(10,10,10);
%      data = smooth3(data,'box',5);
%      p = patch(isosurface(data,.5), ...
%          'FaceColor', 'blue', 'EdgeColor', 'none');
%      p2 = patch(isocaps(data,.5), ...
%          'FaceColor', 'interp', 'EdgeColor', 'none');
%      isonormals(data,p)
%      view(3); axis vis3d tight
%      camlight; lighting phong
%
%   See also ISOSURFACE, ISOCAPS, ISONORMALS, SUBVOLUME, REDUCEVOLUME,
%            REDUCEPATCH.

%   Copyright 1984-2000 The MathWorks, Inc. 
%   $Revision: 1.4 $  $Date: 2000/06/02 04:30:56 $


if nargin==1      % smooth3(data)
  filt = 'b';
  sz = 3;
  arg = .65;
elseif nargin==2 % smooth3(data, filter)
  sz = 3;
  arg = .65;
elseif nargin==3 % smooth3(data, filter, sz)
  arg = .65;
elseif nargin>4 | nargin==0
  error('Wrong number of input arguments.'); 
end

if ndims(data)~=3
  error('V must be a 3D array.');
end

if length(sz)==1
  sz = [sz sz sz];
elseif prod(size(sz))~=3
  error('SIZE must be a scalar or a 3 element vector.')
end

sz = sz(:)';

padSize = (sz-1)/2;

if ~isequal(padSize, floor(padSize)) | any(padSize<0)
  error('All elements of SIZE must be odd integers greater than or equal to 1.');
end

f = lower(filt);

if filt(1)=='g' %gaussian
  smooth = gaussian3(sz,arg);
elseif filt(1)=='b' %box
  smooth = ones(sz)/prod(sz);
else
  error('Unknown filter.');
end

ret=convn(padreplicate(data,padSize),smooth, 'valid');


function h = gaussian3(P1, P2)
%3D Gaussian lowpass filter
%
%   H = gausian3(N,SIGMA) returns a rotationally
%   symmetric 3D Gaussian lowpass filter with standard deviation
%   SIGMA (in pixels). N is a 1-by-3 vector specifying the number
%   of rows, columns, pages in H. (N can also be a scalar, in 
%   which case H is NxNxN.) If you do not specify the parameters,
%   the default values of [3 3 3] for N and 0.65 for
%   SIGMA.


if nargin>0,
  if ~(all(size(P1)==[1 1]) | all(size(P1)==[1 3])),
     error('The first parameter must be a scalar or a 1-by-3 size vector.');
  end
  if length(P1)==1, siz = [P1 P1 P1]; else siz = P1; end
end

if nargin<1, siz = [3 3 3]; end
if nargin<2, std = .65; else std = P2; end
[x,y,z] = meshgrid(-(siz(2)-1)/2:(siz(2)-1)/2, -(siz(1)-1)/2:(siz(1)-1)/2, -(siz(3)-1)/2:(siz(3)-1)/2);
h = exp(-(x.*x + y.*y + z.*z)/(2*std*std*std));
h = h/sum(h(:));


function b=padreplicate(a, padSize)
%Pad an array by replicating values.
numDims = length(padSize);
idx = cell(numDims,1);
for k = 1:numDims
  M = size(a,k);
  onesVector = ones(1,padSize(k));
  idx{k} = [onesVector 1:M M*onesVector];
end

b = a(idx{:});
