smoothsurf

 p=smoothsurf(node,mask,conn,iter,useralpha,usermethod,userbeta)

 smoothing a surface mesh

 author: Qianqian Fang, <q.fang at neu.edu>
 date: 2007/11/21

 input:
    node:  node coordinates of a surface mesh
    mask:  flag whether a node is movable: 0 movable, 1 non-movable
           if mask=[], it assumes all nodes are movable
    conn:  input, a cell structure of length size(node), conn{n}
           contains a list of all neighboring node ID for node n,
           this can be computed from meshconn function
    iter:  smoothing iteration number
    useralpha: scaler, smoothing parameter, v(k+1)=(1-alpha)*v(k)+alpha*mean(neighbors)
    usermethod: smoothing method, including 'laplacian','laplacianhc' and 'lowpass'
    userbeta: scaler, smoothing parameter, for 'laplacianhc'

 output:
    p: output, the smoothed node coordinates

 recommendations
    Based on [Bade2006], 'Lowpass' method outperforms 'Laplacian-HC' in volume
    preserving and both are significantly better than the standard Laplacian method

    [Bade2006]  R. Bade, H. Haase, B. Preim, "Comparison of Fundamental Mesh 
                Smoothing Algorithms for Medical Surface Models," 
                Simulation and Visualization, pp. 289-304, 2006. 

 -- this function is part of iso2mesh toolbox (http://iso2mesh.sf.net)

0001 function p=smoothsurf(node,mask,conn,iter,useralpha,usermethod,userbeta)
0002 %
0003 % p=smoothsurf(node,mask,conn,iter,useralpha,usermethod,userbeta)
0004 %
0005 % smoothing a surface mesh
0006 %
0007 % author: Qianqian Fang, <q.fang at neu.edu>
0008 % date: 2007/11/21
0009 %
0010 % input:
0011 %    node:  node coordinates of a surface mesh
0012 %    mask:  flag whether a node is movable: 0 movable, 1 non-movable
0013 %           if mask=[], it assumes all nodes are movable
0014 %    conn:  input, a cell structure of length size(node), conn{n}
0015 %           contains a list of all neighboring node ID for node n,
0016 %           this can be computed from meshconn function
0017 %    iter:  smoothing iteration number
0018 %    useralpha: scaler, smoothing parameter, v(k+1)=(1-alpha)*v(k)+alpha*mean(neighbors)
0019 %    usermethod: smoothing method, including 'laplacian','laplacianhc' and 'lowpass'
0020 %    userbeta: scaler, smoothing parameter, for 'laplacianhc'
0021 %
0022 % output:
0023 %    p: output, the smoothed node coordinates
0024 %
0025 % recommendations
0026 %    Based on [Bade2006], 'Lowpass' method outperforms 'Laplacian-HC' in volume
0027 %    preserving and both are significantly better than the standard Laplacian method
0028 %
0029 %    [Bade2006]  R. Bade, H. Haase, B. Preim, "Comparison of Fundamental Mesh
0030 %                Smoothing Algorithms for Medical Surface Models,"
0031 %                Simulation and Visualization, pp. 289-304, 2006.
0032 %
0033 % -- this function is part of iso2mesh toolbox (http://iso2mesh.sf.net)
0034 %
0035 
0036 p=node;
0037 if(isempty(mask))
0038     nn=size(node,1);
0039     idx=1:nn;
0040 else
0041     idx=find(mask==0)';
0042     nn=length(idx);
0043 end
0044 alpha=0.5;
0045 method='laplacian';
0046 beta=0.5;
0047 if(nargin>4)
0048     alpha=useralpha;
0049     if(nargin>5)
0050         method=usermethod;
0051         if(nargin>6)
0052             beta=userbeta;
0053         end
0054     end
0055 end
0056 ibeta=1-beta;
0057 ialpha=1-alpha;
0058 
0059 for i=1:nn
0060     if(length(conn{idx(i)})==0)
0061         idx(i)=0;
0062     end
0063 end
0064 idx=idx(idx>0);
0065 nn=length(idx);
0066 
0067 if(strcmp(method,'laplacian'))
0068     for j=1:iter
0069         for i=1:nn
0070             p(idx(i),:)=ialpha*p(idx(i),:)+alpha*mean(node(conn{idx(i)},:)); 
0071         end
0072         node=p;
0073     end
0074 elseif(strcmp(method,'laplacianhc'))
0075     for j=1:iter
0076         q=p;
0077         for i=1:nn
0078             p(idx(i),:)=mean(q(conn{idx(i)},:));
0079         end
0080         b=p-(alpha*node+ialpha*q);
0081         for i=1:nn
0082             p(idx(i),:)=p(idx(i),:)-(beta*b(i,:)+ibeta*mean(b(conn{idx(i)},:))); 
0083         end
0084     end
0085 elseif(strcmp(method,'lowpass'))
0086     beta=-1.02*alpha;
0087     ibeta=1-beta;
0088     for j=1:iter
0089         for i=1:nn
0090             p(idx(i),:)=ialpha*node(idx(i),:)+alpha*mean(node(conn{idx(i)},:)); 
0091         end
0092         node=p;
0093         for i=1:nn
0094             p(idx(i),:)=ibeta *node(idx(i),:)+beta *mean(node(conn{idx(i)},:)); 
0095         end
0096         node=p;
0097     end
0098 end