meshunitsphere

 [node,face,elem]=meshunitsphere(tsize,maxvol)

 create the surface and/or volumetric mesh of a unit sphere 
 centered at [0 0 0] and radius 1

 author: Qianqian Fang, <q.fang at neu.edu>

 input: 
   tsize: maximum size of the surface triangles (from 0 to 1)
   maxvol: maximum volume of the tetrahedron; if one wants to return
           elem without specifying maxvol, maxvol=tsize^3

 output:
   node: node coordinates, 3 columns for x, y and z respectively
   face: integer array with dimensions of NB x 3, each row represents
         a surface mesh face element 
   elem: integer array with dimensions of NE x 4, each row represents
         a tetrahedron. If ignored, this function only produces the surface

 example:
   [node,face]=meshunitsphere(0.05);
   [node,face,elem]=meshunitsphere(0.05,0.01);
   plotmesh(node,elem,'x>0'); axis equal;

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

0001 function [node,face,elem]=meshunitsphere(tsize,maxvol)
0002 %
0003 % [node,face,elem]=meshunitsphere(tsize,maxvol)
0004 %
0005 % create the surface and/or volumetric mesh of a unit sphere
0006 % centered at [0 0 0] and radius 1
0007 %
0008 % author: Qianqian Fang, <q.fang at neu.edu>
0009 %
0010 % input:
0011 %   tsize: maximum size of the surface triangles (from 0 to 1)
0012 %   maxvol: maximum volume of the tetrahedron; if one wants to return
0013 %           elem without specifying maxvol, maxvol=tsize^3
0014 %
0015 % output:
0016 %   node: node coordinates, 3 columns for x, y and z respectively
0017 %   face: integer array with dimensions of NB x 3, each row represents
0018 %         a surface mesh face element
0019 %   elem: integer array with dimensions of NE x 4, each row represents
0020 %         a tetrahedron. If ignored, this function only produces the surface
0021 %
0022 % example:
0023 %   [node,face]=meshunitsphere(0.05);
0024 %   [node,face,elem]=meshunitsphere(0.05,0.01);
0025 %   plotmesh(node,elem,'x>0'); axis equal;
0026 %
0027 % -- this function is part of iso2mesh toolbox (http://iso2mesh.sf.net)
0028 %
0029 
0030 dim=60;
0031 esize=tsize*dim;
0032 thresh=dim/2-1;
0033 [xi,yi,zi]=meshgrid(0:0.5:dim,0:0.5:dim,0:0.5:dim);
0034 dist=thresh-sqrt((xi-30).^2+(yi-30).^2+(zi-30).^2);
0035 dist(find(dist<0))=0;
0036 clear xi yi zi;
0037 
0038 % extract a level-set at v=thresh, being a sphere with R=thresh
0039 % the maximum element size of the surface triangles is tsize*dim
0040 
0041 [node,face]=vol2restrictedtri(dist,1,[dim dim dim],dim*dim*dim,30,esize,esize,40000);
0042 node=(node-0.5)*0.5;
0043 
0044 [node,face]=removeisolatednode(node,face);
0045 
0046 node=(node-30)/28;
0047 r0=sqrt(sum((node.*node)'));
0048 node=node.*repmat(1./r0(:),1,3);
0049 
0050 if(nargout==3)
0051    if(nargin==1) maxvol=tsize*tsize*tsize; end
0052    [node,elem,face]=surf2mesh(node,face,[-1 -1 -1]*1.1,[1 1 1]*1.1,1,maxvol,[],[]);
0053    elem=elem(:,1:4);
0054 end
0055 face=face(:,1:3);