1. Iso2mesh Function List

1.1. Streamlined mesh generation - shortcuts

function [node,elem,face]=v2m(img,isovalues,opt,maxvol,method)

 [node,elem,face]=v2m(img,isovalues,opt,maxvol,method)
 volumetric mesh generation from binary or gray-scale volumetric images
 shortcut for vol2mesh
 inputs and outputs are similar to those defined in vol2mesh

function [no,el,regions,holes]=v2s(img,isovalues,opt,method)

 [no,el,regions,holes]=v2s(img,isovalues,opt,method)
 surface mesh generation from binary or gray-scale volumetric images
 shortcut for vol2surf
 inputs and outputs are similar to those defined in vol2surf

function [node,elem,face]=s2m(v,f,keepratio,maxvol)

 [node,elem,face]=s2m(v,f,keepratio,maxvol)
 volumetric mesh generation from a closed surface, shortcut for surf2mesh
 inputs and outputs are similar to those defined in surf2mesh

function img=s2v(node,face,div)

 img=s2v(node,face,div)
 shortcut for surf2vol, coverting a surface to a volumetric image
 input:
	 node: node list of the triangular surface, 3 columns for x/y/z
	 face: triangle node indices, each row is a triangle
	 div:  division number along the shortest edge of the mesh (resolution)
              if not given, div=50
 output:
	 img: a volumetric binary image at position of ndgrid(xi,yi,zi)

function newnode=sms(node,face,iter,alpha,method)

 newnode=sms(node,face,iter,useralpha,method)
 simplified version of surface mesh smoothing
 input:
    node:  node coordinates of a surface mesh
    face:  face element list of the surface mesh
    iter:  smoothing iteration number
    alpha: scaler, smoothing parameter, v(k+1)=alpha*v(k)+(1-alpha)*mean(neighbors)
    method: same as in smoothsurf, default is 'laplacianhc'
 output:
    newnode: output, the smoothed node coordinates

1.2. Streamlined mesh generation

function [node,elem,face,regions]=vol2mesh(img,ix,iy,iz,opt,maxvol,dofix,method,isovalues)

 [node,elem,face,regions]=vol2mesh(img,ix,iy,iz,opt,maxvol,dofix,method,isovalues)
 convert a binary (or multi-valued) volume to tetrahedral mesh
 input:
	 img: a volumetric binary image
	 ix,iy,iz: subvolume selection indices in x,y,z directions
	 opt: as defined in vol2surf.m
	 maxvol: target maximum tetrahedral elem volume
	 dofix: 1: perform mesh validation&repair, 0: skip repairing
	 method: 'cgalsurf' or omit: use CGAL surface mesher
		 'simplify': use binsurface and then simplify
		 'cgalmesh': use CGAL 3.5 3D mesher for direct mesh generation [new]
		 generally speaking, 'cgalmesh' is the most robust path
		 if you want to product meshes from binary or multi-region
		 volumes, however, its limitations include 1) only accept 
		 uint8 volume, and 2) can not extract meshes from gray-scale
		 volumes. If ones goal is to process a gray-scale volume,
		 he/she should use the 'cgalsurf' option. 'simplify' approach
		 is not recommended unless other options failed.
	 isovalues: a list of isovalues where the levelset is defined
 output:
	 node: output, node coordinates of the tetrahedral mesh
	 elem: output, element list of the tetrahedral mesh, the last 
	       column is the region ID
	 face: output, mesh surface element list of the tetrahedral mesh
	       the last column denotes the boundary ID
    region: optional output. if opt.autoregion is set to 1, region
          saves the interior points for each closed surface component

function [no,el,regions,holes]=vol2surf(img,ix,iy,iz,opt,dofix,method,isovalues)

 [no,el,regions,holes]=vol2surf(img,ix,iy,iz,opt,dofix,method,isovalues)
 converting a 3D volumetric image to surfaces
 input:
	 img: a volumetric binary image; if img is empty, vol2surf will
	      return user defined surfaces via opt.surf if it exists
	 ix,iy,iz: subvolume selection indices in x,y,z directions
	 opt: function parameters
	   if method is 'cgalsurf' or 'cgalpoly':
	     opt=a float number>1: max radius of the Delaunay sphere(element size) 
	     opt.radbound: same as above, max radius of the Delaunay sphere
	     opt.distbound: maximum deviation from the specified isosurfaces
	     opt(1,2,...).radbound: same as above, for each levelset
	   if method is 'simplify':
	     opt=a float number<1: compression rate for surf. simplification
	     opt.keeyratio=a float less than 1: same as above, same for all surf.
	     opt(1,2,..).keeyratio: setting compression rate for each levelset
	   opt(1,2,..).maxsurf: 1 - only use the largest disjointed surface
				0 - use all surfaces for that levelset
          opt(1,2,..).side: - 'upper': threshold at upper interface
                              'lower': threshold at lower interface
	   opt(1,2,..).maxnode: - the maximum number of surface node per levelset
	   opt(1,2,..).holes: user specified holes interior pt list
	   opt(1,2,..).regions: user specified regions interior pt list
	   opt(1,2,..).surf.{node,elem}: add additional surfaces
	   opt(1,2,..).{A,B}: linear transformation for each surface
	   opt.autoregion: if set to 1, vol2surf will try to determine 
              the interior points for each closed surface automatically
	 dofix: 1: perform mesh validation&repair, 0: skip repairing
	 method: - if method is 'simplify', iso2mesh will first call
		   binsurface to generate a voxel-based surface mesh and then
		   use meshresample/meshcheckrepair to create a coarser mesh;
		 - if method is 'cgalsurf', iso2mesh will call the surface
		   extraction program from CGAL to make surface mesh
		 - if method is not specified, 'cgalsurf' is assumed by default
	 isovalues: a list of isovalues where the levelset is defined
 output: 
	 no:  list of nodes on the resulting suface mesh, 3 columns for x,y,z
	 el:  list of trianglular elements on the surface, [n1,n2,n3,region_id]
	 regions: list of interior points for all sub-region, [x,y,z]
	 holes:   list of interior points for all holes, [x,y,z]

function [node,elem,face]=surf2mesh(v,f,p0,p1,keepratio,maxvol,regions,holes,forcebox)

 [node,elem,face]=surf2mesh(v,f,p0,p1,keepratio,maxvol,regions,holes,forcebox)
 create quality volumetric mesh from isosurface patches
 input parameters:
      v: input, isosurface node list, dimension (nn,3)
         if v has 4 columns, the last column specifies mesh density near each node
      f: input, isosurface face element list, dimension (be,3)
      p0: input, coordinates of one corner of the bounding box, p0=[x0 y0 z0]
      p1: input, coordinates of the other corner of the bounding box, p1=[x1 y1 z1]
      keepratio: input, percentage of elements being kept after the simplification
      maxvol: input, maximum tetrahedra element volume
      regions: list of regions, specifying by an internal point for each region
      holes: list of holes, similar to regions
      forcebox: 1: add bounding box, 0: automatic
 outputs:
      node: output, node coordinates of the tetrahedral mesh
      elem: output, element list of the tetrahedral mesh
      face: output, mesh surface element list of the tetrahedral mesh 
             the last column denotes the boundary ID

function img=surf2vol(node,face,xi,yi,zi)

 img=surf2vol(node,face,xi,yi,zi)
 convert a triangular surface to a shell of voxels in a 3D image
 input:
	 node: node list of the triangular surface, 3 columns for x/y/z
	 face: triangle node indices, each row is a triangle
	 xi,yi,zi: x/y/z grid for the resulting volume
 output:
	 img: a volumetric binary image at position of ndgrid(xi,yi,zi)

1.3. iso2mesh main function backend

function [node,elem]=binsurface(img,nface)

 [node,elem]=binsurface(img,nface)
 fast isosurface extraction from 3D binary images
 input: 
   img:  a 3D binary image
   nface: nface=3 or ignored - for triangular faces, 
          nface=4 - square faces
          nface=0 - return a boundary mask image via node
 output
   elem: integer array with dimensions of NE x nface, each row represents
         a surface mesh face element 
   node: node coordinates, 3 columns for x, y and z respectively
 the outputs of this subroutine can be easily plotted using 
     patch('Vertices',node,'faces',elem,'FaceVertexCData',node(:,3),
           'FaceColor','interp');
 if the surface mesh has triangular faces, one can plot it with
     trisurf(elem,node(:,1),node(:,2),node(:,3))

function [node,elem,face]=cgalv2m(vol,opt,maxvol)

 [node,elem,face]=cgalv2m(vol,opt,maxvol)
 wrapper for CGAL 3D mesher (CGAL 3.5 or up)
 convert a binary (or multi-valued) volume to tetrahedral mesh
 http://www.cgal.org/Manual/3.5/doc_html/cgal_manual/Mesh_3/Chapter_main.html
 input:
	 vol: a volumetric binary image
	 ix,iy,iz: subvolume selection indices in x,y,z directions
	 opt: parameters for CGAL mesher, if opt is a structure, then
	     opt.radbound: defines the maximum surface element size
	     opt.angbound: defines the miminum angle of a surface triangle
	     opt.distbound: defines the maximum distance between the 
		 center of the surface bounding circle and center of the 
		 element bounding sphere
	     opt.reratio:  maximum radius-edge ratio
	     if opt is a scalar, it only specifies radbound.
	 maxvol: target maximum tetrahedral elem volume
 output:
	 node: output, node coordinates of the tetrahedral mesh
	 elem: output, element list of the tetrahedral mesh, the last 
	      column is the region id
	 face: output, mesh surface element list of the tetrahedral mesh
	      the last column denotes the boundary ID
	      note: each triangle will appear twice in the face list with each
		    one attaches to each side of the interface. one can remove
		    the redundant triangles by unique(face(:,1:3),'rows')

function [node,elem,face]=cgals2m(v,f,opt,maxvol)

 [node,elem,face]=cgals2m(v,f,opt,maxvol)
 wrapper for CGAL 3D mesher (CGAL 3.5 and newer)
 convert a binary (or multi-valued) volume to tetrahedral mesh
 http://www.cgal.org/Manual/3.5/doc_html/cgal_manual/Mesh_3/Chapter_main.html
 input:
	 v: the node coordinate list of a surface mesh (nn x 3)
	 f: the face element list of a surface mesh (be x 3)
	 opt: parameters for CGAL mesher, if opt is a structure, then
	     opt.radbound: defines the maximum surface element size
	     opt.angbound: defines the miminum angle of a surface triangle
	     opt.distbound: defines the maximum distance between the 
		 center of the surface bounding circle and center of the 
		 element bounding sphere
	     opt.reratio:  maximum radius-edge ratio
	     if opt is a scalar, it only specifies radbound.
	 maxvol: target maximum tetrahedral elem volume
 output:
	 node: output, node coordinates of the tetrahedral mesh
	 elem: output, element list of the tetrahedral mesh, the last 
	      column is the region id
	 face: output, mesh surface element list of the tetrahedral mesh
	      the last column denotes the boundary ID

function [node,elem]=vol2restrictedtri(vol,thres,cent,brad,ang,radbound,distbound,maxnode)

 [node,elem]=vol2restrictedtri(vol,thres,cent,brad,ang,radbound,distbound,maxnode)
 surface mesh extraction using CGAL mesher
 input:
       vol: a 3D volumetric image
       thres: a scalar as the threshold of of the extraction
       cent: a 3d position (x,y,z) which locates inside the resulting
             mesh, this is automatically computed from vol2surf
       brad: maximum bounding sphere squared of the resulting mesh
       ang: minimum angular constrains of the resulting tranglar elements
            (in degrees)
       radbound: maximum triangle delaunay circle radius
       distbound: maximum delaunay sphere distances
       maxnode: maximum number of surface nodes (even radbound is not reached)
 output:
       node: the list of 3d nodes in the resulting surface (x,y,z)
       elem: the element list of the resulting mesh (3 columns of integers)

function img=surf2volz(node,face,xi,yi,zi)

 img=surf2volz(node,face,xi,yi,zi)
 convert a triangular surface to a shell of voxels in a 3D image
 along the z-axis
 input:
	 node: node list of the triangular surface, 3 columns for x/y/z
	 face: triangle node indices, each row is a triangle
	 xi,yi,zi: x/y/z grid for the resulting volume
 output:
	 img: a volumetric binary image at position of ndgrid(xi,yi,zi)

1.4. iso2mesh primitive meshing functions

function [node,elem,face]=meshabox(p0,p1,opt,nodesize)

 [node,elem,face]=meshabox(p0,p1,opt,maxvol)
 create the surface and tetrahedral mesh of a box geometry
 input: 
   p0:  coordinates (x,y,z) for one end of the box diagnoal
   p1:  coordinates (x,y,z) for the other end of the box diagnoal
   opt: maximum volume of the tetrahedral elements
   nodesize: 1 or a 8x1 array, size of the element near each vertex
 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 
 example:
   [node,elem,face]=meshabox([2 3 2],[6 12 15],0.1,1);
   plotmesh(node,elem,'x>4');

function [node,face,elem]=meshasphere(c0,r,tsize,maxvol)

 [node,face,elem]=meshasphere(c0,r,tsize,maxvol)
 create the surface and tetrahedral mesh of a sphere
 input: 
   c0:  center coordinates (x0,y0,z0) of the sphere
   r:   radius of the sphere
   tsize: maximum surface triangle size on the sphere
   maxvol: maximu volume of the tetrahedral elements
 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 

function [node,face,elem]=meshanellip(c0,rr,tsize,maxvol)

 [node,face,elem]=meshanellip(c0,rr,opt)
 create the surface and tetrahedral mesh of an ellipsoid
 input: 
   c0:  center coordinates (x0,y0,z0) of the ellipsoid
   rr:  radii of an ellipsoid, 
        if rr is a scalar, this is a sphere with radius rr
        if rr is a 1x3 or 3x1 vector, it specifies the ellipsoid radii [a,b,c]
        if rr is a 1x5 or 5x1 vector, it specifies [a,b,c,theta,phi]
           where theta and phi are the rotation angles along z and x 
           axes, respectively. Rotation is applied before translation.
   tsize: maximum surface triangle size on the sphere
   maxvol: maximu volume of the tetrahedral elements
 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, only produces the surface
 example:
   [node,face,elem]=meshanellip([10,10,-10],[30,20,10,pi/4,pi/4],0.5,0.4);
   plotmesh(node,elem,'x>10');axis equal;

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

 [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
 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;

1.5. Mesh decomposition and query

function facecell=finddisconnsurf(f)

 facecell=finddisconnsurf(f)
 subroutine to extract disconnected surfaces from a 
 cluster of surfaces
 Date: 2008/03/06
 input: 
     f: faces defined by node indices for all surface triangles
 output:
     facecell: separated disconnected surface node indices

function openedge=surfedge(f)

 openedge=surfedge(f)
 find the edge of an open surface or surface of a volume
 input:
      f: input, surface face element list, dimension (be,3)
 output:
      openedge: list of edges of the specified surface

function openface=volface(t)

 openface=volface(t)
 find the surface patches of a volume
 input:
      t: input, volumetric element list, dimension (ne,4)
 output:
      openface: list of faces of the specified volume

function loops=extractloops(edges)

 loops=extractloops(edges)
 extract individual loops from an edge table of a loop
 collection
 input:   
    edges:  two column matrix recording the starting/ending 
             points of all edge segments
 output:
    loops:  output, a single vector separated by NaN, each segment
             is a close-polygon consisted by node IDs

function [conn,connnum,count]=meshconn(elem,nn)

 [conn,connnum,count]=meshconn(elem,nn)
 create node neighbor list from a mesh
 input:
    elem:  element table of a mesh
    nn  :  total node number of the mesh
 output:
    conn:  output, a cell structure of length nn, conn{n}
           contains a list of all neighboring node ID for node n
    connnum: vector of length nn, denotes the neighbor number of each node
    count: total neighbor numbers

function centroid=meshcentroid(v,f)

 centroid=meshcentroid(v,f)
 compute the centroids of a mesh defined by nodes and elements
 (surface or tetrahedra) in R^n space
 input:
      v: surface node list, dimension (nn,3)
      f: surface face element list, dimension (be,3)
 output:
      centroid: centroid positions, one row for each element

function nodevol=nodevolume(node,elem)

 nodevol=nodevolume(node,elem)
 calculate the Voronoi volume of each node in a simplex mesh
 input:
    node:  node coordinates
    elem:  element table of a mesh
 output:
    nodevol:   volume values for all nodes

function vol=elemvolume(node,elem,option)

 vol=elemvolume(node,elem,option)
 calculate the volume for a list of simplexes
 input:
    node:  node coordinates
    elem:  element table of a mesh
    option: if option='signed', the volume is the raw determinant,
            else, the results will be the absolute values
 output
    vol:   volume values for all elements

function [conn,connnum,count]=neighborelem(elem,nn);

 [conn,connnum,count]=neighborelem(elem,nn)
 create node neighbor list from a mesh
 input:
    elem:  element table of a mesh
    nn  :  total node number of the mesh
 output:
    conn:  output, a cell structure of length nn, conn{n}
           contains a list of all neighboring elem ID for node n
    connnum: vector of length nn, denotes the neighbor number of each node
    count: total neighbor numbers

function facenb=faceneighbors(t,opt)

 facenb=faceneighbors(t,opt)
 to find 4 face-neighboring elements of a tetrahedron
 input:
     t: tetrahedron element list, 4 columns of integers
     opt: if opt='surface', return boundary triangle list 
          (should be the same as the face output from v2m)
          otherwise, return the element list for each element:
          each row contains 4 numbers, representing the element
          indices sharing triangular faces [1 2 3],[1 2 4],[1 3 4]
          and [2 3 4] in order, where 1~4 is the node local index.
          if the index is 0, indicating the face has no neighbor
          (i.e. a boundary face)
 output:
     facenb: see opt

function edgenb=edgeneighbors(t,opt)

 edgenb=edgeneighbors(t,opt)
 to find neighboring triangular elements in a triangule surface
 input:
     t: a triangular surface element list, 3 columns of integers
     opt: if opt='general', return the edge neighbors for a general
          triangular surface: each edge can be shared by more than 2
          triangles; if ignored, we assume all triangles are shared by no
          more than 2 triangles.
 output:
     edgenb: if opt is not supplied, edgenb is a size(t,1) by 3 array with
     each element being the triangle ID of the edge neighbor of that
     triangle. For each row, the order of the neighbors is listed as those
     sharing edges [1 2], [2 3] and [3 1] between the triangle nodes.
     when opt='general', edgenb is a cell array with a length of size(t).
     each member of the cell array is a list of edge neighbors (the order 
     is not defined).

function f=maxsurf(facecell)

 f=maxsurf(facecell)
 return the surface with the maximum element number (not 
 necessarily in area) from a cell arry of surfaces
 input:
    facecell: a cell array, each element is a face array
 output:
    f: the surface data (node indices) for the surface with most elements

function mask=flatsegment(node,edge)

 mask=flatsegment(node,edge)
 decompose edge loops into flat segments alone arbitrary planes of the bounding box
 this code is fragile: it can not handle curves with many co-linear
 nodes near the corner point
 input:   
    node:  x,y,z coordinates of each node of the mesh
    edge:  input, a single vector separated by NaN, each segment
           is a close-polygon consisted by node IDs 
 output:
    mask:  output, a cell, each element is a close-polygon 
           on x/y/z plane 

function newedge=orderloopedge(edge)

 [newedge]=orderloopedge(edge)
 order the node list of a simple loop based on connection sequence
 input: 
        edge: a loop consisted by a sequence of edges, each row 
              is an edge with two integers: start/end node index
 output:
        newedge: reordered edge node list

function [X,V,E,F]=mesheuler(face)

 [X,V,E,F]=mesheuler(face)
 Euler's charastistics of a mesh
 input: 
   face: a closed surface mesh
 output:
   X: Euler's charastistics
   V: number of vertices 
   E: number of edges
   F: number of faces

function seg=bbxflatsegment(node,loop)

 seg=bbxflatsegment(node,loop)
 decompose edge loops into flat segments alone x/y/z 
 planes of the bounding box
 input:   
    node:  x,y,z coordinates of each node of the mesh
    loop:  input, a single vector separated by NaN, each segment
             is a close-polygon consisted by node IDs 
 output:
    seg:   output, a single vector separated by NaN, each segment
             is a close-polygon on x/y/z plane 

function plane=surfplane(node,face)

 plane=surfplane(node,face)
 plane equation coefficients for each face in a surface
 input:
   node: a list of node coordinates (nn x 3)
   face: a surface mesh triangle list (ne x 3)
 output:
   plane: a (ne x 4) array, in each row, it has [a b c d]
        to denote the plane equation as "a*x+b*y+c*z+d=0"

function [pt,p0,v0,t,idx]=surfinterior(node,face)

 [pt,p0,v0,t,idx]=surfinterior(node,face)
 identify a point that is enclosed by the (closed) surface
 input:
   node: a list of node coordinates (nn x 3)
   face: a surface mesh triangle list (ne x 3)
 output:
   pt: the interior point coordinates [x y z]
   p0: ray origin used to determine the interior point
   v0: the vector used to determine the interior point
   t : ray-tracing intersection distances (with signs) from p0. the
       intersection coordinates can be expressed as p0+t(i)*v0
   idx: index to the face elements that intersect with the ray, order
       match that of t

function seeds=surfseeds(node,face)

 seeds=surfseeds(node,face)
 calculate a set of interior points with each enclosed by a closed
 component of a surface
 input:
   node: a list of node coordinates (nn x 3)
   face: a surface mesh triangle list (ne x 3)
 output:
   seeds: the interior points coordinates for each closed-surface
          component

function quality=meshquality(node,elem)

 quality=meshquality(node,elem)
 compute Joe-Liu mesh quality measure of a tetrahedral mesh
 input:
    node:  node coordinates of the mesh (nn x 3)
    elem:  element table of a tetrahedral mesh (ne x 4)
 output
    edge:  edge list; each row is an edge, specified by the starting and
           ending node indices, the total edge number is
           size(elem,1) x nchoosek(size(elem,2),2). All edges are ordered
           by looping through each element first. 

function edges=meshedge(elem)

 edges=meshedge(elem)
 return all edges in a surface or volumetric mesh
 input:
    elem:  element table of a mesh (support N-d space element)
 output
    edge:  edge list; each row is an edge, specified by the starting and
           ending node indices, the total edge number is
           size(elem,1) x nchoosek(size(elem,2),2). All edges are ordered
           by looping through each element first. 

1.6. Mesh processing and reparing

function [node,elem]=meshcheckrepair(node,elem,opt)

 [node,elem]=meshcheckrepair(node,elem,opt)
 check and repair a surface mesh
 input/output:
      node: input/output, surface node list, dimension (nn,3)
      elem: input/output, surface face element list, dimension (be,3)
      opt: options, including
            'duplicated': remove duplicated elements
            'isolated': remove isolated nodes
            'deep': call external jmeshlib to remove non-manifold vertices

function newelem=meshreorient(node,elem)

 newelem=meshreorient(node,elem)
 reorder nodes in a surface or tetrahedral mesh to ensure all
 elements are oriented consistently
 input:
    node: list of nodes
    elem: list of elements (each row are indices of nodes of each element)
 output:
    newelem: the element list with consistent ordering

function elem=removedupelem(elem)

 elem=removedupelem(elem)
 remove doubly duplicated elements
 input:
    elem: list of elements (node indices)
 output:
    elem: element list after removing the duplicated elements

function [newnode,newelem]=removedupnodes(node,elem)

 [newnode,newelem]=removedupnodes(node,elem)
 removing the duplicated nodes from a mesh
 input:
   elem: integer array with dimensions of NE x 4, each row contains
         the indices of all the nodes for each tetrahedron
   node: node coordinates, 3 columns for x, y and z respectively
 output:
   newnode: nodes without duplicates
   newelem: elements with only the unique nodes

function [no,el]=removeisolatednode(node,elem)

 [no,el]=removeisolatednode(node,elem)
 remove isolated nodes: nodes that are not included in any element
 input:
     node: list of node coordinates
     elem: list of elements of the mesh
 output:
     no: node coordinates after removing the isolated nodes
     el: element list of the resulting mesh

function fnew=removeisolatedsurf(v,f,maxdiameter)

 fnew=removeisolatedsurf(v,f,maxdiameter)
 remove disjointed surface fragment by using mesh diameter
 input:
    v: list of nodes of the input surface
    f: list of triangles of the input surface
    maxdiameter: maximum bounding box size for surface removal
 ouput:
    fnew: new face list after removing the components smaller than 
          maxdiameter

function f=surfaceclean(f,v)

 f=surfaceclean(f,v)
 remove surface patches that are located inside 
               the bounding box faces
 input: 
      v: surface node list, dimension (nn,3)
      f: surface face element list, dimension (be,3)  
 output:
      f: faces free of those on the bounding box

function eid=getintersecttri(tmppath)

 eid=getintersecttri(tmppath)
 get the IDs of self-intersecting elements from tetgen
 call this when tetgen complains about self-intersection
 input: 
   tmppath: working dir, use mwpath('') in most cases
 output:
   eid: an array of all intersecting surface elements, 
     one can read the corresponding node/elem by
     [no,el]=readoff(mwpath('post_vmesh.off'));

function elem=delendelem(elem,mask)

 elem=delendelem(elem,mask)
 delete elements whose nodes are all edge nodes
 input/output: 
      elem: input/output, surface/volumetric element list
      mask: of length of node number, =0 for internal nodes, =1 for edge nodes

1.7. Mesh resampling and optimization

function [node,elem]=meshresample(v,f,keepratio)

 [node,elem]=meshresample(v,f,keepratio)
 resample mesh using CGAL mesh simplification utility
 input:
    v: list of nodes
    f: list of surface elements (each row for each triangle)
    keepratio: decimation rate, a number less than 1, as the percentage
               of the elements after the sampling
 output:
    node: the node coordinates of the sampled surface mesh
    elem: the element list of the sampled surface mesh

function [newno,newfc]=remeshsurf(node,face,opt)

 [newno,newfc]=remeshsurf(node,face,opt)
 remesh a triangular surface and the output is guaranteed to be
 free of self-intersecting element. This function is similar to 
 meshresample, but it can both downsample or upsample a mesh
 input:
	 node: list of nodes on the input suface mesh, 3 columns for x,y,z
	 face: list of trianglular elements on the surface, [n1,n2,n3,region_id]
	 opt: function parameters
	   opt.gridsize:  resolution for the voxelization of the mesh
	   opt.closesize: if there are openings, set the closing diameter
	   opt.elemsize:  the size of the element of the output surface
	   if opt is a scalar, it defines the elemsize and gridsize=opt/4
 output:
	 newno:  list of nodes on the resulting suface mesh, 3 columns for x,y,z
	 newfc:  list of trianglular elements on the surface, [n1,n2,n3,region_id]

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

 p=smoothsurf(node,mask,conn,iter,useralpha,usermethod,userbeta)
 smoothing a surface mesh
 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)=alpha*v(k)+(1-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. 

function [no,el,fc,nodemap]=sortmesh(origin,node,elem,ecol,face,fcol)

 [no,el,fc]=sortmesh(origin,node,elem,face)
 sort nodes and elements in a mesh so that the indexed
 nodes and elements are closer to each order
 (this may reduce cache-miss in a calculation)
 input:
    origin: sorting all nodes and elements with the distance and
            angles wrt this location, if origin=[], it will be 
            node(1,:)
    node: list of nodes
    elem: list of elements (each row are indices of nodes of each element)
    ecol: list of columns in elem to participate sorting
    face: list of surface triangles (this can be omitted)
    fcol: list of columns in face to participate sorting
 output:
    no: node coordinates in the sorted order
    el: the element list in the sorted order
    fc: the surface triangle list in the sorted order (can be ignored)
    nodemap: the new node mapping order, no=node(nodemap,:)

function [newnode,newelem]=mergemesh(node,elem,varargin)

 [newnode,newelem]=mergemesh(node,elem,varargin)
 merge two or more tetrahedral meshes or triangular surfaces
 input: 
      node: node coordinates, dimension (nn,3)
      elem: tetrahedral element or triangle surface (nn,3) to (nn,5)
 output:
      newnode: the node coordinates after merging, dimension (nn,3)
      newelem: tetrahedral element or surfaces after merging (nn,4) or (nhn,5)
 note: you can call meshcheckrepair for the output newnode and
 newelem to remove the duplicated nodes or elements
 example:
   [node1,elem1,face1]=meshabox([0 0 0],[10 10 10],1,1);
   [node2,face2,elem2]=meshasphere([5 5 13.1],3,0.3,3);
   [newnode,newelem]=mergemesh(node1,elem1,node2,elem2);
   plotmesh(newnode,newelem);
   figure;
   [newnode,newface]=mergemesh(node1,face1,node2,face2);
   plotmesh(newnode,newface,'x>5');

1.8. File I/O

function saveasc(v,f,fname)

 saveasc(v,f,fname)
 save a surface mesh to FreeSurfer ASC mesh format
 input:
      v: input, surface node list, dimension (nn,3)
      f: input, surface face element list, dimension (be,3)
      fname: output file name

function savedxf(node,face,elem,fname)

 savedxf(node,face,elem,fname)
 save a surface mesh to DXF format
 input:
      node: input, surface node list, dimension (nn,3)
      face: input, surface face element list, dimension (be,3)
      elem: input, tetrahedral element list, dimension (ne,4)
      fname: output file name

function saveinr(vol,fname)

 saveinr(vol,fname)
 save a surface mesh to INR Format
 input:
      vol: input, a binary volume
      fname: output file name

function saveoff(v,f,fname)

 saveoff(v,f,fname)
 save a surface mesh to Geomview Object File Format (OFF)
 input:
      v: input, surface node list, dimension (nn,3)
      f: input, surface face element list, dimension (be,3)
      fname: output file name

function savesmf(v,f,fname)

 savesmf(v,f,fname)
 save a surface mesh to smf format
 input:
      v: input, surface node list, dimension (nn,3)
      f: input, surface face element list, dimension (be,3)
      fname: output file name

function savesurfpoly(v,f,holelist,regionlist,p0,p1,fname,forcebox)

 savesurfpoly(v,f,holelist,regionlist,p0,p1,fname)
 save a set of surfaces into poly format (for tetgen)
 input:
      v: input, surface node list, dimension (nn,3)
         if v has 4 columns, the last column specifies mesh density near each node
      f: input, surface face element list, dimension (be,3)
      holelist: list of holes, each hole is represented by an internal point
      regionlist: list of regions, similar to holelist
      p0: coordinate of one of the end of the bounding box
      p1: coordinate for the other end of the bounding box
      fname: output file name
      forcebox: non-empty: add bounding box, []: automatic
                if forcebox is a 8x1 vector, it will be used to 
                specify max-edge size near the bounding box corners

function savevrml(node,face,elem,fname)

 savevrml(node,face,elem,fname)
 save a surface mesh to VRML 1.0 format
 input:
      node: input, surface node list, dimension (nn,3)
      face: input, surface face element list, dimension (be,3)
      elem: input, tetrahedral element list, dimension (ne,4)
      fname: output file name

function [node,elem]=readasc(fname)

 [node,elem]=readasc(fname)
 read FreeSurfer ASC mesh format
 input:
      fname: name of the asc file
 output:
      node: node positions of the mesh
      elem: element list of the mesh

function dat=readinr(fname)

 vol=readinr(fname)
 load a volume from an INR file
 input:
      fname: input file name
 output:
      dat: output, data read from the inr file

function [node,elem,face]=readmedit(filename)

 [node,elem,face]=readmedit(filename)
 read Medit mesh format
 input:
    fname: name of the medit data file
 output:
    node: node coordinates of the mesh
    elem: list of elements of the mesh	    
    face: list of surface triangles of the mesh	    

function [node,elem]=readoff(fname)

 [node,elem]=readoff(fname)
 read Geomview Object File Format (OFF)
 input:
    fname: name of the OFF data file
 output:
    node: node coordinates of the mesh
    elem: list of elements of the mesh	    

function [node,elem]=readsmf(fname)

 [node,elem]=readsmf(fname)
 read simple model format (SMF)
 input: 
    fname: name of the	SMF data file
 output:
    node: node coordinates of the mesh
    elem: list of elements of the mesh

function [node,elem,face]=readtetgen(fstub)

 [node,elem,face]=readtetgen(fstub)
 read tetgen output files
 input:
    fstub: file name stub
 output:
    node: node coordinates of the tetgen mesh
    elem: tetrahedra element list of the tetgen mesh
    face: surface triangles of the tetgen mesh

function flag=deletemeshfile(fname)

 flag=deletemeshfile(fname)
 delete a given work mesh file under the working directory
 input: 
     fname: specified file name (without path)
 output:
     flag: not used

function binname=mcpath(fname)

 binname=mcpath(fname)
 get full executable path by prepending a command directory path
 parameters:
 input:
    fname: input, a file name string
 output:
    binname: output, full file name located in the bin directory
    if global variable ISO2MESH_BIN is set in 'base', it will
    use [ISO2MESH_BIN filesep cmdname] as the command full path,
    otherwise, let matlab pass the cmdname to the shell, which
    will search command in the directories listed in system
    $PATH variable.

function tempname=mwpath(fname)

 tempname=meshtemppath(fname)
 get full temp-file name by prepend working-directory and current session name
 input:
    fname: input, a file name string
 output:
    tempname: output, full file name located in the working directory
    if global variable ISO2MESH_TEMP is set in 'base', it will use it
    as the working directory; otherwise, will use matlab function tempdir
    to return a working directory.
    if global variable ISO2MESH_SESSION is set in 'base', it will be
    prepended for each file name, otherwise, use supplied file name.

function savemedit(node,face,elem,fname)

 savedmedit(node,face,elem,fname)
 save a surface or tetrahedral mesh to Medit format
 input:
      node: input, surface node list, dimension (nn,3 or 4)
      face: input, surface face element list, dimension (be,3 or 4)
      elem: input, tetrahedral element list, dimension (ne,4 or 5)
      fname: output file name

1.9. Volumetric image pre-processing

function islands=bwislands(img)

 islands=bwislands(img)
 return the indices of non-zero elements in a 2D or 3D image
 grouped by connected regions in a cell array
 input:
	 img: a 2D or 3D array
 output:
	 islands: a cell array, each cell records the indices 
		  of the non-zero elements in img for a connected 
		  region (or an island)

function resimg=fillholes3d(img,ballsize)

 resimg=fillholes3d(img,ballsize)
 close a 3D image with the speicified gap size and then fill the holes
 input:
    img: a 3D binary image
    ballsize: maximum gap size for image closing
 output:
    resimg: the image free of holes
 this function requires the image processing toolbox for matlab/octave

function cleanimg=deislands2d(img,sizelim)

 cleanimg=deislands2d(img,sizelim)
 remove isolated islands on a 2D image below speicified size limit
 input:
 	img: a 2D binary image
 	sizelim: a integer as the maximum pixel size of a isolated region
 output:
 	cleanimg: a binary image after removing islands below sizelim

function cleanimg=deislands3d(img,sizelim)

 cleanimg=deislands3d(img,sizelim)
 remove isolated islands for 3D image (for each slice)
 input:
      img: a 3D volumetric image
      sizelim: maximum island size (in pixels) for each x/y/z slice
 output:
      cleanimg: 3D image after removing the islands

function imgdiff=imedge3d(binimg,isdiff)

 imgdiff=imedge3d(binimg,isdiff)
 Extract the boundary voxels from a binary image
 author: Aslak Grinsted <ag at glaciology.net>
 input: 
   binimg: a 3D binary image
   isdiff: if isdiff=1, output will be all voxels which 
         is different from its neighbors; if isdiff=0 or 
         ignored, output will be the edge voxels of the 
         non-zero regions in binimg
 output:
   imgdiff: a 3D logical array with the same size as binimg
            with 1 for voxels on the boundary and 0 otherwise 

function p=internalpoint(v,aloop)

 p=internalpoint(v,aloop)
 imperical function to find an internal point
 of a planar polygon
 input:   
    v:     x,y,z coordinates of each node of the mesh
    aloop:  input, a single vector separated by NaN, each segment
             is a close-polygon consisted by node IDs 
 output:
    p:   output, [x y z] of an internal point of aloop

function vol=smoothbinvol(vol,layer)

 vol=smoothbinvol(vol,layer)
 perform a memory-limited 3D image smoothing
 input:
     vol: a 3D volumetric image to be smoothed
     layer: number of iterations for the smoothing
 output:
     vol: the volumetric image after smoothing

function vol=thickenbinvol(vol,layer)

 vol=thickenbinvol(vol,layer)
 thickening a binary volume by a given pixel width
 this is similar to bwmorph(vol,'thicken',3) except 
 this does it in 3d and only does thickening for 
 non-zero elements (and hopefully faster)
 input:
     vol: a volumetric binary image
     layer: number of iterations for the thickenining
 output:
     vol: the volume image after the thickening

function vol=thinbinvol(vol,layer)

 vol=thinbinvol(vol,layer)
 thinning a binary volume by a given pixel width
 this is similar to bwmorph(vol,'thin',n) except 
 this does it in 3d and only does thinning for 
 non-zero elements (and hopefully faster)
 input:
     vol: a volumetric binary image
     layer: number of iterations for the thickenining
 output:
     vol: the volume image after the thickening

1.10. Mesh plotting

function hm=plotmesh(node,varargin)

 hm=plotmesh(node,face,elem,opt)
 plot surface and volumetric meshes
 input: 
      node: a node coordinate list, 3 columns for x/y/z; if node has a 
            4th column, it will be used to set the color at each node.
      face: a triangular surface face list; if face has a 4th column,
            it will be used to separate the surface into 
            sub-surfaces and display them in different colors.
      elem: a tetrahedral element list; if elem has a 5th column,
            it will be used to separate the mesh into 
            sub-domains and display them in different colors.
      opt:  additional options for the plotting
            for simple point plotting, opt can be markers
            or color options, such as 'r.', or opt can be 
            a logic statement to select a subset of the mesh,
            such as 'x>0 & y+z<1'; opt can have more than one
            items to combine these options, for example: 
            plotmesh(...,'x>0','r.'); the range selector must
            appear before the color/marker specifier
 in the event where all of the above inputs have extra settings related to 
 the color of the plot, the priorities are given in the following order:
          opt > node(:,4) > elem(:,5) > face(:,4)
 output:
   hm: handle or handles (vector) to the plotted surfaces
 example:
   h=plotmesh(node,'r.');
   h=plotmesh(node,'x<20','r.');
   h=plotmesh(node,face);
   h=plotmesh(node,face,'y>10');
   h=plotmesh(node,face,'facecolor','r');
   h=plotmesh(node,elem,'x<20');
   h=plotmesh(node,elem,'x<20 & y>0');
   h=plotmesh(node,face,elem);
   h=plotmesh(node,face,elem,'linestyle','--');

function hm=plotsurf(node,face,varargin)

 hm=plotsurf(node,face,opt)
 plot 3D surface meshes
 input: 
      node: node coordinates, dimension (nn,3); if node has a 
            4th column, it will be used to set the color at each node.
      face: triangular surface face list; if face has a 4th column,
            it will be used to separate the surface into 
            sub-surfaces and display them in different colors.
      opt:  additional options for the plotting, see plotmesh
 output:
   hm: handle or handles (vector) to the plotted surfaces
 example:
   h=plotsurf(node,face);
   h=plotsurf(node,face,'facecolor','r');

function hm=plottetra(node,elem,varargin)

 hm=plottetra(node,elem,opt)
 plot 3D surface meshes
 input: 
      node: a node coordinate list, 3 columns for x/y/z; if node has a 
            4th column, it will be used to set the color at each node.
      elem: a tetrahedral element list; if elem has a 5th column,
            it will be used to separate the mesh into 
            sub-domains and display them in different colors.
      opt:  additional options for a patch object, see plotmesh
 output:
   hm: handle or handles (vector) to the plotted surfaces
 example:
   h=plottetra(node,elem);
   h=plottetra(node,elem,'facealpha',0.5);

function [cutpos,cutvalue,facedata]=qmeshcut(elem,node,value,plane)

 [cutpos,cutvalue,facedata]=qmeshcut(elem,node,value,plane)
 fast tetrahedral mesh cross-section plot
 input: 
   elem: integer array with dimensions of NE x 4, each row contains
         the indices of all the nodes for each tetrahedron
   node: node coordinates, 3 columns for x, y and z respectively
   value: a scalar array with the length of node numbers, can have 
          multiple columns 
   plane: defines a plane by 3 points: plane=[x1 y1 z1;x2 y2 z2;x3 y3 z3]
 output:
   cutpos: all the intersections of mesh edges by the plane
           cutpos is similar to node, containing 3 columns for x/y/z
   cutvalue: interpolated values at the intersections, with row number
           being the num. of the intersections, column number being the 
           same as "value".
   facedata: define the intersection polygons in the form of patch "Faces"
 the outputs of this subroutine can be easily plotted using 
     patch('Vertices',cutpos,'Faces',facedata,'FaceVertexCData',cutvalue,...
           'FaceColor','interp');

function plottetview(session,method)

 plottetview(session,method)
 wrapper for tetview to plot the generated mesh
 input:
	 session: a string to identify the output files for plotting, '' for
	          the default session
    method:  method can be 'cgalsurf' (default), 'simplify', 'cgalpoly'
             'cgalmesh' and 'remesh'

1.11. Miscellaneous functions

function valnew=surfdiffuse(node,tri,val,ddt,iter,type1,opt)

 valnew=surfdiffuse(node,tri,val,ddt,iter,type1,opt)
 apply a smoothing/diffusion process on a surface
 input:
     node: list of nodes of the surface mesh
     tri: triangular element list of the surface
     val: vector, scalar value for each node
     ddt: diffusion coefficient multiplied by delta t
     iter: iterations for applying the smoothing
     type1: indices of the nodes which will not be updated
     opt: method, 'grad' for gradient based, and 'simple' for simple average
 output:
     valnew: nodal value vector after the smoothing

function [node,elem,face]=volmap2mesh(img,ix,iy,iz,elemnum,maxvol,thickness,Amat,Bvec)

 [node,elem,face]=volmap2mesh(img,ix,iy,iz,thickness,elemnum,maxvol,A,B)
 convert a binary volume to tetrahedral mesh followed by an Affine transform
 input: 
        img, ix,iy,iz, elemnum and  maxvol: see vol2mesh.m
        thickness: scale z-dimension of the mesh to specified thickness, 
                   if thickness==0, scaling is bypassed
        Amat: a 3x3 transformation matrix
        Bvec: a 3x1 vector
        Amat and Bvec maps the image index space to real world coordnate system by
                   [x,y,z]_new=Amat*[x,y,z]_old+Bvec

function isoctave=isoctavemesh

 isoctave=isoctavemesh
 determine whether the code is running in octave
 output:
   isoctave: 1 if in octave, otherwise 0

function p=getvarfrom(ws,name)

 p=getvarfrom(ws,name)
 get variable value by name from specified work-space
 input:
    ws: name of the work-space, for example, 'base'
    name: name string of the variable
 output:
    p: the value of the specified variable, if the variable does not
       exist, return empty array

function [t,u,v]=raytrace(p,v,node,face)

 [t,u,v]=raytrace(p,v,node,face)
 perform a Havel-styled ray tracing for a triangular surface
 input:
   p: starting point coordinate of the ray
   v: directional vector of the ray
   node: a list of node coordinates (nn x 3)
   face: a surface mesh triangle list (ne x 3)
 output:
   t: signed distance from p to the intersection point
   u: bary-centric coordinate 1 of the intersection point
   v: bary-centric coordinate 2 of the intersection point
      the final bary-centric triplet is [u,v,1-u-v]
  users can find the IDs of the elements intersecting with the ray by
    idx=find(u>=0 & v>=0 & u+v<=1.0);
 Reference: 
  [1] J. Havel and A. Herout, "Yet faster ray-triangle intersection (using 
          SSE4)," IEEE Trans. on Visualization and Computer Graphics,
          16(3):434-438 (2010)
  [2] Q. Fang, "Comment on 'A study on tetrahedron-based inhomogeneous 
          Monte-Carlo optical simulation'," Biomed. Opt. Express, (in
          press)

function [a,b,c,d]=getplanefrom3pt(plane)

 [a,b,c,d]=getplanefrom3pt(plane)
 define a plane equation ax+by+cz+d=0 from three 3D points
 input: 
    plane: a 3x3 matrix with each row specifying a 3D point (x,y,z)
 output:
    a,b,c,d: the coefficient for plane equation ax+by+cz+d=0

function exesuff=getexeext()

 exesuff=getexeext()
 get meshing external tool extension names for the current platform
 output:
     exesuff: file extension for iso2mesh tool binaries

function exesuff=fallbackexeext(exesuffix, exename)

 exesuff=fallbackexeext(exesuffix, exename)
 get the fallback external tool extension names for the current platform
 input:
     exesuffix: the output executable suffix from getexeext
     exename: the executable name
 output:
     exesuff: file extension for iso2mesh tool binaries

function [major,minor,patchnum,extra]=iso2meshver

 [major,minor,patchnum,extra]=iso2meshver
      or
 v=iso2meshver
 get the version number of iso2mesh toolbox
 output:
    if you ask for a single output:
      v: a string denotes the current version number; the string is 
       typically in the following format: "major.minor.patch-extra"
       where major/minor/patch are typically integers, and extra can
       be an arbitrary string and is optional
    if you ask for 4 outputs:
     [major,minor,patchnum,extra] are each field of the version string