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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,method)
[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 if method='cgalpoly', s2m will call cgals2m and keepratio should be a structure (as the 'opt' input in cgals2m)
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,varargin)
[node,elem,face]=cgals2m(v,f,opt,maxvol) wrapper for CGAL 3D mesher (CGAL 3.5 and newer) convert a triangular surface 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,face,elem]=meshabox(p0,p1,opt,nodesize)
[node,face,elem]=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,face,elem]=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;
function [node,face,elem]=meshacylinder(c0,c1,r,tsize,maxvol,ndiv)
[node,face]=meshacylinder(c0,c1,r,tsize,maxvol,ndiv)
or
[node,face,elem]=meshacylinder(c0,c1,r,tsize,maxvol,ndiv)
create the surface and (optionally) tetrahedral mesh of a 3D cylinder
input:
c0, c1: cylinder axis end points
r: radius of the cylinder
tsize: maximum surface triangle size on the sphere
maxvol: maximu volume of the tetrahedral elements
ndiv: approximate the cylinder surface into ndiv flat pieces, if
ignored, ndiv is set to 20
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 triangle
elem: (optional) integer array with dimensions of NE x 4, each row
represents a tetrahedron
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 maxsize]=maxsurf(facecell,node)
[f maxsize]=maxsurf(facecell,node)
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
node: optional, node list, if given, the output is the
surface with the largest surface area.
output:
f: the surface data (node indices) for the surface with most elements
maxsize: if node is not given, maxisize is row number of f;
otherwise, maxsize is the total area of f
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 elist=surfpart(f,loopedge)
elist=surfpart(f,loopedge)
partition a triangular surface using a closed loop defined by existing edges
input:
f: input, surface face element list, dimension (be,3)
loopedge: a 2-column array, specifying a closed loop in CCW order
output:
elist: list of triangles that is enclosed by the loop
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 the 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:
quality: a vector of the same length as size(elem,1), with
each element being the Joe-Liu mesh quality metric (0-1) of
the corresponding element. A value close to 1 represents
higher mesh quality (1 means equilateral tetrahedron);
a value close to 0 means nearly degenerated element.
reference:
A. Liu, B. Joe, Relationship between tetrahedron shape measures,
BIT 34 (2) (1994) 268–287.
function edges=meshedge(elem,varargin)
edges=meshedge(elem,opt)
return all edges in a surface or volumetric mesh
input:
elem: element table of a mesh (support N-d space element)
opt: optional input, giving the additional options. If opt
is a struct, it can have the following field:
opt.nodeorder: if 1, assuming the elem node indices is in CCW
orientation; 0 use nchoosek() output to order edges
you can replace opt by a series of ('param', value) pairs.
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 snorm=surfnorm(node,face,varargin)
snorm=surfnorm(node,face)
or
snorm=surfnorm(node,face,'Normalize',0)
compute the normal vectors for a triangular surface
input:
node: a list of node coordinates (nn x 3)
face: a surface mesh triangle list (ne x 3)
opt: a list of optional parameters, currently surfnorm supports:
'Normalize': [1|0] if set to 1, the normal vectors will be
unitary (default)
output:
snorm: output surface normal vector at each face
function [edges,idx,edgemap]=uniqedges(elem)
[edges,idx,edgemap]=uniqedges(elem)
return the unique edge list from a surface or tetrahedral mesh
input:
elem: a list of elements, each row is a list of nodes for an element.
elem can have 2, 3 or 4 columns
output:
edge: unique edges in the mesh, denoted by a pair of node indices
idx: index of the output in the raw edge list (returned by meshedge)
edgemap: index of the raw edges in the output list (for triangular mesh)
function [elist,nextfront]=advancefront(edges,loop,elen)
[elist,nextfront]=advancefront(edges,loop,elen)
advance an edge-front on an oriented surface to the next separated by
one-element width
input:
edges: edge list of an oriented surface mesh, must be in CCW order
loop: a 2-column array, specifying a closed loop in CCW order
elen: node number inside each element, if ignored, elen is set to 3
output:
elist: list of triangles that is enclosed between the two
edge-fronts
nextfront: a new edge loop list representing the next edge-front
1.6. Mesh processing and reparing
function [node,elem]=meshcheckrepair(node,elem,opt,varargin)
[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
function [newnode,newface]=surfreorient(node,face)
[newnode,newface]=surfreorient(node,elem)
reorder nodes in a single closed surface to ensure the norms of all
triangles are pointing outward
input:
node: list of nodes
face: list of surface triangles (each row are indices of nodes of each triangle)
output:
newnode: the output node list, in most cases it equals node
newface: the face list with consistent ordering
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)=(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.
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,face1,elem1]=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');
function [newnode,newelem,newface]=meshrefine(node,elem,varargin)
[newnode,newelem,newface]=meshrefine(node,elem,face,opt)
refine a tetrahedral mesh by adding new nodes or constraints
input parameters:
node: existing tetrahedral mesh node list
elem: existing tetrahedral element list
face: (optional) existing tetrahedral mesh surface triangle list
opt: options for mesh refinement:
if opt is a Nx3 array, opt is treated as a list of new nodes to
be inserted into the mesh (must be located on the surface or inside)
if opt is a struct, it can have the following fields:
opt.newnode: same as setting opt to an Nx3 array
opt.reratio: radius-edge ratio, by default, iso2mesh uses 1.414
opt.maxvol: maximum element volume
outputs:
newnode: node coordinates of the tetrahedral mesh
newelem: element list of the tetrahedral mesh
newface: mesh surface element list of the tetrahedral mesh
the last column denotes the boundary ID
function [newnode,newelem]=mergesurf(node,elem,varargin)
[newnode,newelem]=mergesurf(node1,elem1,node2,elem2,...)
merge two or more triangular meshes and split intersecting elements
input:
node: node coordinates, dimension (nn,3)
elem: tetrahedral element or triangle surface (nn,3)
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,face1,elem1]=meshabox([0 0 0],[10 10 10],1,1);
[node2,face2,elem2]=meshasphere([5 5 10],3,0.3,3);
[newnode,newface]=mergemesh(node1,face1,node2,face2);
plotmesh(newnode,newface,'x>5');
function [newnode,newelem,newelem0]=surfboolean(node,elem,varargin)
[newnode,newelem,newelem0]=surfboolean(node1,elem1,op2,node2,elem2,op3,node3,elem3,...)
merge two or more triangular meshes and resolve intersecting elements
input:
node: node coordinates, dimension (nn,3)
elem: tetrahedral element or triangle surface (ne,3)
op: a string of a boolean operator, possible op values include
'union' or 'or': the outter surface of the union of the enclosed space
'inter' or 'and': the surface of the domain contained by both meshes
'diff' or '-': the surface of the domain in mesh 1 excluding that of
mesh 2
'all' or 'xor' or '+': the output contains 4 subsurfaces, identified by the 4th
column of newelem:
1: mesh 1 outside of mesh 2
2: mesh 2 outside of mesh 1
3: mesh 1 inside of mesh 2
4: mesh 2 inside of mesh 1
you can use newelem(find(mod(newelem(:,4),2)==1),:) to
get mesh 1 cut by mesh 2, or newelem(find(mod(newelem(:,4),2)==0),:)
to get mesh 2 cut by mesh 1;
'first': combine 1 and 3 from the output of 'all'
'second': combine 2 and 4 from the output of 'all'
'self': test for self-intersections; only the first mesh is
tested; other inputs are ignored.
'decouple': separate two shells and make sure there is no intersection;
the input surfaces must be closed and ordered from outer to inner
output:
newnode: the node coordinates after boolean operations, dimension (nn,3)
newelem: tetrahedral element or surfaces after boolean operations (nn,4) or (nhn,5)
newelem0: when the operator is 'self', return the intersecting
element list in terms of the input node list (experimental)
example:
[node1,face1,elem1]=meshabox([0 0 0],[10 10 10],1,1);
[node2,face2,elem2]=meshabox([0 0 0]+5,[10 10 10]+5,1,1);
[newnode,newface]=surfboolean(node1,face1,'union',node2,face2);
plotmesh(newnode,newface);
figure;
[newnode,newface]=surfboolean(node1,face1,'diff',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 savestl(node,elem,fname,solidname)
savestl(node,elem,fname,solidname)
save a tetrahedral mesh to an STL (Standard Tessellation Language) file
input:
node: input, surface node list, dimension Nx3
elem: input, tetrahedral element list; if size(elem,2)==3, it is a surface
fname: output file name
solidname: an optional string for the name of the object
function savebinstl(node,elem,fname,solidname)
savebinstl(node,elem,fname,solidname)
save a tetrahedral mesh to a binary STL (Standard Tessellation Language) file
input:
node: input, surface node list, dimension Nx3
elem: input, tetrahedral element list; if size(elem,2)==3, it is a surface
fname: output file name
solidname: an optional string for the name of the object
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 nedge=savegts(v,f,fname,edges)
nedge=savegts(v,f,fname,edges)
save a surface mesh to GNU Triangulated Surface Format (GTS)
input:
v: input, surface node list, dimension (nn,3)
f: input, surface face element list, dimension (be,3)
fname: output file name
edges: edge list, if ignored, savegts will compute
output:
nedge: the number of unique edges in the mesh
function [node,elem,edges,edgemap]=readgts(fname)
[node,elem,edges,edgemap]=readgts(fname)
read GNU Triangulated Surface Format (GTS)
input:
fname: name of the OFF data file
output:
node: node coordinates of the mesh
elem: list of elements of the surface mesh
edges: the edge list section in the GTS file (optional)
edgemap: the face section (in terms of edge indices) in the GTS file
(optional)
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)
savemedit(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
function json=savejson(rootname,obj,varargin)
json=savejson(rootname,obj,filename)
or
json=savejson(rootname,obj,opt)
json=savejson(rootname,obj,'param1',value1,'param2',value2,...)
convert a MATLAB object (cell, struct or array) into a JSON (JavaScript
Object Notation) string
created on 2011/09/09
$Id: savejson.m 394 2012-12-18 17:58:11Z fangq $
input:
rootname: name of the root-object, if set to '', will use variable name
obj: a MATLAB object (array, cell, cell array, struct, struct array)
filename: a string for the file name to save the output JSON data
opt: a struct for additional options, use [] if all use default
opt can have the following fields (first in [.|.] is the default)
opt.FileName [''|string]: a file name to save the output JSON data
opt.FloatFormat ['%.10g'|string]: format to show each numeric element
of a 1D/2D array;
opt.ArrayIndent [1|0]: if 1, output explicit data array with
precedent indentation; if 0, no indentation
opt.ArrayToStruct[0|1]: when set to 0, savejson outputs 1D/2D
array in JSON array format; if sets to 1, an
array will be shown as a struct with fields
"_ArrayType_", "_ArraySize_" and "_ArrayData_"; for
sparse arrays, the non-zero elements will be
saved to _ArrayData_ field in triplet-format i.e.
(ix,iy,val) and "_ArrayIsSparse_" will be added
with a value of 1; for a complex array, the
_ArrayData_ array will include two columns
(4 for sparse) to record the real and imaginary
parts, and also "_ArrayIsComplex_":1 is added.
opt.ParseLogical [0|1]: if this is set to 1, logical array elem
will use true/false rather than 1/0.
opt.NoRowBracket [1|0]: if this is set to 1, arrays with a single
numerical element will be shown without a square
bracket, unless it is the root object; if 0, square
brackets are forced for any numerical arrays.
opt.ForceRootName [0|1]: when set to 1 and rootname is empty, savejson
will use the name of the passed obj variable as the
root object name; if obj is an expression and
does not have a name, 'root' will be used; if this
is set to 0 and rootname is empty, the root level
will be merged down to the lower level.
opt.Inf ['"$1_Inf_"'|string]: a customized regular expression pattern
to represent +/-Inf. The matched pattern is '([-+]*)Inf'
and $1 represents the sign. For those who want to use
1e999 to represent Inf, they can set opt.Inf to '$11e999'
opt.NaN ['"_NaN_"'|string]: a customized regular expression pattern
to represent NaN
opt.JSONP [''|string]: to generate a JSONP output (JSON with padding),
for example, if opt.JSON='foo', the JSON data is
wrapped inside a function call as 'foo(...);'
opt.UnpackHex [1|0]: conver the 0x[hex code] output by loadjson
back to the string form
opt can be replaced by a list of ('param',value) pairs. The param
string is equivallent to a field in opt.
output:
json: a string in the JSON format (see http://json.org)
examples:
a=struct('node',[1 9 10; 2 1 1.2], 'elem',[9 1;1 2;2 3],...
'face',[9 01 2; 1 2 3; NaN,Inf,-Inf], 'author','FangQ');
savejson('mesh',a)
savejson('',a,'ArrayIndent',0,'FloatFormat','\t%.5g')
license:
BSD or GPL version 3, see LICENSE_{BSD,GPLv3}.txt files for details
function data = loadjson(fname,varargin)
data=loadjson(fname,opt)
or
data=loadjson(fname,'param1',value1,'param2',value2,...)
parse a JSON (JavaScript Object Notation) file or string
Nedialko Krouchev: http://www.mathworks.com/matlabcentral/fileexchange/25713
François Glineur: http://www.mathworks.com/matlabcentral/fileexchange/23393
Joel Feenstra:
http://www.mathworks.com/matlabcentral/fileexchange/20565
$Id: loadjson.m 394 2012-12-18 17:58:11Z fangq $
input:
fname: input file name, if fname contains "{}" or "[]", fname
will be interpreted as a JSON string
opt: a struct to store parsing options, opt can be replaced by
a list of ('param',value) pairs. The param string is equivallent
to a field in opt.
output:
dat: a cell array, where {...} blocks are converted into cell arrays,
and [...] are converted to arrays
license:
BSD or GPL version 3, see LICENSE_{BSD,GPLv3}.txt files for details
function savejmesh(node,face,elem,fname,varargin)
savejmesh(node,face,elem,fname,opt)
export a mesh to the JMesh format
input:
node: input, node list, dimension (nn,3)
face: input, optional, surface face element list, dimension (be,3)
elem: input, tetrahedral element list, dimension (ne,4)
fname: output file name
opt: additional parameters in the form of 'parameter',value pairs
valid parameters include:
'Dimension': 0 - a user defined mesh, 2- a 2D mesh, 3- a 3D mesh
'Author': a string to set the author of the mesh
'MeshTitle': a string to set the title of the mesh
'MeshTag': a value as the tag of the mesh data
'MeshGroup': a value to group this mesh with other mesh data
'Comment': a string as the additional note for the mesh data
==== function savemphtxt(node, face, elem, filename)
====
savemphtxt(node, face, elem, filename)
save tetrahedron mesh to comsol file (.mphtxt)
author: Donghyeon Kim (danielkim<at> gist.ac.kr)
input:
node: input, node list, dimension (nn,3)
face: input, surface face element list with label, dimension (be,4)
elem: input, tetrahedron element list with label, dimension (ne,5)
filename: input, output file name
function savetetgenele(elem,fname)
savetetgenele(elem,fname)
save a mesh tetrahedral element list to tetgen .ele format
input:
elem: tetrahedral element list, dimension (ne,4)
columns beyound the 4rd column are treated as
markers and attributes associated with the element
fname: output file name
function savetetgennode(node,fname)
savetetgennode(node,fname)
save a mesh node list to tetgen .node format
input:
node: node coordinates, dimension (nn,3)
columns beyound the 3rd column are treated as
markers and attributes associated with the node
fname: output file name
function saveabaqus(node,face,elem,fname,heading)
saveabaqus(node,fname)
saveabaqus(node,face,fname)
saveabaqus(node,face,elem,fname)
save a tetrahedral and/or surface mesh as an ABAQUS input file
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
heading: optional, a descriptive string for the mesh
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,maxgap)
resimg=fillholes3d(img,maxgap)
close a 3D image with the speicified gap size and then fill the holes
input:
img: a 3D binary image
maxgap: 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;
face can be a cell array, each element of the array represents
a polyhedral facet of the mesh, if an element is an array with
two array subelements, the first one is the node index, the
second one is a scalar as the group id of the facet.
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;
face can be a cell array, each element of the array represents
a polyhedral facet of the mesh, if an element is an array with
two array subelements, the first one is the node index, the
second one is a scalar as the group id of the facet.
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,elemid]=qmeshcut(elem,node,value,cutat,varargin)
[cutpos,cutvalue,facedata,elemid]=qmeshcut(elem,node,value,cutat)
fast tetrahedral mesh slicer
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
cutat: cutat can have different forms:
if cutat is a 3x3 matrix, it defines a plane by 3 points:
cutat=[x1 y1 z1;x2 y2 z2;x3 y3 z3]
if cutat is a vector of 4 element, it defines a plane by
a*x+b*y+c*z+d=0 and cutat=[a b c d]
if cutat is a single scalar, it defines an isosurface
inside the mesh at value=cutat
if cutat is a string, it defines an implicit surface
at which the cut is made. it must has form expr1=expr2
where expr1 expr2 are expressions made of x,y,z,v and
constants
if cutat is a cell in the form of {'expression',scalar},
the expression will be evaluated at each node to
produce a new value, then an isosurface is produced
at the levelset where new value=scalar; the
expression can contain constants and x,y,z,v
output:
cutpos: all the intersections of mesh edges by the cutat
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"
elemid: the index of the elem in which each intersection polygon locates
the outputs of this subroutine can be easily plotted using
% if value has a length of node:
patch('Vertices',cutpos,'Faces',facedata,'FaceVertexCData',cutvalue,'FaceColor','interp');
% if value has a length of elem:
patch('Vertices',cutpos,'Faces',facedata,'CData',cutvalue,'FaceColor','flat');
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 verinfo]=isoctavemesh
[isoctave verinfo]=isoctavemesh determine whether the code is running in octave output: isoctave: 1 if in octave, otherwise 0 verinfo: a string, showing the version of octave (OCTAVE_VERSION)
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,idx]=raytrace(p0,v0,node,face)
[t,u,v,idx]=raytrace(p0,v0,node,face)
perform a Havel-styled ray tracing for a triangular surface
input:
p0: starting point coordinate of the ray
v0: 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 for each surface
triangle, if ray is parallel to the triangle, t is set to Inf
u: bary-centric coordinate 1 of all intersection points
v: bary-centric coordinate 2 of all intersection points
the final bary-centric triplet is [u,v,1-u-v]
idx: optional output, if requested, idx lists the IDs of the face
elements that intersects the ray; users can manually calc idx by
idx=find(u>=0 & v>=0 & u+v<=1.0 & ~isinf(t));
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
function [t,u,v,idx,xnode]=raysurf(p0,v0,node,face)
[t,u,v,idx,xnode]=raysurf(p,v,node,face)
perform a Havel-styled ray tracing for a triangular surface
input:
p0: list of starting points of the rays
v0: directional vector of the rays,
node: a list of node coordinates (nn x 3)
face: a surface mesh triangle list (ne x 3)
output:
t: distance from p0 to the intersection point for each surface
triangle, if t(i)=NaN, no intersection was found for that ray
u: bary-centric coordinate 1 of all intersection points
v: bary-centric coordinate 2 of all intersection points
the final bary-centric triplet is [u,v,1-u-v]
idx: idx lists the IDs of the face elements that intersects
each ray
xnode: optional output, if requested, xnode gives the intersection
point coordinates; to compute manually, xnode=p0+repmat(t,1,3).*v0
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 val=getoptkey(key,default,varargin)
val=getoptkey(key,default,opt)
or
val=getoptkey(key,default,'key1',val1,'key2',val2, ...)
query the value of a key from a structure or a list of key/value pairs
input:
key: a string name for the target struct field name
default: the default value of the key is not found
opt: a struct object; the field names will be searched to match the
key input, opt can be a list of 'keyname'/value pairs
output:
val: val=opt.key if found, otherwise val=default
function newpt=rotatevec3d(pt,v1,u1,p0)
newpt=rotatevec3d(pt,v1,u1,p0)
rotate 3D points from one Cartesian coordinate system to another
input:
pt: 3D points defined in a standard Cartesian system where a unitary
z-vector is (0,0,1), 3 columns for x, y and z
v1: the unitary z-vector for the target coordinate system
u1: the unitary z-vector for the source coordinate system, if ignored,
u1=(0,0,1)
p0: offset of the new coordinate system, if ignored, p0=(0,0,0)
output:
newpt: the transformed 3D points
function [R,s]=rotmat2vec(u,v)
[R,s]=rotmat2vec(u,v) the rotation matrix from vector u to v, satisfying R*u*s=v author: Bruno Luong URL:http://www.mathworks.com/matlabcentral/newsreader/view_original/827969 input: u: a 3D vector in the source coordinate system; v: a 3D vector in the target coordinate system; output: R: a rotation matrix to transform normalized u to normalized v s: a scaling factor, so that R*u(:)*s=v(:)
function opt=varargin2struct(varargin)
opt=varargin2struct('param1',value1,'param2',value2,...)
or
opt=varargin2struct(...,optstruct,...)
convert a series of input parameters into a structure
input:
'param', value: the input parameters should be pairs of a string and a value
optstruct: if a parameter is a struct, the fields will be merged to the output struct
output:
opt: a struct where opt.param1=value1, opt.param2=value2 ...
license:
BSD or GPL version 3, see LICENSE_{BSD,GPLv3}.txt files for details
function val=jsonopt(key,default,varargin)
val=jsonopt(key,default,optstruct)
setting options based on a struct. The struct can be produced
by varargin2struct from a list of 'param','value' pairs
$Id: loadjson.m 371 2012-06-20 12:43:06Z fangq $
input:
key: a string with which one look up a value from a struct
default: if the key does not exist, return default
optstruct: a struct where each sub-field is a key
output:
val: if key exists, val=optstruct.key; otherwise val=default
license:
BSD or GPL version 3, see LICENSE_{BSD,GPLv3}.txt files for details
function s=mergestruct(s1,s2)
s=mergestruct(s1,s2)
merge two struct objects into one
input:
s1,s2: a struct object, s1 and s2 can not be arrays
output:
s: the merged struct object. fields in s1 and s2 will be combined in s.
license:
BSD or GPL version 3, see LICENSE_{BSD,GPLv3}.txt files for details