"Iso2mesh" is a Matlab/Octave-based mesh generation toolbox designed for easy creation of high quality surface and tetrahedral meshes from 3D volumetric images. It contains a rich set of mesh processing scripts/programs, functioning independently or interfacing with external free meshing utilities. Iso2mesh toolbox can operate directly on 3D binary, segmented or gray-scale images, such as those from MRI or CT scans, making it particularly suitable for multi-modality medical imaging data analysis or multi-physics modeling.
Creating quality surface or tetrahedral meshes from volumetric images has been a challenging task where very limited software and resources could be found. Commercial tools, such as Mimics and Amira, are both expensive and limited in functionalities. Iso2mesh was developed as a free alternative to these expensive commercial tools and provides researchers a highly flexible, modularized and streamlined image-based mesh generation pipeline. It defines simple interfaces to perform a wide varieties of meshing tasks, ranging from 3D volumetric image pre-processing (hole-filling, thinning and thickening), surface mesh modeling (extraction, remeshing, repairing, and smoothing) to volumetric mesh creation. Iso2mesh is cross-platform and is compatible with both Matlab and GNU Octave (a free Matlab clone).
The details of this toolbox can be found in the following reference:
[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
[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; In v2s, method can be set to 'cgalmesh' in addition to those allowed by vol2surf.
[node,elem,face]=s2m(v,f,keepratio,maxvol,method) [node,elem,face]=s2m(v,f,keepratio,maxvol,'tetgen',regions,holes)
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)
input default values: method: if ignored, iso2mesh uses surf2mesh ('tetgen') to do the tetrahedral mesh generation regions,holes: if ignored, iso2mesh assumes both are empty
[img,v2smap]=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) v2smap (optional): a 4x4 matrix denoting the Affine transformation to map the voxel coordinates back to the mesh space. One can use the v2smap to convert a mesh generated from the rasterized volume into the original input mesh space (work coordinate system). For example:
[img,map]=s2v(node,face); [no,el]=v2s(img,0.5,5); newno=map*[no ones(length(no),1)]'; newno=newno(1:3,:)'; % newno and el now go back to the world coordinates
vol=m2v(node,face,Nxyz) or vol=m2v(node,face,xi,yi,zi)
shortcut for mesh2vol, rasterizing a teterahedral mesh to a volume using graphics
input/output: please see details in the help for mesh2vol
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
newworkspace=i2m; or newworkspace=i2m(workspace)
Shortcut for img2mesh, a GUI for iso2mesh
input/output: please see details in the help for img2mesh
[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 when method='cgalmesh', maxvol can specify the target for each label (subregion index) by the following syntax 'label1=size1:label2=size2:...' 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 has 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
[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.keepratio=a float less than 1: same as above, same for all surf. opt(1,2,..).keepratio: 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]
[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
[img, v2smap]=surf2vol(node,face,xi,yi,zi,'options',values,...)
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 if face contains the 4th column, it indicates the label of the face triangles (each face componment must be closed); if face contains 5 columns, it stores a tetrahedral mesh with labels, where the first 4 columns are the element list and the last column is the element label; xi,yi,zi: x/y/z grid for the resulting volume options: 'fill', if set to 1, the enclosed voxels are labeled by 1 'label', if set to 1, the enclosed voxels are labeled by the corresponding label of the face or element; setting 'label' to 1 also implies 'fill'.
output: img: a volumetric binary image at position of ndgrid(xi,yi,zi) v2smap (optional): a 4x4 matrix denoting the Affine transformation to map the voxel coordinates back to the mesh space.
[mask weight]=mesh2vol(node,face,Nxyz) [mask weight]=mesh2vol(node,face,[Nx,Ny,Nz]) [mask weight]=mesh2vol(node,face,xi,yi,zi,hf) or newval=mesh2vol(node_val,face,...)
fast rasterization of a 3D mesh to a volume with tetrahedron index labels
date for initial version: Feb 10,2014
input: node: node coordinates, dimension N by 2 or N by 3 array nodeval: a 4-column array, the first 3 columns are the node coordinates, the last column denotes the values associated with each node face: a triangle surface, N by 3 or N by 4 array Nx,Ny,Nxy: output image in x/y dimensions, or both xi,yi: linear vectors for the output pixel center positions in x/y hf: the handle of a pre-created figure window for faster rendering
output: mask: a 3D image, the value of each pixel is the index of the enclosing triangle, if the pixel is outside of the mesh, NaN weight: (optional) a 3 by Nx by Ny array, where Nx/Ny are the dimensions for the mask newval: when the node has 4 columns, the last column represents the values (color) at each node, the output newval is the rasterized mesh value map over the specified grid.
note: This function only works for matlab
example:
[no,el]=meshgrid6(0:5,0:5,0:3); mask=mesh2vol(no,el(:,1:4),0:0.1:5,0:0.1:5,0:0.1:4); imagesc(mask(:,:,3))
Format: newworkspace = img2mesh or imgmesh(workspace)
A GUI for Iso2Mesh for streamlined mesh data processing
Input: workspace (optional): a struct containing the below fields .graph: a digraph object containing the i2m workspace data Output: newworkspace (optional): the updated workspace, with the same subfields as the input.
If a user supplys an output variable, the GUI will not return until the user closes the window; if a user does not provide any output, the call will return immediately.
Please find more information at http://iso2mesh.sf.net/
[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))
[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')
[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
[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)
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)
[mask weight]=mesh2mask(node,face,Nxy) or [mask weight]=mesh2mask(node,face,[Nx,Ny]) or [mask weight]=mesh2mask(node,face,xi,yi,hf)
fast rasterization of a 2D mesh to an image with triangle index labels
date for initial version: July 18,2013
input: node: node coordinates, dimension N by 2 or N by 3 array face: a triangle surface, N by 3 or N by 4 array Nx,Ny,Nxy: output image in x/y dimensions, or both xi,yi: linear vectors for the output pixel center positions in x/y hf: (optional) the handle of a pre-created figure window, for faster rendering
output: mask: a 2D image, the value of each pixel is the index of the enclosing triangle, if the pixel is outside of the mesh, NaN weight: (optional) a 3 by Nx by Ny array, where Nx/Ny are the dimensions for the mask
note: This function only works in MATLAB when the DISPLAY is not disabled. The maximum size of the mask output is limited by the screen size.
example:
[no,fc]=meshgrid6(0:5,0:5); [mask weight]=mesh2mask(no,fc,-1:0.1:5,0:0.1:5); imagesc(mask);
[node,face,elem]=meshabox(p0,p1,opt,nodesize)
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');
[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
[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;
[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;
[node,face]=meshacylinder(c0,c1,r,tsize,maxvol,ndiv) or [node,face,elem]=meshacylinder(c0,c1,r,tsize,maxvol,ndiv) [nplc,fplc]=meshacylinder(c0,c1,r,0,0,ndiv);
create the surface and (optionally) tetrahedral mesh of a 3D cylinder
input: c0, c1: cylinder axis end points r: radius of the cylinder; if r contains two elements, it outputs a cone trunk, with each r value specifying the radius on each end tsize: maximum surface triangle size on the sphere maxvol: maximu volume of the tetrahedral elements
if both tsize and maxvol is set to 0, this function sill return the piecewise-linear-complex (PLC) in the form of the nodes (as node) and a cell array (as face).
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
==== function [node,elem]=meshgrid5(varargin)
====
[node,elem]=meshgrid5(v1,v2,v3,...)
mesh an ND rectangular lattice by splitting each hypercube into 5 tetrahedra
inspired by John D'Errico URL: http://www.mathworks.com/matlabcentral/newsreader/view_thread/107191
input: v1,v2,v3,... - numeric vectors defining the lattice in each dimension. Each vector must be of length >= 1
output: node - factorial lattice created from (v1,v2,v3,...) Each row of this array is one node in the lattice elem - integer array defining simplexes as references to rows of "node".
example: [node,elem]=meshgrid5(0:5,0:6,0:4); plotmesh(node,elem);
==== function [node,elem]=meshgrid6(varargin)
====
[node,elem]=meshgrid6(v1,v2,v3,...)
mesh an ND rectangular lattice by splitting each hypercube into 6 tetrahedra
author: John D'Errico URL: http://www.mathworks.com/matlabcentral/newsreader/view_thread/107191
input: v1,v2,v3,... - numeric vectors defining the lattice in each dimension. Each vector must be of length >= 1
output: node - factorial lattice created from (v1,v2,v3,...) Each row of this array is one node in the lattice elem - integer array defining simplexes as references to rows of "node".
example: [node,elem]=meshgrid6(0:5,0:6,0:4); plotmesh(node,elem);
[node,face,centroids]=latticegrid(xrange,yrange,zrange,...)
generate a 3D lattice
input: xrange, yrange, zrange ...: 1D vectors specifying the range of each dimension of the lattice
output: node: the vertices of the 3D lattice face: the list of cell faces of the lattice, including both internal and external facets. By default, face is in the form of a cell array, with each row representing a face. One can use cell2mat(face) to convert it to an array centroids: the centroids of each lattice cell
example: % generate a 3D lattice [node,face,c0]=latticegrid([1 2 4],1:3,1:4); plotmesh(node,face)
% mesh the 3D lattice based on the face info [no,el]=surf2mesh(node,face,[],[],1,0.01,c0); figure; plotmesh(no,el)
% mesh a 2-layer structure using a simple lattice [node,face,c0]=latticegrid([0 10],[0 5],[0 3.5 4]); c0(:,4)=[0.01;0.001]; [no,el]=surf2mesh(node,face,[],[],1,[],c0); figure; plotmesh(no,el)
[node,face,yz0,yz1]=extrudecurve(xy, yz, Nx, Nz, Nextrap, spacing, anchor)
create a triangular surface mesh by swining a 2D spline along another 2D spline curve
input: xy: a 2D spline path, along which the surface is extruded, defined on the x-y plane yz: a 2D spline which will move along the path to form a surface, defined on the y-z plane Nx: the count of sample points along the extrusion path (xy), if ignored, it is 40 Nz: the count of sample points along the curve to be extruded (yz), if ignored, it is 40 Nextrap: number of points to extrapolate outside of the xy/yz curves, 0 if ignored spacing: define a spacing scaling factor for spline interpolations, 1 if ignored anchor: the 3D point in the extruded curve plane (yz) that is aligned at the nodes long the extrusion path. this point does not have to be located on the yz curve; orig = [ox oy oz], if ignored, it is set as the point on the interpolated yz with the largested y-value dotopbottom: a flag, if set to 1, tessellated top and bottom faces will be added. default is 0.
output: node: 3D node coordinates for the generated surface mesh face: triangular face patches of the generated surface mesh, each row represents a triangle denoted by the indices of the 3 nodes
[node,face]=meshcylinders(c0, v, len, r,tsize,maxvol,ndiv) or [node,face,elem]=meshacylinder(c0, v, len, r, tsize,maxvol,ndiv) [nplc,fplc]=meshacylinder(c0, v, len,r,0,0,ndiv);
create the surface and (optionally) tetrahedral mesh of a 3D cylinder
input: c0, cylinder list axis's starting point v: directional vector of the cylinder len: a scalar or a vector denoting the length of each cylinder segment along the direction of v tsize, maxvol, ndiv: please see the help for meshacylinder for details
output: node, face, elem: please see the help for meshacylinder for details
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
[openedge,elemid]=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 elemid (optional): the corresponding index of the tetrahedron of an open-edge or triangle, elemid has the same length as openedge.
[openface,elemid]=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 elemid (optional): the corresponding index of the tetrahedron of an open-edge or triangle, elemid has the same length as openedge.
loops=extractloops(edges)
extract individual loop or polyline segment from a collection of edges
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 3D polyline or loop consisted of node IDs
example: edges=[1 2;2 3;1 4;3 4;7 3;1 9;5 6;6 7;10 9; 8 10;1 8;9 3;11 11;11 12]; loops=extractloops(edges)
[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
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
nodevol=nodevolume(node,elem)
calculate the volumes of the cells in the barycentric dual-mesh (this is different from the Voronoi cells, which blong to the circumcentric dual mesh)
input: node: node coordinates elem: element table of a mesh
output: nodevol: volume values for all nodes
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
[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
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) if opt='rowmajor', same as 'surface', except the order of the triangles are in the row-major order%
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
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).
[f maxsize]=maxsurf(facecell,node)
return the surface with the maximum element number or total 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 the most elements (or largest area when node is given) maxsize: if node is not given, maxisize is row number of f; otherwise, maxsize is the total area of f
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
[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
[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
seg=bbxflatsegment(node,loop)
decompose edge loops into flat segments along the 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
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"
[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
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
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
quality=meshquality(node,elem)
compute the Joe-Liu mesh quality measure of an N-D mesh (N<=3)
input: node: node coordinates of the mesh (nn x 3) elem: element table of an N-D mesh (ne x (N+1))
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.
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.
faces=meshface(elem,opt)
return all faces 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 faces you can replace opt by a series of ('param', value) pairs.
output: face: face list; each row is an face, specified by the starting and ending node indices, the total face number is size(elem,1) x nchoosek(size(elem,2),2). All faces are ordered by looping through each element first.
snorm=surfacenorm(node,face) or snorm=surfacenorm(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 surfacenorm supports: 'Normalize': [1|0] if set to 1, the normal vectors will be unitary (default)
output: snorm: output surface normal vector at each face
[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)
[faces,idx,facemap]=uniqfaces(elem)
return the unique face list from a 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: face: unique faces in the mesh, denoted by a triplet of node indices idx: index of the output in the raw face list (returned by meshface) facemap: index of the raw faces in the output list (for triangular mesh)
[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
outface=innersurf(node,face,outface)
extract the interior triangles (shared by two enclosed compartments) of a complex surface
input: node: node coordinates face: surface triangle list outface: (optional) the exterior triangle list, if not given, will be computed using outersurf().
output: inface: the collection of interior triangles of the surface mesh
outface=outersurf(node,face)
extract the out-most shell of a complex surface mesh
input: node: node coordinates face: surface triangle list
output: outface: the out-most shell of the surface mesh
vol=surfvolume(node,face,option)
calculate the enclosed volume for a closed surface
input: node: node coordinates face: surface triangle list
output: vol: total volume of the enclosed space
tf=innersurf(node,face,points)
test if a set of 3D points is located inside a 3D triangular surface
input: node: node coordinates face: surface triangle list points: a set of 3D points (Nx3 array)
output: tf: a vector with the same length of points, a value of 1 means the point is inside of the surface, and a value of 0 means the point is outside of the surface.
[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 'dupnode': remove duplicated nodes 'dupelem' or 'duplicated': remove duplicated elements 'dup': both above 'isolated': remove isolated nodes 'open': abort when open surface is found 'deep': call external jmeshlib to remove non-manifold vertices 'meshfix': repair a closed surface by the meshfix utility (new) it can remove self-intersecting elements and fill holes 'intersect': test a surface for self-intersecting elements
[newelem, evol]=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 evol: the signed element volume before reorientation
elem=removedupelem(elem)
remove doubly duplicated (folded) elements
input: elem: list of elements (node indices)
output: elem: element list after removing the duplicated elements
[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
[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, can be a regular array or a cell array for PLCs
output: no: node coordinates after removing the isolated nodes el: element list of the resulting mesh
fnew=removeisolatedsurf(v,f,maxdiameter)
remove disjointed surface fragment filtered 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
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
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'));
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
[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
[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
[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]
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.
[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,:)
[newnode,newelem]=mergemesh(node,elem,varargin)
concatenate 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. mergemesh does detect self-intersecting elements when merging; to remove self-intersecting elements, you need to use mergesurf().
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');
[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. the new nodes must be located on the surface or inside the original mesh. external nodes are discarded, unless the opt.extcmdopt is specified. if opt is a vector with a length that equals to that of node, it will be used to specify the desired edge-length at each node; setting a node value to 0 will by-pass the refinement at this node if opt is a vector with a length that equals to that of elem, it will be used as the desired maximum element volume of each tetrahedron; setting to 0 will by-pass the refinement of that element. 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 opt.sizefield: a vector specifying either the desired edge-length at each node, or the maximum volume constraint within each tetrahedron, see above for details. opt.extcmdopt: by default, meshrefine can only insert nodes that are inside the original mesh. if one prefers to insert nodes that are outside of the original mesh, one can define this parameter to specify the meshing option (for tetgen) for the extended domain, i.e. the convex hull including both the original and the external nodes. If not defined, '-Y' option is used by default (prevent tetgen from inserting new nodes on the surface). opt.extlabel: when external nodes are inserted, the new elements will be assigned with an element label to group them together, by default, this label is 0, unless opt.extlabel is given opt.extcorelabel: when external nodes are inserted, par of the new elements share the polyhedra between the inserted nodes, these special elements will be marked by opt.extcorelabel, otherwise the label will be set to -1
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
examples:
[node,face,elem]=meshasphere([0 0 0],24,1,2); elem(:,5)=1;
% inserting nodes that are inside the original mesh innernodes=double([1 1 1; 2 2 2; 3 3 3]); [newno,newel]=meshrefine(node,elem,innernodes); all(ismember(round(innernodes*1e10)*1e-10,round(newno*1e10)*1e-10,'rows')) plotmesh(newno,[],newel,'x>-3')
% inserting nodes that are external to the original mesh extnodes=double([-5 -5 25;-5 5 25;5 5 25;5 -5 25]); [newno,newel]=meshrefine(node,elem,struct('newnode',extnodes,'extcmdopt','-Y')); figure; plotmesh(newno,[],newel,'x>-3')
[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');
[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: triangle surfaces (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');
[no,el]=fillsurf(node,face)
calculate the enclosed volume for a closed surface
input: node: node coordinates face: surface triangle list
output: vol: total volume of the enclosed space
[newnode,newelem]=highordertet(node,elem)
generate high-order straight-edge tetrahedral mesh from the 1st order tetrahedral mesh
input: node: list of nodes elem: list of elements (each row are indices of nodes of each element) order: optional, the order of the generated mesh; if missing, order=2
output: newnode: all new edge-nodes on the output mesh newelem: the indices of the edge nodes for each original tet element
currently, this function only supports order=2 to combine the newnode/newelem with the old mesh, one should use
elemfull=[elem(:,1:4) newelem+size(node,1)]; % 10-node element nodefull=[node;newnode];
[newnode,newelem]=elemfacecenter(node,elem)
generate barycentric dual-mesh face center nodes and indices per element very similar to highordertet which finds edge-centers instead of face-centers
input: node: list of nodes elem: list of elements (each row are indices of nodes of each element)
output: newnode: all new face-nodes on the output mesh newelem: the indices of the face nodes for each original tet element
to combine the newnode/newelem with the old mesh, one should use
elemfull=[elem(:,1:4) newelem+size(node,1)]; nodefull=[node;newnode];
[newnode,newelem]=barydualmesh(node,elem)
generate barycentric dual-mesh by connecting edge, face and elem centers
input: node: list of input mesh nodes elem: list of input mesh elements (each row are indices of nodes of each element) flag: if is 'cell', output newelem as cell arrays (each has 1x4 nodes)
output: newnode: all new nodes in the barycentric dual-mesh (made of edge/face/elem centers) newelem: the indices of the face nodes for each original tet element
example: [node,elem]=meshgrid6([0 60],[0 60],[0 60]); [newnode,newelem]=barydualmesh(node,elem,'cell'); plotmesh(newnode,newelem); hold on; plotmesh(node,[],elem,'facecolor','none','edgecolor','b')
newval=meshinterp(fromval,elemid,elembary,fromelem)
Interpolate nodal values from the source mesh to the target mesh based on a linear interpolation
input: fromval: values defined at the source mesh nodes, the row or column number must be the same as the source mesh node number, which is the same as the elemid length elemid: the IDs of the source mesh element that encloses the nodes of the target mesh nodes; a vector of length of target mesh node count; elemid and elembary can be generated by calling
[elemid,elembary]=tsearchn(node_src, elem_src, node_target);
note that the mapping here is inverse to that in meshremap()
elembary: the bary-centric coordinates of each target mesh nodes within the source mesh elements, sum of each row is 1, expect 3 or 4 columns (or can be N-D) fromelem: the element list of the source mesh
output: newval: a 2D array with rows equal to the target mesh nodes (nodeto), and columns equals to the value numbers defined at each source mesh node example:
[n1,f1,e1]=meshabox([0 0 0],[10 20 5],1); % target mesh [n2,f2,e2]=meshabox([0 0 0],[10 20 5],2); % src mesh [id, ww]=tsearchn(n2,e2,n1); % project target to src mesh value_src=n2(:,[2 1 3]); % create dummy values at src mesh newval=meshinterp(value_src,id, ww, e2);
newval=meshremap(fromval,elemid,elembary,toelem,nodeto)
Redistribute nodal values from the source mesh to the target mesh so that the sum of each property on each mesh is the same
input: fromval: values defined at the source mesh nodes, the row or column number must be the same as the source mesh node number, which is the same as the elemid length elemid: the IDs of the target mesh element that encloses the nodes of the source mesh nodes; a vector of length of src mesh node count; elemid and elembary can be generated by calling
[elemid,elembary]=tsearchn(node_target, elem_target, node_src);
note that the mapping here is inverse to that in meshinterp()
elembary: the bary-centric coordinates of each source mesh nodes within the target mesh elements, sum of each row is 1, expect 3 or 4 columns (or can be N-D) toelem: the element list of the target mesh nodeto: the total number of target mesh nodes
output: newval: a 2D array with rows equal to the target mesh nodes (nodeto), and columns equals to the value numbers defined at each source mesh node example:
[n1,f1,e1]=meshabox([0 0 0],[10 20 5],1); % src mesh [n2,f2,e2]=meshabox([0 0 0],[10 20 5],2); % target mesh [id, ww]=tsearchn(n2,e2,n1); % project src to target mesh value_src=n1(:,[2 3 1]); % create dummy values at src mesh newval=meshremap(value_src,id,ww,e2,size(n2,1)); % map to target
[node,face]=extrudesurf(no,fc,vec)
create a enclosed surface mesh by extruding an open surface
input:
output: node: 3D node coordinates for the generated surface mesh face: triangular face patches of the generated surface mesh, each row represents a triangle denoted by the indices of the 3 nodes
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
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
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
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
saveinr(vol,fname)
save a surface mesh to INR Format
input: vol: input, a binary volume fname: output file name
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
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
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
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
[node,elem,edges,edgemap]=readgts(fname)
read GNU Triangulated Surface files (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)
savemsh(node,elem,fname,rname)
save a tetrahedral mesh to GMSH mesh format
author: Riccardo Scorretti (riccardo.scorretti<at> univ-lyon1.fr)
input: node: input, node list, dimension (nn,3) elem: input, tetrahedral mesh element list, dimension (ne,4) or (ne,5) for multi-region meshes fname: output file name rname: name of the regions, cell-array of strings (optional)
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
[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
vol=readinr(fname)
load a volume from an INR file
input: fname: input file name
output: dat: output, data read from the inr file
[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
[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
[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
[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
flag=deletemeshfile(fname)
delete a given work mesh file under the working directory
input: fname: specified file name (without path)
output: flag: not used
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.
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.
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
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
$Id$
input: rootname: the name of the root-object, when set to '', the root name is ignored, however, when opt.ForceRootName is set to 1 (see below), the MATLAB variable name will be used as the root name. obj: a MATLAB object (array, cell, cell array, struct, struct array, class instance). filename: a string for the file name to save the output JSON data. opt: a struct for additional options, ignore to use default values. 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.SingletArray [0|1]: 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.SingletCell [1|0]: if 1, always enclose a cell with "[]" even it has only one element; if 0, brackets are ignored when a cell has only 1 element. 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.JSONP='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.SaveBinary [0|1]: 1 - save the JSON file in binary mode; 0 - text mode. opt.Compact [0|1]: 1- out compact JSON format (remove all newlines and tabs)
opt can be replaced by a list of ('param',value) pairs. The param string is equivallent to a field in opt and is case sensitive. output: json: a string in the JSON format (see http://json.org)
examples: jsonmesh=struct('MeshNode',[0 0 0;1 0 0;0 1 0;1 1 0;0 0 1;1 0 1;0 1 1;1 1 1],... 'MeshTetra',[1 2 4 8;1 3 4 8;1 2 6 8;1 5 6 8;1 5 7 8;1 3 7 8],... 'MeshTri',[1 2 4;1 2 6;1 3 4;1 3 7;1 5 6;1 5 7;... 2 8 4;2 8 6;3 8 4;3 8 7;5 8 6;5 8 7],... 'MeshCreator','FangQ','MeshTitle','T6 Cube',... 'SpecialData',[nan, inf, -inf]); savejson('jmesh',jsonmesh) savejson('',jsonmesh,'ArrayIndent',0,'FloatFormat','\t%.5g')
license: BSD or GPL version 3, see LICENSE_{BSD,GPLv3}.txt files for details
data=loadjson(fname,opt) or data=loadjson(fname,'param1',value1,'param2',value2,...)
parse a JSON (JavaScript Object Notation) file or string
created on 2011/09/09, including previous works from
Nedialko Krouchev: http://www.mathworks.com/matlabcentral/fileexchange/25713 created on 2009/11/02 François Glineur: http://www.mathworks.com/matlabcentral/fileexchange/23393 created on 2009/03/22 Joel Feenstra: http://www.mathworks.com/matlabcentral/fileexchange/20565 created on 2008/07/03
$Id$
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. opt can have the following fields (first in [.|.] is the default)
opt.SimplifyCell [0|1]: if set to 1, loadjson will call cell2mat for each element of the JSON data, and group arrays based on the cell2mat rules. opt.FastArrayParser [1|0 or integer]: if set to 1, use a speed-optimized array parser when loading an array object. The fast array parser may collapse block arrays into a single large array similar to rules defined in cell2mat; 0 to use a legacy parser; if set to a larger-than-1 value, this option will specify the minimum dimension to enable the fast array parser. For example, if the input is a 3D array, setting FastArrayParser to 1 will return a 3D array; setting to 2 will return a cell array of 2D arrays; setting to 3 will return to a 2D cell array of 1D vectors; setting to 4 will return a 3D cell array. opt.ShowProgress [0|1]: if set to 1, loadjson displays a progress bar.
output: dat: a cell array, where {...} blocks are converted into cell arrays, and [...] are converted to arrays
examples: dat=loadjson('{"obj":{"string":"value","array":[1,2,3]}}') dat=loadjson(['examples' filesep 'example1.json']) dat=loadjson(['examples' filesep 'example1.json'],'SimplifyCell',1)
license: BSD or GPL version 3, see LICENSE_{BSD,GPLv3}.txt files for details
json=saveubjson(rootname,obj,filename) or json=saveubjson(rootname,obj,opt) json=saveubjson(rootname,obj,'param1',value1,'param2',value2,...)
convert a MATLAB object (cell, struct or array) into a Universal Binary JSON (UBJSON) binary string
created on 2013/08/17
$Id$
input: rootname: the name of the root-object, when set to '', the root name is ignored, however, when opt.ForceRootName is set to 1 (see below), the MATLAB variable name will be used as the root name. obj: a MATLAB object (array, cell, cell array, struct, struct array, class instance) filename: a string for the file name to save the output UBJSON data opt: a struct for additional options, ignore to use default values. opt can have the following fields (first in [.|.] is the default)
opt.FileName [''|string]: a file name to save the output JSON data opt.ArrayToStruct[0|1]: when set to 0, saveubjson 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 [1|0]: if this is set to 1, logical array elem will use true/false rather than 1/0. opt.SingletArray [0|1]: 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.SingletCell [1|0]: if 1, always enclose a cell with "[]" even it has only one element; if 0, brackets are ignored when a cell has only 1 element. opt.ForceRootName [0|1]: when set to 1 and rootname is empty, saveubjson 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.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 and is case sensitive. output: json: a binary string in the UBJSON format (see http://ubjson.org)
examples: jsonmesh=struct('MeshNode',[0 0 0;1 0 0;0 1 0;1 1 0;0 0 1;1 0 1;0 1 1;1 1 1],... 'MeshTetra',[1 2 4 8;1 3 4 8;1 2 6 8;1 5 6 8;1 5 7 8;1 3 7 8],... 'MeshTri',[1 2 4;1 2 6;1 3 4;1 3 7;1 5 6;1 5 7;... 2 8 4;2 8 6;3 8 4;3 8 7;5 8 6;5 8 7],... 'MeshCreator','FangQ','MeshTitle','T6 Cube',... 'SpecialData',[nan, inf, -inf]); saveubjson('jsonmesh',jsonmesh) saveubjson('jsonmesh',jsonmesh,'meshdata.ubj')
license: BSD or GPL version 3, see LICENSE_{BSD,GPLv3}.txt files for details
data=loadubjson(fname,opt) or data=loadubjson(fname,'param1',value1,'param2',value2,...)
parse a JSON (JavaScript Object Notation) file or string
created on 2013/08/01
$Id$
input: fname: input file name, if fname contains "{}" or "[]", fname will be interpreted as a UBJSON 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. opt can have the following fields (first in [.|.] is the default)
opt.SimplifyCell [0|1]: if set to 1, loadubjson will call cell2mat for each element of the JSON data, and group arrays based on the cell2mat rules. opt.IntEndian [B|L]: specify the endianness of the integer fields in the UBJSON input data. B - Big-Endian format for integers (as required in the UBJSON specification); L - input integer fields are in Little-Endian order. opt.NameIsString [0|1]: for UBJSON Specification Draft 8 or earlier versions (JSONLab 1.0 final or earlier), the "name" tag is treated as a string. To load these UBJSON data, you need to manually set this flag to 1.
output: dat: a cell array, where {...} blocks are converted into cell arrays, and [...] are converted to arrays
examples: obj=struct('string','value','array',[1 2 3]); ubjdata=saveubjson('obj',obj); dat=loadubjson(ubjdata) dat=loadubjson(['examples' filesep 'example1.ubj']) dat=loadubjson(['examples' filesep 'example1.ubj'],'SimplifyCell',1)
license: BSD or GPL version 3, see LICENSE_{BSD,GPLv3}.txt files for details
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
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
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
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
savenirfast(nirfaststruct,filestub) or savenirfast(v,f,filestub, nodeseg, proptype, proptype)
save a tetrahedral or surface mesh and associated properties to NIRFAST format
input: nirfaststruct: a structure storing the NIRFAST mesh data, type 'help readnirfast' to read more; alternatively one can use: v: input, node list, the first 3 columns are the x/y/z positions, the remaining columns are combined with nodeprop as node-based (optical) parameters f: input, tetrahedral or surface element list, dimension (ne,3) filestub: output file stub, output will include multiple files filestub.node: node file filestub.elem: element file to store the surface or tet mesh filestub.param: parameter file filestub.region: node label file nodeseg: optional, an integer label field to group nodes into segmentations, same length as v, number starting from 0; or empty nodeprop: optional, additional nodal parameters, typically defined as mua (1/mm), musp (1/mm) and refractive index (n)l; row number equals to that of v, column number is user-defined proptype: optional, the type of the node-property. by default it is 'stnd' - for standard properties; one can also define multi-row header using a cell-array.
example: [node,face,elem]=meshabox([0 0 0],[10 10 10],0.3,1); savenirfast(node,elem,'test', [], ones(size(node)), 'user'); mymesh=readnirfast('test') plotmesh([mymesh.nodes mymesh.bndvtx], mymesh.elements,'x>5')
nirfastmesh=readnirfast(v,f,filestub)
load a group of mesh files saved in the NIRFAST format
input: filestub: output file stub, output will include multiple files filestub.node: node file filestub.elem: element file to store the surface or tet mesh filestub.param: parameter file filestub.region: node label file filestub.excoef: extinction coeff list
output: nirfastmesh.nodes: node list, 3 columns nirfastmesh.elements: element list, 3 or 4 columns integers nirfastmesh.bndvtx: boundary flag for each node, 1: on the boundary nirfastmesh.region: node segmentation labels nirfastmesh.dimension: dimension of the mesh nirfastmesh.excoef: extinction coeff list nirfastmesh.excoefheader: extinction coeff list field names nirfastmesh.type: the header of the .param file nirfastmesh.prop: optical property list (non-standard, need further processing)
format definition see http://www.dartmouth.edu/~nir/nirfast/tutorials/NIRFAST-Intro.pdf
example: [node,face,elem]=meshabox([0 0 0],[10 10 10],0.3,1); savenirfast(node,elem,'test', [], ones(size(node)), 'user'); mymesh=readnirfast('test') plotmesh([mymesh.nodes mymesh.bndvtx], mymesh.elements,'x>5')
nii=readnifti(filename)
Read a Nifti (*.nii) or Analyze 7.5 (*.hdr/*.img) image file
input: fname: the file name to a .nii file, or an Analyze 7.5 file (*.hdr,*.img)
output: nii.img: the data volume read from the nii file nii.datatype: the data type of the voxel, in matlab data type string nii.datalen: data count per voxel - for example RGB data has 3x uint8 per voxel, so datatype='uint8', datalen=3 nii.voxelbyte: total number of bytes per voxel: for RGB data, voxelbyte=3; also voxelbyte=header.bitpix/8 nii.hdr: file header info, a structure has the full nii header key subfileds include
sizeof_hdr: must be 348 if the input is nifti dim: short array, dim(2: dim(1)+1) defines the array size datatype: the type of data stored in each voxel bitpix: total bits per voxel magic: must be 'ni1\0' or 'n+1\0'
For the detailed nii header, please see https://nifti.nimh.nih.gov/pub/dist/src/niftilib/nifti1.h
this file was ported from mcxloadnii.m from the MCX Project (http://mcx.space)
vol=readmptiff(fname)
load a volume from a multi-page TIFF file
input: fname: input file name
output: dat: output, data read from the TIFF file
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)
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
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
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
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
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
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
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
vol=thinbinvol(vol,layer,nobd)
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 run thinning for non-zero elements (and hopefully faster)
input: vol: a volumetric binary image layer: number of iterations for the thickenining nobd: (optional) if set to 1, boundaries will not erode. if not given, nobd=0.
output: vol: the volume image after the thinning operations
dist=maskdist(vol)
return the distance in each voxel towards the nearest label boundaries
input: vol: a 2D or 3D array
output: dist: an integer array, storing the distance, in voxel unit, towards the nearest boundary between two distinct non-zero voxels, the zero voxels in the domain and space outside of the array are also treated as a unique non-zero label. If the goal is to get the minimum distance measured from the center of the voxel, one should use (dist-0.5).
example:
a=ones(60,60,60); a(:,:,1:10)=2; a(:,:,11:20)=3; im=maskdist(a); imagesc(squeeze(im(:,30,:)))
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', or an equation defining a plane at which a mesh cross-section is plotted, for example 'y=2*x'; 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','--'); h=plotmesh(node,elem,'z=20');
hm=plotsurf(node,face,opt)
plot 3D surface meshes (2d manifold) or polylines (1d manifold)
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'); h=plotsurf(node,edges,'linestyle','-','linewidth',2,'color','r');
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, and the 5th column are all integers, it will be treated as labels of sub-domains and display them in different colors. if the 5th column contains non-integer values, it will be used to map to the color of triangles. 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);
hm=plotedges(node,edges,opt) or hm=plotedges(node,loops,opt)
plot a 3D polyline or close loop (1d manifold)
input: node: node coordinates, dimension (nn,3); if node has a 4th column, it will be used to set the color at each node. edges:edge list: a 2-column index array, with each row being an edge connecting the two indexed node loops:loops is an NaN separated integer array, with each segment denoting a 3D polyline or loop represented by a list of node indices opt: additional options for the plotting, see plotmesh
output: hm: handle or handles (vector) to the plotted surfaces
example:
h=plotedges(node,[1 2 3 4 5 nan 6 7 8 9]); h=plotedges(node,edges,'marker','o','linewidth',2,'color','r');
[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
without any output, qmeshcut generates a cross-section plot
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');
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
[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
[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)
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
[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)
[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
exesuff=getexeext()
get meshing external tool extension names for the current platform
output: exesuff: file extension for iso2mesh tool binaries
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
[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
[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)
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
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
[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(:)
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
-- this function is part of jsonlab toolbox (http://iso2mesh.sf.net/cgi-bin/index.cgi?jsonlab)
len=length(varargin); opt=struct; if(len==0) return; end i=1; while(i<=len)
if(isstruct(varargin{i})) opt=mergestruct(opt,varargin{i}); elseif(ischar(varargin{i}) && i<len) opt=setfield(opt,lower(varargin{i}),varargin{i+1}); i=i+1; else error('input must be in the form of ...,name,value,... pairs or structs'); end i=i+1;end
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
-- this function is part of jsonlab toolbox (http://iso2mesh.sf.net/cgi-bin/index.cgi?jsonlab)
val=default; if(nargin<=2) return; end opt=varargin{1}; if(isstruct(opt))
if(isfield(opt,key)) val=getfield(opt,key); elseif(isfield(opt,lower(key))) val=getfield(opt,lower(key)); endend
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
-- this function is part of jsonlab toolbox (http://iso2mesh.sf.net/cgi-bin/index.cgi?jsonlab)
if(~isstruct(s1) || ~isstruct(s2))
error('input parameters contain non-struct');end if(length(s1)>1 || length(s2)>1)
error('can not merge struct arrays');end fn=fieldnames(s2); s=s1; for i=1:length(fn)
s=setfield(s,fn{i},getfield(s2,fn{i}));end
node=orthdisk(c0,c1,r,ndiv)
Defining a 3D disk that is orthogonal to the vector c1-c0
input: c0: a 1x3 vector for the origin c1: a 1x3 vector to define a direction vector c1-c0 r: the radius of the disk that is orthogonal to c1-c0, passing through c0 ndiv: division count to approximate a circle by a polygon, if ignored, ndiv=20 v1: a 1x3 vector specifying the first point on the output 3D disk. if v1 is not perpendicular to c1-c0, the disk rotation axis is changed to cross(v1,cross(c1-c0,v1)); angle0: angle0 represents the angle (in radian) of the 1st point in the 3D disk if placed on the x-y plane.
output: node: the 3D vertices of the disk
newdata=struct2jdata(data,opt,...)
convert a JData object (in the form of a struct array) into an array
input: data: a struct array. If data contains JData keywords in the first level children, these fields are parsed and regrouped into a data object (arrays, trees, graphs etc) based on JData specification. The JData keywords are "_ArrayType_", "_ArraySize_", "_ArrayData_" "_ArrayIsSparse_", "_ArrayIsComplex_" opt: (optional) a list of 'Param',value pairs for additional options The supported options include 'Recursive', if set to 1, will apply the conversion to every child; 0 to disable
output: newdata: the covnerted data if the input data does contain a JData structure; otherwise, the same as the input.
examples: obj=struct('_ArrayType_','double','_ArraySize_',[2 3], '_ArrayIsSparse_',1 ,'_ArrayData_',null); ubjdata=struct2jdata(obj);
license: BSD or GPL version 3, see LICENSE_{BSD,GPLv3}.txt files for details
This toolbox interacts with a number external meshing tools to perform the essential functionalities. These tools are listed below:
Note: iso2mesh and the above meshing utilities are considered as an "aggregate" rather than "derived work", based on the definitions in GPL FAQ (http://www.gnu.org/licenses/gpl-faq.html#MereAggregation) Therefore, the license of iso2mesh and these utilities are independent. The iso2mesh license only applies to the scripts and documents/data in this package and exclude those programs stored in the bin/ directory. The source codes of the modified meshing utilities are available separately at iso2mesh's website and retain their upstream licenses.
Your acknowledgement of iso2mesh in your publications or presentations would be greatly appreciated by the author of this toolbox. The citation information can be found in the Introduction section.