How to create a spherical mesh with refined mesh densities
In this tutorial, we show an example to use the advanced options iso2mesh to produce a spherical domain inside a cube with refined mesh densities near the regions-of-interest.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Create meshes for a sphere inside a cubic domain
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% preparation
% you have to add the path to iso2mesh toolbox
% addpath('/path/to/iso2mesh/toolbox/');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Part 0. How to Create a Spherical Mesh Using Iso2mesh
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% first create a gray-scale field representing distance from the sphere center
dim=60;
[xi,yi,zi]=meshgrid(0:0.5:dim,0:0.5:dim,0:0.5:dim);
dist=sqrt((xi-30).^2+(yi-30).^2+(zi-30).^2);
clear xi yi zi;
% extract a level-set at v=20, being a sphere with R=20
% the maximum element size of the surface triangles is 2
[v0,f0]=vol2restrictedtri(dist,20,[60 60 60],60*60*20,30,2,2,40000);
v0=(v0-0.5)*0.5;
% iso2mesh will also produce a surface for the bounding box, remove it
facecell=finddisconnsurf(f0);
sphsurf=facecell{1};
if( sum((v0(sphsurf(1,1),:)-[30 30 30]).^2) > 25*25 )
sphsurf=facecell{2};
end
trisurf(sphsurf,v0(:,1),v0(:,2),v0(:,3)); % plot the sphere surface
axis equal;
idx=unique(sphsurf); % this is the index of all the nodes on the sphere
% show the histogram of the displacement error for the nodes on the sphere
r0=sqrt((v0(idx,1)-30).^2+(v0(idx,2)-30).^2+(v0(idx,3)-30).^2);
figure;hist(r0,100);
% we only take the nodes on the surface
[no,el]=removeisolatednode(v0,sphsurf);
[no,el]=meshcheckrepair(no,el);
extracted spherical surface mesh | histogram of the node radius |
| |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Part I. A Coarse Mesh for a Sphere Inside a Box with Refinement
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% generate a coarse volumetric mesh from the sphere with an additional bounding box
% the maximum element volume is 8
ISO2MESH_SESSION='demo_sph3_';
srcpos=[30. 30. 0.]; % set the center of the ROI
fixednodes=[30.,30.,0.1; 30 30 30]; % add control points so we can refine mesh densities there
nodesize=[ones(size(no,1),1) ; 0.2; 4]; % set target edge size of 1 for all nodes on the sphere
% target edge size 0.3 near (30,30,0.05)
% and target edge size 4 near (30,30,30)
nfull=[no;fixednodes]; % append additional control points
[node3,elem3,face3]=surf2mesh([nfull,nodesize],el,[0 0 0],[61 61 61],1,8,[30 30 30],[],[2 2 2 2 6 6 6 6]);
% ^- add node size as the last ^ max volume ^- edge sizes at the 8
% column to node corners of the bounding box
[node3,elem3]=sortmesh(srcpos,node3,elem3,1:4); % reorder the nodes/elements
% so that the nodes near earch order
% are more clustered in the memory
elem3(:,1:4)=meshreorient(node3,elem3(:,1:4)); % reorient elements to ensure the volumns are positive
cross-cut view of the generated mesh |
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Part II. A Dense Mesh for a Sphere Inside a Box with Refinement
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% generate a dense volumetric mesh from the sphere with an additional bounding box
% the maximum element volume is 2
ISO2MESH_SESSION='demo_sph2_';
nodesize=[0.7*ones(size(no,1),1) ; 0.2; 2]; % set target edge size to 0.7 near the sphere
% 0.2 near (30,30,0.5) and 2 near (30,30,30)
[node2,elem2,face2]=surf2mesh([nfull,nodesize],el,[0 0 0],[61 61 61],1,2,[30 30 30],[],[1 1 1 1 5 5 5 5]);
[node2,elem2]=sortmesh(srcpos,node2,elem2,1:4);
elem2(:,1:4)=meshreorient(node2,elem2(:,1:4));
cross-cut view of the generated mesh |
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Part III. A Coarse Mesh for a Sphere Inside a Box without Refinement
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
ISO2MESH_SESSION='demo_sph1_';
% reduce the surface node numbers to 20%
[no2,el2]=meshresample(no,el,0.2); % down sample the sphere mesh
% using the coarse spherical surface, we generate a coarse volumetric
% mesh with maximum volume of 10
[node1,elem1,face1]=surf2mesh(no2,el2,[0 0 0],[61 61 61],1,10,[30 30 30],[],1);
[node1,elem1]=sortmesh(srcpos,node1,elem1,1:4);
elem1(:,1:4)=meshreorient(node1,elem1(:,1:4));
clear ISO2MESH_SESSION
cross-cut view of the generated mesh |
|