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Tet1.m
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Tet1.m
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classdef Tet1 < matlab.mixin.Copyable
%Tet1 P1 Tetrahedral structured mesh rectangle
%o = Tet1(x0,x1,nxe,y0,y1,nye,z0,z1,nze)
%o = Tet1(x0,x1,nxe,y0,y1,nye,z0,z1,nze,type)
% type = 'default'|'fishbone'
properties
Connectivity
Points
Faces
XC
YC
ZC
edges
Element
ElementType
neighs
nnod
nele
end
properties (Access = private)
x0
x1
y0
y1
z0
z1
nxe
nye
nze
end
methods
function o = Tet1(x0,x1,nxe,y0,y1,nye,z0,z1,nze,varargin)
o.nxe = nxe; o.nye = nye; o.nze = nze;
o.x0=x0; o.x1=x1; o.y0=y0; o.y1=y1; o.z0=z0; o.z1=z1;
nx = nxe; ny = nye; nz = nze;
%% Start by creating mesh in the XY-plane
if nargin == 10
if strcmpi(varargin{1},'fishbone')
T = Mesh.fishbone2DP1(x0,x1,y0,y1,nxe,nye);
t = T.Connectivity;
p = T.Points;
[elements,edgess,~]=tritoel(p(:,1),p(:,2),t);
tri=trinode(edgess,elements);
edgess=direction(edgess,p(:,1),p(:,2));
[tet,x3d,y3d,z3d]=extrude3d(edgess,elements,tri,p(:,1),p(:,2),z0,z1,nz);
p = [x3d,y3d,z3d];
else
[X,Y]=meshgrid(linspace(x0,x1,nx+1),linspace(y0,y1,ny+1));
X = [X(:),Y(:)];
t = delaunay(X(:,1),X(:,2));
p = X;
[elements,edgess,~]=tritoel(p(:,1),p(:,2),t);
tri=trinode(edgess,elements);
edgess=direction(edgess,p(:,1),p(:,2));
[tet,x3d,y3d,z3d]=extrude3d(edgess,elements,tri,p(:,1),p(:,2),z0,z1,nz);
p = [x3d,y3d,z3d];
end
else
[X,Y]=meshgrid(linspace(x0,x1,nx+1),linspace(y0,y1,ny+1));
X = [X(:),Y(:)];
t = delaunay(X(:,1),X(:,2));
p = X;
[elements,edgess,~]=tritoel(p(:,1),p(:,2),t);
tri=trinode(edgess,elements);
edgess=direction(edgess,p(:,1),p(:,2));
[tet,x3d,y3d,z3d]=extrude3d(edgess,elements,tri,p(:,1),p(:,2),z0,z1,nz);
p = [x3d,y3d,z3d];
end
%% Extrude upwards
% dl=(z1-z0)/nze;
% z = z0:dl:z1;
% nnod = size(p,1);
% znod = reshape( ones(nnod,1)*z, [], 1);
% xynod = repmat(p,nz+1,1);
% p = [xynod,znod];
% mt = max(t(:));
%
% nzele = size(t,1);
% prism = zeros(nzele*nz,6); % preallocate space for prism elements
% l = (0:nz)*nzele;
% c = 1;
% for iz = 0:nz-1
% lo = l(c)+1;
% up = l(c+1);
% tt = [t(:,:)+mt*iz,t(:,:)+mt*(iz+1)];
% prism(lo:up,:) = tt;
% c=c+1;
% end
%
% prism = unique(prism,'rows');
%
% %% Prism to tet
% tet = [prism(:,[1,2,3,5]);
% prism(:,[1,5,6,4]);
% prism(:,[1,5,6,3])];
%% tet2tri
o.nele = size(tet,1);
o.nnod = size(p,1);
TR = triangulation(tet,p);
tetraTri = zeros(4*size(tet,1),3);
o.Element(o.nele).faces = [];
o.Element(o.nele).edges = [];
o.edges = TR.edges;
for iel = 1:size(tet,1)
eli=tet(iel,:);
iface = [eli([1,2,3]);
eli([1,3,4]);
eli([1,2,4]);
eli([2,3,4])];
tetraTri(4*iel-3:4*iel,:) = iface;
o.Element(iel).faces = iface;
o.Element(iel).edges = [eli([1,2]);
eli([2,3]);
eli([3,4]);
eli([4,1]);
eli([1,3]);
eli([2,4]);];
end
%% Output to Tet1 properties
o.ElementType = 'Tet1Mesh';
o.Connectivity = tet;
o.Points = p;
o.Faces = tetraTri;
o.XC = p(:,1); o.YC = p(:,2); o.ZC = p(:,3);
o.neighs = TR.neighbors;
end
h = vizMesh(o,varargin);
[fi, fix, fiy, fiz, vol] = baseFun(o,iel,X);
end
methods(Hidden)
function lh = addlistener(varargin)
lh = addlistener@handle(varargin{:});
end
function notify(varargin)
notify@handle(varargin{:});
end
function delete(varargin)
delete@handle(varargin{:});
end
function Hmatch = findobj(varargin)
Hmatch = findobj@handle(varargin{:});
end
function p = findprop(varargin)
p = findprop@handle(varargin{:});
end
function TF = eq(varargin)
TF = eq@handle(varargin{:});
end
function TF = ne(varargin)
TF = ne@handle(varargin{:});
end
function TF = lt(varargin)
TF = lt@handle(varargin{:});
end
function TF = le(varargin)
TF = le@handle(varargin{:});
end
function TF = gt(varargin)
TF = gt@handle(varargin{:});
end
function TF = ge(varargin)
TF = ge@handle(varargin{:});
end
end
end
function [elements,edges,nodes]=tritoel(xnod,ynod,tri)
%columns of elements: longest edge, next (counterclock),next,next,
% oppnode, hangnode
%columns of edges: node1, node2, boundary (0 is interior edge),length
x2=xnod(tri(:,2))-xnod(tri(:,1));
y2=ynod(tri(:,2))-ynod(tri(:,1));
x3=xnod(tri(:,3))-xnod(tri(:,1));
y3=ynod(tri(:,3))-ynod(tri(:,1));
detj=x2.*y3-x3.*y2; %Area of elements
%%% Makes sure that the order is counterclockwise
ind=find(detj<0);
t=tri(ind,3);
tri(ind,3)=tri(ind,2);tri(ind,2)=t;
%%%
nele=length(tri(:))/3; %number of elements
%% Find edges
edges=sort([tri(:,1),tri(:,2)],2);
edges=[edges;sort([tri(:,2),tri(:,3)],2)];
edges=[edges;sort([tri(:,1),tri(:,3)],2)];
edges=[edges,zeros(length(edges(:,1)),1),zeros(length(edges(:,1)),1)];
% Tr = TriRep(tri,xnod,ynod);
% edges2 = Tr.edges
%% Find doublets and remove them, add 1 or zero to the 3rd coulumn depending
% on if that row did not contain double
% Add length of edge to the fourth column
i1=1;
while i1 <= length(edges) %Size of edges changes...
ind=find(edges(i1,1)==edges(:,1) & edges(i1,2)==edges(:,2));
if(length(ind)==1)
edges(i1,3)=1;
n1=edges(i1,1);n2=edges(i1,2);
edges(i1,4)=sqrt((xnod(n1)-xnod(n2))^2+(ynod(n1)-ynod(n2))^2);
else
n1=edges(ind(1),1);n2=edges(ind(1),2);
edges(ind(1),4)=sqrt((xnod(n1)-xnod(n2))^2+(ynod(n1)-ynod(n2))^2);
ind(1)=[];
edges(ind,:)=[];
end
i1 = i1 + 1;
end
% edges
elements=zeros(nele,8);
for iel=1:nele
ed1=sort([tri(iel,1),tri(iel,2)],2);
ed1=find(ed1(1)==edges(:,1) & ed1(2)==edges(:,2));
ed2=sort([tri(iel,3),tri(iel,2)],2);
ed2=find(ed2(1)==edges(:,1) & ed2(2)==edges(:,2));
ed3=sort([tri(iel,1),tri(iel,3)],2);
ed3=find(ed3(1)==edges(:,1) & ed3(2)==edges(:,2));
ed=[ed1,ed2,ed3,ed1,ed2];
len=[edges(ed1,4),edges(ed2,4),edges(ed3,4)];
ind=find(len==max(len));ind=ind(1);
elements(iel,1:3)=[ed(ind),ed(ind+1),ed(ind+2)];
nod=unique([edges(ed1,1:2),edges(ed2,1:2),edges(ed3,1:2)]);
elements(iel,5)=setdiff(nod,edges(ed(ind),1:2));
end
nodes=[xnod,ynod];
end
function tri=trinode(edges,elements)
%
[nele,s]=size(elements);
tri=zeros(nele,3);
%el=elements(:,1:3);
ed1=elements(:,1);ed2=elements(:,2);ed3=elements(:,3);
e1=edges(ed1,1:2);e2=edges(ed2,1:2);e3=edges(ed3,1:2);
% find number on e2 ~= number on e1
ind=find(e1(:,1)~=e2(:,1) & e1(:,1)~=e2(:,2));
tri1=e1(:,2);tri1(ind)=e1(ind,1);
ind=find(e2(:,1)~=e3(:,1) & e2(:,1)~=e3(:,2));
tri2=e2(:,2);tri2(ind)=e2(ind,1);
ind=find(e3(:,1)~=e1(:,1) & e3(:,1)~=e1(:,2));
tri3=e3(:,2);tri3(ind)=e3(ind,1);
tri=[tri1,tri2,tri3];
end
function edges=direction(edges,xnod,ynod)
nedges=size(edges,1);
edges=edges(:,1:2);
for ed=1:nedges
v=[xnod(edges(ed,2))-xnod(edges(ed,1)),ynod(edges(ed,2))-ynod(edges(ed,1))];
if(dot(v,[1,0]) < 0)
edges(ed,1:2)=fliplr(edges(ed,1:2));
end
end
end
function [tri3d,x3d,y3d,z3d]=extrude3d(edges,elements,tri,xnod,ynod,zmin,zmax,nlayer)
%
% 4 ------ 6
% |\ /|
% | \ / |
% | \/ 5|
% | | |
% | | |
% \ | / 3
% 1 \ | /
% \ |/
% \/
% 2
% z=0 to z=1, built upwards
%
dl=(zmax-zmin)/nlayer;
[nrtri,s]=size(tri);
nno=length(xnod);
tri3d=zeros(nrtri,4);
x3d=zeros(2*nno,1);y3d=x3d;z3d=x3d;
nele3=1;
nod=0;
for iel=1:nrtri
edel=elements(iel,1:3);
if(edges(edel(3),1)== edges(edel(1),1))
nod=1;
elseif(edges(edel(1),1) == edges(edel(2),1))
nod=2;
elseif(edges(edel(2),1)==edges(edel(3),1))
nod=3;
end
switch nod
case 1
tri3d(nele3,1:4)=[tri(iel,1),tri(iel,2)+nno,tri(iel,3)+nno,tri(iel,1)+nno];
if(edges(edel(2),1)== tri(iel,2))
tri3d(nele3+1,1:4)=[tri(iel,1:3),tri(iel,3)+nno];
tri3d(nele3+2,1:4)=[tri(iel,1),tri(iel,2),tri(iel,3)+nno,tri(iel,2)+nno]; % OK
else
tri3d(nele3+1,1:4)=[tri(iel,1:3),tri(iel,2)+nno];
tri3d(nele3+2,1:4)=[tri(iel,1),tri(iel,2)+nno,tri(iel,3),tri(iel,3)+nno]; % OK
end
nele3=nele3+3;
case 2
tri3d(nele3,1:4)=[tri(iel,2),tri(iel,2)+nno,tri(iel,3)+nno,tri(iel,1)+nno];
if(edges(edel(3),1)== tri(iel,3))
tri3d(nele3+1,1:4)=[tri(iel,1:3),tri(iel,1)+nno];
tri3d(nele3+2,1:4)=[tri(iel,1)+nno,tri(iel,2),tri(iel,3),tri(iel,3)+nno]; %OK
else
tri3d(nele3+1,1:4)=[tri(iel,1:3),tri(iel,3)+nno];
tri3d(nele3+2,1:4)=[tri(iel,1)+nno,tri(iel,1),tri(iel,3)+nno,tri(iel,2)]; %OK
end
nele3=nele3+3;
case 3
tri3d(nele3,1:4)=[tri(iel,1)+nno,tri(iel,2)+nno,tri(iel,3),tri(iel,3)+nno];
if(edges(edel(1),1)== tri(iel,1))
tri3d(nele3+1,1:4)=[tri(iel,1:3),tri(iel,2)+nno];
tri3d(nele3+2,1:4)=[tri(iel,1)+nno,tri(iel,2)+nno,tri(iel,1),tri(iel,3)]; %OK
else
tri3d(nele3+1,1:4)=[tri(iel,1:3),tri(iel,1)+nno];
tri3d(nele3+2,1:4)=[tri(iel,1)+nno,tri(iel,2),tri(iel,3),tri(iel,2)+nno];
end
nele3=nele3+3;
end
end
x3d(1:nno)=xnod;x3d(nno+1:end)=xnod;
y3d(1:nno)=ynod;y3d(nno+1:end)=ynod;
% z3d(1:nno)=0; %Original
z3d(1:nno)=zmin;
z3d(nno+1:end)=zmin+dl;
z3dstart = unique(z3d);
z3dstart = z3dstart(2);
if(nlayer > 1)
triex0=tri3d;
for ilayer=2:nlayer
triex=tri3d(:)+(ilayer-1)*nno;
triex0=[triex0;reshape(triex,size(tri3d))];
x3d=[x3d;xnod];y3d=[y3d;ynod];
% z3d=[z3d;ones(size(xnod))*ilayer*dl]; % Original
z3d=[z3d;ones(size(xnod))*(z3dstart+(ilayer-1)*dl)];
end
tri3d=triex0;
end
end