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ns_t1Transition.m
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%% Execute a single T1 trnasition.
function [vrtxN,edgeN,faceN]=...
ns_t1Transition(vrtx,edge,face,rg,gmp,mcp,t1Id)
%% Define output variables.
[vrtxN,edgeN,faceN]=deal(vrtx,edge,face);
%% Find vertex ID, edge ID, and face ID of local T1 configuration.
% local edge ID.
cvId=edgeN{1}(t1Id,rg.ei(1):rg.ef(1));
eId=[setdiff(vrtxN(cvId(1),rg.vi(1):rg.vf(1)),t1Id),...
setdiff(vrtxN(cvId(2),rg.vi(1):rg.vf(1)),t1Id)];
ef1=edgeN{1}(eId(1),rg.ei(2):rg.ef(2));
ef1=ef1(ef1~=0);
if size(ef1,2)==1
eId(1:2)=[eId(2),eId(1)];
ef1=edgeN{1}(eId(1),rg.ei(2):rg.ef(2));
ef1=ef1(ef1~=0);
end
ef2=edgeN{1}(eId(4),rg.ei(2):rg.ef(2));
ef2=ef2(ef2~=0);
if size(ef2,2)==1
eId(3:4)=[eId(4),eId(3)];
ef2=edgeN{1}(eId(4),rg.ei(2):rg.ef(2));
ef2=ef2(ef2~=0);
end
if isempty(intersect(ef1,ef2))==0
eId(3:4)=[eId(4),eId(3)];
end
% local vertex ID.
vId=zeros(4,1);
for ii=1:2
vId(ii)=setdiff(edgeN{1}(eId(ii),rg.ei(1):rg.ef(1)),cvId(1));
end
for ii=3:4
vId(ii)=setdiff(edgeN{1}(eId(ii),rg.ei(1):rg.ef(1)),cvId(2));
end
% local face ID.
fId=[intersect(edgeN{1}(t1Id,3:4),edgeN{1}(eId(1),3:4)),...
intersect(edgeN{1}(t1Id,3:4),edgeN{1}(eId(2),3:4)),...
setdiff(edgeN{1}(eId(1),3:4),edgeN{1}(t1Id,3:4)),...
setdiff(edgeN{1}(eId(3),3:4),edgeN{1}(t1Id,3:4))];
%% Reassign vertex-edge relation.
if eId(1)~=eId(3)
vrtxN(cvId(1),rg.vi(1):rg.vf(1))=sort([t1Id,eId(1),eId(3)]);
else
vrtxN(cvId(1),rg.vi(1):rg.vf(1))=sort([0,t1Id,eId(1)]);
end
if eId(2)~=eId(4)
vrtxN(cvId(2),rg.vi(1):rg.vf(1))=sort([t1Id,eId(2),eId(4)]);
else
vrtxN(cvId(2),rg.vi(1):rg.vf(1))=sort([0,t1Id,eId(2)]);
end
%% Reassign vertex-face relation.
vrtxN(cvId(1),rg.vi(2):rg.vf(2))=sort([fId(1),fId(3),fId(4)]);
vrtxN(cvId(2),rg.vi(2):rg.vf(2))=sort([fId(2),fId(3),fId(4)]);
%% Reassign edge-vertex relation.
edgeN{1}(eId(2),rg.ei(1):rg.ef(1))=sort([cvId(2),vId(2)]);
edgeN{1}(eId(3),rg.ei(1):rg.ef(1))=sort([cvId(1),vId(3)]);
%% Reassign edge-face relation.
edgeN{1}(t1Id,rg.ei(2):rg.ef(2))=sort([fId(3),fId(4)]);
%% Adjust vertex coordinates for T1 vertices.
vCrdTmp=ns_crdLocal(vrtxN(cvId,rg.vi(3):rg.vf(3)),gmp.bs,gmp.sstn);
t1CrdTmp=repmat(1/2*sum(vCrdTmp(:)),2)-[vCrdTmp(2,2),vCrdTmp(1,1);...
vCrdTmp(1,2),vCrdTmp(2,1)];
emd1=edgeN{2}{eId(1)};
if edge{1}(eId(1),1)==vId(1)
emd1(end,:)=t1CrdTmp(1,:);
if vId(1)==cvId(2)
emd1=emd1(2:end,:);
end
else
emd1(1,:)=t1CrdTmp(1,:);
if vId(1)==cvId(2)
emd1=emd1(1:end-1,:);
end
end
emd2=edgeN{2}{eId(2)};
if edge{1}(eId(2),1)==vId(2)
emd2(end,:)=t1CrdTmp(2,:);
if vId(2)==cvId(2)
emd2=emd2(2:end,:);
end
else
emd2(1,:)=t1CrdTmp(2,:);
if vId(2)==cvId(2)
emd1=emd1(1:end-1,:);
end
end
emdc=ns_crdLocal([emd1;emd2],gmp.bs,gmp.sstn);
emd1=emdc(1:size(emd1,1),:);
emd2=emdc(size(emd1,1)+1:end,:);
ec=0;
for ii=1:size(emd1,1)-1
for jj=1:size(emd2,1)-1
[ecCs,~]=ns_lineCross([emd1(ii:ii+1,:);emd2(jj:jj+1,:)]);
if ecCs==1
ec=1;
end
end
end
if ec==1
vrtxN(cvId(1),rg.vi(3):rg.vf(3))=t1CrdTmp(2,:);
vrtxN(cvId(2),rg.vi(3):rg.vf(3))=t1CrdTmp(1,:);
else
vrtxN(cvId(1),rg.vi(3):rg.vf(3))=t1CrdTmp(1,:);
vrtxN(cvId(2),rg.vi(3):rg.vf(3))=t1CrdTmp(2,:);
end
%% Update intermediate edge coordinates.
eVr=ns_crdLocal(vrtxN(edgeN{1}(t1Id,rg.ei(1):rg.ef(1)),...
rg.vi(3):rg.vf(3)),gmp.bs,gmp.sstn);
[edgeN{2}{t1Id},edgeN{1}(t1Id,rg.ei(4))]=...
ns_edgeMidVrtxAverage(eVr,gmp.edpc);
if eId(1)~=eId(3)
for ii=[1,3]
if edge{1}(eId(ii),1)==vId(ii)
emd=edge{2}{eId(ii)}(1:end-1,:);
if edgeN{1}(eId(ii),1)==vId(ii)
emdc=[emd;vrtxN(cvId(1),rg.vi(3):rg.vf(3))];
else
emdc=[vrtxN(cvId(1),rg.vi(3):rg.vf(3));flipud(emd)];
end
else
emd=edge{2}{eId(ii)}(2:end,:);
if edgeN{1}(eId(ii),2)==vId(ii)
emdc=[vrtxN(cvId(1),rg.vi(3):rg.vf(3));emd];
else
emdc=[flipud(emd);vrtxN(cvId(1),rg.vi(3):rg.vf(3))];
end
end
eMd=ns_crdLocal(emdc,gmp.bs,gmp.sstn);
[edgeN{2}{eId(ii)},edgeN{1}(eId(ii),rg.ei(4))]...
=ns_edgeMidVrtxAverage(eMd,gmp.edpc);
end
else
emd=edge{2}{eId(1)}(2:end-1,:);
emdc=[vrtxN(cvId(1),rg.vi(3):rg.vf(3));emd;...
vrtxN(cvId(1),rg.vi(3):rg.vf(3))];
eMd=ns_crdLocal(emdc,gmp.bs,gmp.sstn);
[edgeN{2}{eId(1)},edgeN{1}(eId(1),rg.ei(4))]...
=ns_edgeMidVrtxAverage(eMd,gmp.edpc);
end
if eId(2)~=eId(4)
for ii=[2,4]
if edge{1}(eId(ii),1)==vId(ii)
emd=edge{2}{eId(ii)}(1:end-1,:);
if edgeN{1}(eId(ii),1)==vId(ii)
emdc=[emd;vrtxN(cvId(2),rg.vi(3):rg.vf(3))];
else
emdc=[vrtxN(cvId(2),rg.vi(3):rg.vf(3));flipud(emd)];
end
else
emd=edge{2}{eId(ii)}(2:end,:);
if edgeN{1}(eId(ii),2)==vId(ii)
emdc=[vrtxN(cvId(2),rg.vi(3):rg.vf(3));emd];
else
emdc=[flipud(emd);vrtxN(cvId(2),rg.vi(3):rg.vf(3))];
end
end
eMd=ns_crdLocal(emdc,gmp.bs,gmp.sstn);
[edgeN{2}{eId(ii)},edgeN{1}(eId(ii),rg.ei(4))]...
=ns_edgeMidVrtxAverage(eMd,gmp.edpc);
end
else
emd=edge{2}{eId(2)}(2:end-1,:);
emdc=[vrtxN(cvId(2),rg.vi(3):rg.vf(3));emd;...
vrtxN(cvId(2),rg.vi(3):rg.vf(3))];
eMd=ns_crdLocal(emdc,gmp.bs,gmp.sstn);
[edgeN{2}{eId(2)},edgeN{1}(eId(2),rg.ei(4))]...
=ns_edgeMidVrtxAverage(eMd,gmp.edpc);
end
%% Calculate new edge length.
edgeN{4}{t1Id}=ns_edgeLen(edgeN{2}{t1Id});
edgeN{1}(t1Id,rg.ei(5):rg.ef(5))=ns_edgeRange(edgeN,t1Id);
for ii=1:4
edgeN{4}{eId(ii)}=ns_edgeLen(edgeN{2}{eId(ii)});
edgeN{1}(eId(ii),rg.ei(5):rg.ef(5))=ns_edgeRange(edgeN,eId(ii));
end
%% Reassign face-vertex relation.
% Insert vertex 2 in face 1 and vertex 1 in face 2.
for ii=[1,2]
if fId(ii)>0
fvrInd=faceN{2}{fId(ii)};
faceN{2}{fId(ii)}=fvrInd(fvrInd~=cvId(mod(ii,2)+1));
end
end
for ii=[3,4]
if fId(ii)>0
fvrInd=faceN{2}{fId(ii)};
fvrInd=ns_faceVrtxIdInsert(cvId(mod(ii-1,2)+1),vId(ii-1),...
cvId(mod(ii,2)+1),fvrInd);
faceN{2}{fId(ii)}=fvrInd;
end
end
%% Reassign face-edge relation.
for ii=1:4
if fId(ii)>0
faceN{3}{fId(ii)}=ns_faceEdgeId(edgeN,faceN,gmp,rg,fId(ii));
end
end
%% Calculate new face area, number of neighbors, perimeter.
for ii=1:4
if fId(ii)>0
fEd=faceN{3}{fId(ii)};
[faceN{1}(fId(ii),rg.fi(2)),faceN{1}(fId(ii),rg.fi(6):rg.ff(6))]...
=ns_faceArea(fEd,edgeN{2},gmp.bs,gmp.sstn);
if faceN{1}(fId(ii),rg.fi(2))<0
faceN{2}{fId(ii)}=fliplr(faceN{2}{fId(ii)});
faceN{3}{fId(ii)}=ns_faceEdgeId(edgeN,faceN,gmp,rg,fId(ii));
fEd=faceN{3}{fId(ii)};
[faceN{1}(fId(ii),rg.fi(2)),faceN{1}(fId(ii),rg.fi(6):rg.ff(6))]...
=ns_faceArea(fEd,edgeN{2},gmp.bs,gmp.sstn);
end
faceN{1}(fId(ii),rg.fi(3))=0;
for jj=1:size(fEd,2)
faceN{1}(fId(ii),rg.fi(3))=faceN{1}(fId(ii),rg.fi(3))+...
sum(edgeN{4}{abs(fEd(jj))});
end
faceN{1}(fId(ii),rg.fi(4))=ns_faceNeiCount...
(fEd,edgeN{1}(:,rg.ei(2):rg.ef(2)),fId(ii));
faceN{1}(fId(ii),rg.fi(5))=size(fEd,2);
end
end
%% Compute edge tension for T1 edge.
% eTn=[ns_edgeFixedTension(face,edge,rg,mcp,t1Id),...
% ns_edgeFixedTension(faceN,edgeN,rg,mcp,t1Id)];
%
% edgeN{1}(t1Id,rg.ei(3))=edgeN{1}(t1Id,rg.ei(3))-(eTn(1)-eTn(2));
end