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bisect.m
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bisect.m
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function [mesh] = bisect(mesh)
%BISECT bisect cells in a mesh object.
%-----------------------------------------------------------
% Darren Engwirda
% github.com/dengwirda/jigsaw-matlab
% 08-Aug-2019
%-----------------------------------------------------------
%
if(~inspect(mesh,'point','coord') )
return ;
end
%------------------------------ map elements to unique edges
hexa = [] ; quad = [] ; edge = [] ;
hmap = [] ; qmap = [] ; emap = [] ;
if (inspect(mesh,'edge2','index') && ...
~isempty(mesh.edge2.index) )
%-------------------------- map EDGE2's onto JOIN arrays
nedg = size(edge,1) ;
ncel = size(mesh.edge2.index,1);
edge = [edge;
mesh.edge2.index(:,[1,2])
] ;
emap.edge2.index =zeros(ncel,1);
emap.edge2.index(:, 1 ) = ...
(1:ncel)' + ncel*0 + nedg ;
end
if (inspect(mesh,'tria3','index') && ...
~isempty(mesh.tria3.index) )
%-------------------------- map TRIA3's onto JOIN arrays
nedg = size(edge,1) ;
ncel = size(mesh.tria3.index,1);
edge = [edge;
mesh.tria3.index(:,[1,2])
mesh.tria3.index(:,[2,3])
mesh.tria3.index(:,[3,1])
] ;
emap.tria3.index =zeros(ncel,3);
emap.tria3.index(:, 1 ) = ...
(1:ncel)' + ncel*0 + nedg ;
emap.tria3.index(:, 2 ) = ...
(1:ncel)' + ncel*1 + nedg ;
emap.tria3.index(:, 3 ) = ...
(1:ncel)' + ncel*2 + nedg ;
end
if (inspect(mesh,'quad4','index') && ...
~isempty(mesh.quad4.index) )
%-------------------------- map QUAD4's onto JOIN arrays
nedg = size(edge,1) ;
nfac = size(quad,1) ;
ncel = size(mesh.quad4.index,1);
quad = [quad;
mesh.quad4.index(:, 1:4 )
] ;
edge = [edge;
mesh.quad4.index(:,[1,2])
mesh.quad4.index(:,[2,3])
mesh.quad4.index(:,[3,4])
mesh.quad4.index(:,[4,1])
] ;
qmap.quad4.index =zeros(ncel,1);
qmap.quad4.index(:, 1 ) = ...
(1:ncel)' + ncel*0 + nfac ;
emap.quad4.index =zeros(ncel,4);
emap.quad4.index(:, 1 ) = ...
(1:ncel)' + ncel*0 + nedg ;
emap.quad4.index(:, 2 ) = ...
(1:ncel)' + ncel*1 + nedg ;
emap.quad4.index(:, 3 ) = ...
(1:ncel)' + ncel*2 + nedg ;
emap.quad4.index(:, 4 ) = ...
(1:ncel)' + ncel*3 + nedg ;
end
if (inspect(mesh,'tria4','index') && ...
~isempty(mesh.tria4.index) )
%-------------------------- map TRIA4's onto JOIN arrays
nedg = size(edge,1) ;
ncel = size(mesh.tria4.index,1);
edge = [edge;
mesh.tria4.index(:,[1,2])
mesh.tria4.index(:,[2,3])
mesh.tria4.index(:,[3,1])
mesh.tria4.index(:,[1,4])
mesh.tria4.index(:,[2,4])
mesh.tria4.index(:,[3,4])
] ;
emap.tria4.index =zeros(ncel,6);
emap.tria4.index(:, 1 ) = ...
(1:ncel)' + ncel*0 + nedg ;
emap.tria4.index(:, 2 ) = ...
(1:ncel)' + ncel*1 + nedg ;
emap.tria4.index(:, 3 ) = ...
(1:ncel)' + ncel*2 + nedg ;
emap.tria4.index(:, 4 ) = ...
(1:ncel)' + ncel*3 + nedg ;
emap.tria4.index(:, 5 ) = ...
(1:ncel)' + ncel*4 + nedg ;
emap.tria4.index(:, 6 ) = ...
(1:ncel)' + ncel*5 + nedg ;
end
if (inspect(mesh,'hexa8','index') && ...
~isempty(mesh.hexa8.index) )
%-------------------------- map HEXA8's onto JOIN arrays
warning( ...
'HEXA-8 currently unsupported');
end
if (inspect(mesh,'wedg6','index') && ...
~isempty(mesh.wedg6.index) )
%-------------------------- map WEDG6's onto JOIN arrays
warning( ...
'WEDG-6 currently unsupported');
end
if (inspect(mesh,'pyra5','index') && ...
~isempty(mesh.pyra5.index) )
%-------------------------- map PYRA5's onto JOIN arrays
warning( ...
'PYRA-5 currently unsupported');
end
%------------------------------ unique joins and re-indexing
[ ~ , efwd, erev] = ...
unique(sort(edge, 2), 'rows');
[ ~ , qfwd, qrev] = ...
unique(sort(quad, 2), 'rows');
[ ~ , hfwd, hrev] = ...
unique(sort(hexa, 2), 'rows');
edge = edge(efwd,:) ;
quad = quad(qfwd,:) ;
hexa = hexa(hfwd,:) ;
%------------------------------ map unique joins to elements
if (inspect(mesh,'edge2','index'))
emap.edge2.index(:,1) = erev( ...
emap.edge2.index(:,1)) ;
end
if (inspect(mesh,'tria3','index'))
emap.tria3.index(:,1) = erev( ...
emap.tria3.index(:,1)) ;
emap.tria3.index(:,2) = erev( ...
emap.tria3.index(:,2)) ;
emap.tria3.index(:,3) = erev( ...
emap.tria3.index(:,3)) ;
end
if (inspect(mesh,'quad4','index'))
qmap.quad4.index(:,1) = qrev( ...
qmap.quad4.index(:,1)) ;
emap.quad4.index(:,1) = erev( ...
emap.quad4.index(:,1)) ;
emap.quad4.index(:,2) = erev( ...
emap.quad4.index(:,2)) ;
emap.quad4.index(:,3) = erev( ...
emap.quad4.index(:,3)) ;
emap.quad4.index(:,4) = erev( ...
emap.quad4.index(:,4)) ;
end
if (inspect(mesh,'tria4','index'))
emap.tria4.index(:,1) = erev( ...
emap.tria4.index(:,1)) ;
emap.tria4.index(:,2) = erev( ...
emap.tria4.index(:,2)) ;
emap.tria4.index(:,3) = erev( ...
emap.tria4.index(:,3)) ;
emap.tria4.index(:,4) = erev( ...
emap.tria4.index(:,4)) ;
emap.tria4.index(:,5) = erev( ...
emap.tria4.index(:,5)) ;
emap.tria4.index(:,6) = erev( ...
emap.tria4.index(:,6)) ;
end
%------------------------------ create new midpoint vertices
enew = [] ; qnew = [] ; hnew = [] ;
if (~isempty(edge))
emid = mesh.point.coord(edge(:,1),:) ...
+ mesh.point.coord(edge(:,2),:) ;
emid = emid / +2. ;
enew = [(1:size(emid,1))' + ...
size(mesh.point.coord,1)] ;
mesh.point.coord = [
mesh.point.coord ; emid ] ;
end
if (~isempty(quad))
qmid = mesh.point.coord(quad(:,1),:) ...
+ mesh.point.coord(quad(:,2),:) ...
+ mesh.point.coord(quad(:,3),:) ...
+ mesh.point.coord(quad(:,4),:) ;
qmid = qmid / +4. ;
qnew = [(1:size(qmid,1))' + ...
size(mesh.point.coord,1)] ;
mesh.point.coord = [
mesh.point.coord ; qmid ] ;
end
if (~isempty(hexa))
hmid = mesh.point.coord(hexa(:,1),:) ...
+ mesh.point.coord(hexa(:,2),:) ...
+ mesh.point.coord(hexa(:,3),:) ...
+ mesh.point.coord(hexa(:,4),:) ...
+ mesh.point.coord(hexa(:,5),:) ...
+ mesh.point.coord(hexa(:,6),:) ...
+ mesh.point.coord(hexa(:,7),:) ...
+ mesh.point.coord(hexa(:,8),:) ;
hmid = hmid / +8. ;
hnew = [(1:size(hmid,1))' + ...
size(mesh.point.coord,1)] ;
mesh.point.coord = [
mesh.point.coord ; hmid ] ;
end
if (inspect(mesh,'edge2','index'))
%------------------------------ create new indexes for EDGE2
mesh.edge2.index = [
% 1st sub-edge
mesh.edge2.index(:,1) , ...
enew(emap.edge2.index(:,1)), ...
mesh.edge2.index(:,3)
% 2nd sub-edge
enew(emap.edge2.index(:,1)), ...
mesh.edge2.index(:,2) , ...
mesh.edge2.index(:,3)
] ;
end
if (inspect(mesh,'tria3','index'))
%------------------------------ create new indexes for TRIA3
mesh.tria3.index = [
% 1st sub-tria
mesh.tria3.index(:,1) , ...
enew(emap.tria3.index(:,1)), ...
enew(emap.tria3.index(:,3)), ...
mesh.tria3.index(:,4)
% 2nd sub-tria
mesh.tria3.index(:,2) , ...
enew(emap.tria3.index(:,2)), ...
enew(emap.tria3.index(:,1)), ...
mesh.tria3.index(:,4)
% 3rd sub-tria
mesh.tria3.index(:,3) , ...
enew(emap.tria3.index(:,3)), ...
enew(emap.tria3.index(:,2)), ...
mesh.tria3.index(:,4)
% 4th sub-tria
enew(emap.tria3.index(:,1)), ...
enew(emap.tria3.index(:,2)), ...
enew(emap.tria3.index(:,3)), ...
mesh.tria3.index(:,4)
] ;
end
if (inspect(mesh,'quad4','index'))
%------------------------------ create new indexes for QUAD4
mesh.quad4.index = [
% 1st sub-quad
mesh.quad4.index(:,1) , ...
enew(emap.quad4.index(:,1)), ...
qnew(qmap.quad4.index(:,1)), ...
enew(emap.quad4.index(:,4)), ...
mesh.quad4.index(:,5)
% 2nd sub-quad
mesh.quad4.index(:,2) , ...
enew(emap.quad4.index(:,2)), ...
qnew(qmap.quad4.index(:,1)), ...
enew(emap.quad4.index(:,1)), ...
mesh.quad4.index(:,5)
% 3rd sub-quad
mesh.quad4.index(:,3) , ...
enew(emap.quad4.index(:,3)), ...
qnew(qmap.quad4.index(:,1)), ...
enew(emap.quad4.index(:,2)), ...
mesh.quad4.index(:,5)
% 4th sub-quad
mesh.quad4.index(:,4) , ...
enew(emap.quad4.index(:,4)), ...
qnew(qmap.quad4.index(:,1)), ...
enew(emap.quad4.index(:,3)), ...
mesh.quad4.index(:,5)
] ;
end
if (inspect(mesh,'tria4','index'))
%------------------------------ create new indexes for TRIA4
% 1st subdiv. of octahedron
triaA = [
enew(emap.tria4.index(:,3)), ...
enew(emap.tria4.index(:,5)), ...
enew(emap.tria4.index(:,1)), ...
enew(emap.tria4.index(:,2)), ...
mesh.tria4.index(:,5)
] ;
triaB = [
enew(emap.tria4.index(:,3)), ...
enew(emap.tria4.index(:,5)), ...
enew(emap.tria4.index(:,2)), ...
enew(emap.tria4.index(:,6)), ...
mesh.tria4.index(:,5)
] ;
triaC = [
enew(emap.tria4.index(:,3)), ...
enew(emap.tria4.index(:,5)), ...
enew(emap.tria4.index(:,6)), ...
enew(emap.tria4.index(:,4)), ...
mesh.tria4.index(:,5)
] ;
triaD = [
enew(emap.tria4.index(:,3)), ...
enew(emap.tria4.index(:,5)), ...
enew(emap.tria4.index(:,4)), ...
enew(emap.tria4.index(:,1)), ...
mesh.tria4.index(:,5)
] ;
costA = triscr3( ...
mesh.point.coord(:,1:3), ...
triaA(:,1:4) ) ;
costB = triscr3( ...
mesh.point.coord(:,1:3), ...
triaB(:,1:4) ) ;
costC = triscr3( ...
mesh.point.coord(:,1:3), ...
triaC(:,1:4) ) ;
costD = triscr3( ...
mesh.point.coord(:,1:3), ...
triaD(:,1:4) ) ;
% 2nd subdiv. of octahedron
triaE = [
enew(emap.tria4.index(:,1)), ...
enew(emap.tria4.index(:,6)), ...
enew(emap.tria4.index(:,5)), ...
enew(emap.tria4.index(:,2)), ...
mesh.tria4.index(:,5)
] ;
triaF = [
enew(emap.tria4.index(:,1)), ...
enew(emap.tria4.index(:,6)), ...
enew(emap.tria4.index(:,2)), ...
enew(emap.tria4.index(:,3)), ...
mesh.tria4.index(:,5)
] ;
triaG = [
enew(emap.tria4.index(:,1)), ...
enew(emap.tria4.index(:,6)), ...
enew(emap.tria4.index(:,3)), ...
enew(emap.tria4.index(:,4)), ...
mesh.tria4.index(:,5)
] ;
triaH = [
enew(emap.tria4.index(:,1)), ...
enew(emap.tria4.index(:,6)), ...
enew(emap.tria4.index(:,4)), ...
enew(emap.tria4.index(:,5)), ...
mesh.tria4.index(:,5)
] ;
costE = triscr3( ...
mesh.point.coord(:,1:3), ...
triaE(:,1:4) ) ;
costF = triscr3( ...
mesh.point.coord(:,1:3), ...
triaF(:,1:4) ) ;
costG = triscr3( ...
mesh.point.coord(:,1:3), ...
triaG(:,1:4) ) ;
costH = triscr3( ...
mesh.point.coord(:,1:3), ...
triaH(:,1:4) ) ;
% 3rd subdiv. of octahedron
triaI = [
enew(emap.tria4.index(:,2)), ...
enew(emap.tria4.index(:,4)), ...
enew(emap.tria4.index(:,1)), ...
enew(emap.tria4.index(:,5)), ...
mesh.tria4.index(:,5)
] ;
triaJ = [
enew(emap.tria4.index(:,2)), ...
enew(emap.tria4.index(:,4)), ...
enew(emap.tria4.index(:,5)), ...
enew(emap.tria4.index(:,6)), ...
mesh.tria4.index(:,5)
] ;
triaK = [
enew(emap.tria4.index(:,2)), ...
enew(emap.tria4.index(:,4)), ...
enew(emap.tria4.index(:,6)), ...
enew(emap.tria4.index(:,3)), ...
mesh.tria4.index(:,5)
] ;
triaL = [
enew(emap.tria4.index(:,2)), ...
enew(emap.tria4.index(:,4)), ...
enew(emap.tria4.index(:,3)), ...
enew(emap.tria4.index(:,1)), ...
mesh.tria4.index(:,5)
] ;
costI = triscr3( ...
mesh.point.coord(:,1:3), ...
triaI(:,1:4) ) ;
costJ = triscr3( ...
mesh.point.coord(:,1:3), ...
triaJ(:,1:4) ) ;
costK = triscr3( ...
mesh.point.coord(:,1:3), ...
triaK(:,1:4) ) ;
costL = triscr3( ...
mesh.point.coord(:,1:3), ...
triaL(:,1:4) ) ;
cost1 = ...
[costA, costB, costC, costD];
cost2 = ...
[costE, costF, costG, costH];
cost3 = ...
[costI, costJ, costK, costL];
cost1 = min (cost1, [], 2) ;
cost2 = min (cost2, [], 2) ;
cost3 = min (cost3, [], 2) ;
[~,index] = sort( ...
[cost1,cost2,cost3], +2) ;
mesh.tria4.index = [
% 1st sub-tria
mesh.tria4.index(:,1) , ...
enew(emap.tria4.index(:,1)), ...
enew(emap.tria4.index(:,3)), ...
enew(emap.tria4.index(:,4)), ...
mesh.tria4.index(:,5)
% 2nd sub-tria
mesh.tria4.index(:,2) , ...
enew(emap.tria4.index(:,2)), ...
enew(emap.tria4.index(:,1)), ...
enew(emap.tria4.index(:,5)), ...
mesh.tria4.index(:,5)
% 3rd sub-tria
mesh.tria4.index(:,3) , ...
enew(emap.tria4.index(:,3)), ...
enew(emap.tria4.index(:,2)), ...
enew(emap.tria4.index(:,6)), ...
mesh.tria4.index(:,5)
% 4th sub-tria
enew(emap.tria4.index(:,4)), ...
enew(emap.tria4.index(:,5)), ...
enew(emap.tria4.index(:,6)), ...
mesh.tria4.index(:,4) , ...
mesh.tria4.index(:,5)
% 1st subdiv. of octahedron
triaA(index(:,3)==1,:)
triaB(index(:,3)==1,:)
triaC(index(:,3)==1,:)
triaD(index(:,3)==1,:)
% 2nd subdiv. of octahedron
triaE(index(:,3)==2,:)
triaF(index(:,3)==2,:)
triaG(index(:,3)==2,:)
triaH(index(:,3)==2,:)
% 3rd subdiv. of octahedron
triaI(index(:,3)==3,:)
triaJ(index(:,3)==3,:)
triaK(index(:,3)==3,:)
triaL(index(:,3)==3,:)
] ;
end
end