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Using Netgen to create general (arbitrary) EIDORS Models

EIDORS can use Netgen to create sophisticated 2D and 3D models

Here are some examples of the varity of models which can be generated using the function: ng_mk_gen_models.

Shape 1

 shape_str = ['solid cyl    = cylinder (0,0,0; 0,0,1; 1); \n', ...
              'solid p1= plane(0,0,0;0,0.5,-1);\n' ...
              'solid p2= plane(0,0,2;0.5,0, 1);\n' ...
              'solid mainobj= p1 and p2 and cyl -maxh=0.3;\n'];
 elec_pos = []; elec_shape = []; elec_obj = {};
 fmdl = ng_mk_gen_models(shape_str, elec_pos, elec_shape, elec_obj);
 show_fem( fmdl );

Shape 2

 shape_str = ['solid cyl    = cylinder (0,0,0; 0,0,1; 1); \n', ...
              'solid mainobj= plane(0,0,0;0,0,-1)\n' ...
                        'and  plane(0,0,1.5;0.2,0.2,1)\n' ...
                        'and  cyl -maxh=0.3;\n'];
 elec_pos = [ -1,  0,  1,   1,  0,  0;
               0, -1,1.2,   0,  1,  0]; 
 elec_shape=[0.1,0,0;0.2,0.3,0.02];
 elec_obj = 'cyl';
 fmdl = ng_mk_gen_models(shape_str, elec_pos, elec_shape, elec_obj);
 show_fem( fmdl );

Shape 3

 shape_str = ['solid cyl    = cylinder (0,0,0; 0,0,1; 1); \n', ...
              'solid mainobj= orthobrick(-2,-2,0;2,2,2) and cyl -maxh=0.3;\n'];
 th = linspace(0,2*pi,15)'; th(end) = [];
 cs = [cos(th), sin(th)];
 elec_pos = [  cs, th/2/pi + 0.5, cs, 0*th];
 elec_shape=[0.1];
 elec_obj = 'cyl';
 fmdl = ng_mk_gen_models(shape_str, elec_pos, elec_shape, elec_obj);
 show_fem( fmdl );

Shape 4

 shape_str = ['solid cyl    = cylinder (0,0,0; 0,0,1; 1); \n', ...
              'solid mainobj= orthobrick(-2,-2,0;2,2,2) and cyl -maxh=0.3;\n'];
 th = linspace(0,2*pi,15)'; th(end) = [];
 cs = [cos(th), sin(th)];
 elec_pos = [  cs, th/2/pi + 0.5, cs, 0*th];
 elec_shape=[0.1*th/2/pi + 0.05];
 elec_obj = 'cyl';
 fmdl = ng_mk_gen_models(shape_str, elec_pos, elec_shape, elec_obj);
 show_fem( fmdl );

Shape 5

 shape_str = ['solid cyl    = cylinder (0,0,0; 1,0,0; 1); \n', ...
              'solid mainobj= plane(0,0,0;-1,0,0)\n' ...
                        'and  plane(2,0,0;1,0,0)\n' ...
                        'and  plane(0,0,-0.5;0,0,-1)\n' ...
                        'and  cyl -maxh=0.3;\n'];
 elec_pos = [  1,  0,  1,   0,  0,  1;
             1.2,  1,  0,   0,  1,  0]; 
 elec_shape=[0.1];
 elec_obj = 'cyl';
 fmdl = ng_mk_gen_models(shape_str, elec_pos, elec_shape, elec_obj);
 show_fem( fmdl );

Shape 6

 shape_str = ['solid cyl    = cylinder (0,0,0; 0,0,1; 1); \n', ...
              'solid bottom = plane(0,0,0;0,0,-1);\n' ...
              'solid top    = plane(0,0,2;0,0,1);\n' ...
              'solid mainobj= top and bottom and cyl -maxh=0.3;\n'];
 elec_pos = [  1,  0,  1,   1,  0,  0;
               0,  1,1.2,   0,  1,  0;
               0.8,  0,  0, 0,  0, -1]; 
 elec_shape=[0.1];
 elec_obj = {'cyl','cyl','bottom'};
 fmdl = ng_mk_gen_models(shape_str, elec_pos, elec_shape, elec_obj);
 show_fem( fmdl );

Shape 7

 shape_str = ['solid top    = plane(0,0,0;0,0,1);\n' ...
              'solid mainobj= top and orthobrick(-2,-2,-2;2,2,0);\n'];
 elec_pos = [  1,  0,  0,   0,  0,  1;
               0,  0,  0,   0,  0,  1;
              -1,  0,  0,   0,  0,  1];
 elec_shape=[0.1];
 elec_obj = 'top';
 fmdl = ng_mk_gen_models(shape_str, elec_pos, elec_shape, elec_obj);
 show_fem( fmdl );

Shape 8

 shape_str = ['solid top    = plane(0,0,0;0,0,1);\n' ...
              'solid cyl    = ellipticcylinder(0,0,0;2.5,0,0;0,1,0);\n' ...
              'solid mainobj= top and cyl and orthobrick(-2,-2,-2;2,2,0);\n'];
 elec_pos = [  1,  0,  0,   0,  0,  1;
               0,  0,  0,   0,  0,  1;
              -1,  0,  0,   0,  0,  1;
               1, -1,-1.2,  0, -1,  0;
               0, -1,-1.0,  0, -1,  0;
              -1, -1,-0.8,  0, -1,  0];
 elec_shape=[0.1];
 elec_obj = {'top','top','top','cyl','cyl','cyl'};
 fmdl = ng_mk_gen_models(shape_str, elec_pos, elec_shape, elec_obj);
 show_fem( fmdl );

Shape 9

 shape_str = ['solid top    = plane(0,0,0;0,0,1);\n' ...
              'solid ball   = sphere(-1.25,0,-1;0.5); tlo ball;\n' ...
              'solid mainobj= top and orthobrick(-2,-1,-2;2,1,0) and not ball -maxh=0.5;\n'];
 elec_pos = linspace( -1.5,1.5,5)';
 elec_pos = [  elec_pos, elec_pos*[0,0,0,0], elec_pos*0+1];
 elec_shape=[0.3];
 elec_obj = 'top';
 fmdl = ng_mk_gen_models(shape_str, elec_pos, elec_shape, elec_obj);

 img = mk_image( fmdl, 1);
 img.elem_data(fmdl.mat_idx{2}) = 1.1; 
 show_fem( img );

Shape 10

 shape_str = ['solid top    = plane(0,0,0;0,0,1);\n' ...
              'solid mainobj= top and orthobrick(-3,-3,-2;3,3,0) -maxh=0.5;\n'];
 [elec_pos_x,elec_pos_y] = meshgrid(linspace( -1.5,1.5,5),linspace(-2,2,7));
 elec_pos = [  elec_pos_x(:), elec_pos_y(:), ones(size(elec_pos_x(:)))*[0,0,0,1] ];
 elec_shape=[0.2];
 elec_obj = 'top';
 fmdl = ng_mk_gen_models(shape_str, elec_pos, elec_shape, elec_obj);

Shape 11

This shape could represent an elliptical fish or submarine generating electrical signals in a tank with electrodes on the tank boundary.
shape_str = ['solid cyl    = cylinder (0,0,0; 0,0,1; 1.0); \n', ...
             'solid tank   = orthobrick(-2,-2,0;2,2,0.4) and cyl; \n', ...
             'solid fish   = ellipsoid(0.2,0.2,0.2;0.2,0,0;0,0.1,0;0,0,0.1); tlo fish;\n', ...
             'solid mainobj= tank and not fish -maxh=0.3;\n'];
n_elec = 7;
th = linspace(0,2*pi,n_elec+1)'; th(end) = [];
cs = [cos(th), sin(th)];
elec_pos = [  cs, 0.2+0*th, cs, 0*th];
elec_shape=[0.05];
for i=1:n_elec; elec_obj{i} = 'cyl'; end
i=i+1;elec_pos(i,:) = [ 0  ,0.2,0.2,-1,0,0]; elec_obj{i} = 'fish';
i=i+1;elec_pos(i,:) = [ 0.4,0.2,0.2, 1,0,0]; elec_obj{i} = 'fish';
fmdl = ng_mk_gen_models(shape_str, elec_pos, elec_shape, elec_obj);

Tank with 7 electrodes on the boundary an two electrodes on the inclusion.

Shape 12

shape_str = ['solid top     = ellipsoid(0,0,0; 0,0,1; 1,0,0; 0,1,0); \n' ...
    'solid mainobj= top and orthobrick(-2,-2,0;2,2,2) -maxh=0.1;\n'];
deg2rad = pi/180;
th = (-70:20:70)'*deg2rad;
elec_pos = [0*th,sin(th),cos(th),0*th,sin(th),cos(th); ...
            sin(th),0*th,cos(th),sin(th),0*th,cos(th)];
elec_shape=[0.05];
elec_obj = 'top';
fmdl = ng_mk_gen_models(shape_str, elec_pos, elec_shape, elec_obj);

Half sphere with top surface electrodes

Shape 13

 shape_str = ['solid cyl    = cylinder (0,0,0; 0,1,0; 1); \n', ...
              'solid bottom = plane(0, 0,0;0,-1,0);\n' ...
              'solid top    = plane(0,10,0;0, 1,0);\n' ...
              'solid cut1   = plane(0, 4,0;0,-1,0);\n' ...
              'solid cut2   = plane(0, 6,0;0, 1,0);\n' ...
              'solid ball   = cyl and cut1 and cut2;  tlo ball;\n' ...
              'solid mainobj= ( top and (not cut2) and cyl ) or ' ...
                      '(bottom      and (not cut1) and cyl ) -maxh=0.8;\n'];
 elec_pos = [ 0, 10,  0, 0,  1,  0; 
              0,  0,  0, 0, -1,  0]; 
 elec_shape=[1.0];
 elec_obj = {'top','bottom'};
 fmdl = ng_mk_gen_models(shape_str, elec_pos, elec_shape, elec_obj);
 img  = mk_image(fmdl,1); 
 img.elem_data(fmdl.mat_idx{2}) = 1.1;

Fem model of a cylindrical resistor with electrodes at the ends

Shape 14

shape_str = ['solid cyl    = cylinder (0,0,0; 0,1,0; 1); \n', ...
             'solid bottom = plane(0, 0,0;0,-1,0);\n' ...
             'solid top    = plane(0,15,0;0, 1,0);\n' ...
             'solid cut1   = plane(0, 6,0;0,-1,0);\n' ...
             'solid cut2   = plane(0, 9,0;0, 1,0);\n' ...
             'solid rod   = cyl and (top and not cut2) or cyl and (bottom and not cut1);\n' ... 
             'tlo rod -maxh=0.8;\n',...
             'solid mainobj= orthobrick(-5,-5,-5;5,20,5) and not rod;\n'];

elec_pos = [0,15, 0, 0, 1, 0; %top end electrode
            0,13, 0,-1, 0, 0; %top cylinder electrode
            0, 0, 0, 0,-1, 0; %bot end electrode
            0, 2, 0, 1, 0, 0];%bot cylinder electrode
elec_shape=[6,0,0];
elec_obj = {'rod','rod','rod','rod'};
[fmdl,mat_idx] = ng_mk_gen_models(shape_str, elec_pos, elec_shape, elec_obj);
img  = mk_image(fmdl,1); 

% join electrodes
fmdl.electrode(3).nodes = unique(horzcat(fmdl.electrode(3:4).nodes));
fmdl.electrode(4) = [];
fmdl.electrode(1).nodes = unique(horzcat(fmdl.electrode(1:2).nodes));
fmdl.electrode(2) = [];

Bare conductive wires within a tank

Shape 15

shape_str = [ ...
  'solid cyl     = cylinder (-2,0,0;-2,0,1; 0.1); \n', ...
  'solid borehole= cyl and plane (0,0,-2;0,0,-1); \n', ...
  'solid cel1= orthobrick(-10,-10,-1.1;10,10,-1.0) and cyl; tlo cel1 -maxh=0.5;\n' ...
  'solid cel2= orthobrick(-10,-10,-1.6;10,10,-1.5) and cyl; tlo cel2 -maxh=0.5;\n' ...
  'solid top    = plane(0,0,0;0,0,1);\n' ...
  'solid top_obj= top and orthobrick(-5,-5,-5;5,5,0) -maxh=0.5;\n' ...
  'solid mainobj= top_obj and not borehole;\n'];
[elec_pos_x,elec_pos_y] = meshgrid(linspace( -1.5,1.5,3),linspace(-2,2,4));
elec_pos = [  elec_pos_x(:), elec_pos_y(:), ones(size(elec_pos_x(:)))*[0,0,0,1] ];
elec_shape=[0.1];
elec_obj = repmat({'top'}, 1, size(elec_pos,1));
elec_pos(end+1,:) = [-2.0,0,-1.05,0,0,1]; elec_obj(end+1)   = {'cel1'};
elec_pos(end+1,:) = [-2.0,0,-1.55,0,0,1]; elec_obj(end+1)   = {'cel2'};
[fmdl,mat_idx] = ng_mk_gen_models(shape_str, elec_pos, elec_shape, elec_obj);
To crop the model, use the code
crop_model([], inline('z<-2 | abs(x)>2.5 | abs(y)>2.5','x','y','z'));
axis([-2.5,2.5,-2.5,2.5,-2,0]);

Surface electrodes and ring electrodes on a borehole

Shape 16

 shape_str = ['solid top    = plane( 0, 0, 0; 0, 0, 1);\n' ...
              'solid bot    = plane( 0, 0,-1; 0, 0,-1);\n' ...
              'solid xmax   = plane( 3, 0, 0; 1, 0, 0);\n' ...
              'solid xmin   = plane(-3, 0, 0;-1, 0, 0);\n' ...
              'solid ymax   = plane( 0, 2, 0; 0, 2, 0);\n' ...
              'solid ymin   = plane( 0,-2, 0; 0,-2, 0);\n' ...
              'solid mainobj= top and bot and xmax and xmin and ymax and ymin;'];
 elec_pos = [  1, -2,  0,   0,  1,  0;
               0, -2,  0,   0,  1,  0;
              -1, -2,  0,   0,  1,  0;
              -1,  2,  0,   0, -1,  0;
              -3,  1,  0,  -1,  0,  0];
 elec_shape=[0.4,1,0.05];
 elec_obj = {'ymin', 'ymin', 'ymin','ymax','xmin'};
 fmdl = ng_mk_gen_models(shape_str, elec_pos, elec_shape, elec_obj);
To crop the z=0 layer, use
 fmdl = mdl2d_from3d(fmdl);

A 2D slice of a model on the z=0 plane

Shape 17

 shape_str = [ ...
  'solid cyl    = cylinder (0,0,0; 0,0,1; 1); \n', ...
  'solid mainobj= plane(0,0,0;0,0,-1)\n' ...
        'and  plane(0,0,2;0,0,1)\n' ...
        'and  cyl -maxh=0.3;\n' ...
  'solid in_elec = sphere(0,-1,1;0.2)' ...
        'and not    sphere(0,-1,1;0.15) -maxh=0.05;\n' ...
        'solid in_elec0= in_elec  and mainobj;\n' ...
        'tlo in_elec0 cyl;\n' ...
  'solid out_elec = sphere(0,-1,1;0.4)' ...
        'and not    sphere(0,-1,1;0.35) -maxh=0.05;\n' ...
        'solid out_elec0= out_elec  and mainobj;\n' ...
        'tlo out_elec0 cyl;\n'];
 % Find a background electrode (for all) first. This will stop errors in the next
 elec_pos = [  0, -1,   0, NaN,NaN,NaN;
               1,  0,   1,   1,  0,  0;
               0,  1, 1.2,   0,  1,  0;
               0, -1, 1.2, NaN,NaN,NaN;
               0, -1, 1.4, NaN,NaN,NaN];
 elec_shape=[0.1];
 elec_obj = 'cyl';
 fmdl = ng_mk_gen_models(shape_str, elec_pos, elec_shape, elec_obj);
 % Throw away the first electrode (background). We don't need it
 fmdl.electrode = fmdl.electrode(2:end);

Complex electrodes defined from intersection with spheres

Last Modified: $Date: 2017-02-28 13:12:08 -0500 (Tue, 28 Feb 2017) $ by $Author: aadler $