# splitCurveSetMesh

Below is a demonstration of the features of the splitCurveSetMesh function

## Contents

```clear; close all; clc;
```

PLOT SETTINGS

```fontSize=15;
faceAlpha1=1;
faceAlpha2=0.5;
edgeColor=0.25*ones(1,3);
edgeWidth=1.5;
markerSize1=50;
```

## MESHING BIFURCATION BASED ON INPUT CURVES: from narrowed curve to split curves

Create example curves

```t=linspace(0.25*pi,2.25*pi,75);
t=t(1:end-1);
x=sin(t(:));
y=cos(t(:));
[t,r] = cart2pol(x,y);
r=r-0.75*cos(2*t);
[x,y] = pol2cart(t,r);
z=zeros(size(x));
V1=[x(:) y(:) z(:)];

t=linspace(0,2*pi,135);
r2=0.8;
x=r2.*sin(t);
y=r2.*cos(t);
z=0.5*ones(size(x));
V2=[x(:) y(:) z(:)];
V2=V2(1:end-1,:);

V2(:,1)=V2(:,1);
V2(:,2)=V2(:,2)-1.1;

V3=V2;
V3(:,1)=V3(:,1);
V3(:,2)=V3(:,2)+2.2;
```
```ns=5;
V_cell={V1,V2,V3};
smoothPar.Method='HC';
smoothPar.n=0;
smoothPar.Tolerance=0.001;
switch smoothPar.Method
case 'HC'
smoothPar.Alpa=0.1; %Alpha scale factor to push points back to original
smoothPar.Beta=0.5; %Beta
case 'LAP'
smoothPar.LambdaSmooth=0.25;
end
splitMethod='nearMid';
```

Meshing bifurcation

```[F,V,curveIndices,faceMarker]=splitCurveSetMesh(V_cell,ns,patchType,smoothPar,splitMethod);
```
```% Plotting results
cFigure; hold on;
title('Input contours and connected mesh','FontSize',fontSize);
gpatch(F,V,faceMarker);
plotV(V(curveIndices{1},:),'r.-','MarkerSize',25);
plotV(V(curveIndices{2},:),'g.-','MarkerSize',25);
plotV(V(curveIndices{3},:),'b.-','MarkerSize',25);
axisGeom(gca,fontSize);
colormap gjet; icolorbar;
drawnow;
```

## MESHING BIFURCATION BASED ON INPUT CURVES: from ellips curve to split curves

Create example curves

```t=linspace(0.25*pi,2.25*pi,50);
t=t(1:end-1);
x=2*sin(t(:));
y=cos(t(:));
z=zeros(size(x));
V1=[x(:) y(:) z(:)];

t=linspace(0,2*pi,25);
r2=0.8;
x=r2.*sin(t);
y=r2.*cos(t);
z=0.5*ones(size(x));
V2=[x(:) y(:) z(:)];
V2=V2(1:end-1,:);

V2(:,1)=V2(:,1);
V2(:,2)=V2(:,2)-1.1;

V3=V2;
V3(:,1)=V3(:,1);
V3(:,2)=V3(:,2)+2.2;
```
```ns=5;
V_cell={V1,V2,V3};
smoothPar.Method='HC';
smoothPar.n=250;
smoothPar.Tolerance=0.001;
switch smoothPar.Method
case 'HC'
smoothPar.Alpa=0.1; %Alpha scale factor to push points back to original
smoothPar.Beta=0.5; %Beta
case 'LAP'
smoothPar.LambdaSmooth=0.25;
end
splitMethod='nearMid';
```

Meshing bifurcation

```[F_1,V_1,curveIndices_1,faceMarker_1]=splitCurveSetMesh(V_cell,ns,patchType,smoothPar,'nearMid');
[F_2,V_2,curveIndices_2,faceMarker_2]=splitCurveSetMesh(V_cell,ns,patchType,smoothPar,'ortho');
```
```% Plotting results

subplot(1,2,1); hold on;
title('nearMid is inappropriate in this case','FontSize',fontSize);
gpatch(F_1,V_1,faceMarker_1);
plotV(V_1(curveIndices_1{1},:),'r.-','MarkerSize',25);
plotV(V_1(curveIndices_1{2},:),'g.-','MarkerSize',25);
plotV(V_1(curveIndices_1{3},:),'b.-','MarkerSize',25);
axisGeom(gca,fontSize);
colormap(gca,gjet(2)); icolorbar;

subplot(1,2,2); hold on;
title('ortho performs better','FontSize',fontSize);
gpatch(F_2,V_2,faceMarker_2);
plotV(V_2(curveIndices_2{1},:),'r.-','MarkerSize',25);
plotV(V_2(curveIndices_2{2},:),'g.-','MarkerSize',25);
plotV(V_2(curveIndices_2{3},:),'b.-','MarkerSize',25);
axisGeom(gca,fontSize);
colormap(gca,gjet(2)); icolorbar;
drawnow;
```

```ns=5;
V_cell={V1,V2,V3};
splitMethod='ortho';

smoothPar.Method='HC';
smoothPar.n=250;
smoothPar.Tolerance=0.001;
switch smoothPar.Method
case 'HC'
smoothPar.Alpa=0.1; %Alpha scale factor to push points back to original
smoothPar.Beta=0.5; %Beta
case 'LAP'
smoothPar.LambdaSmooth=0.25;
end
[F_1,V_1,curveIndices_1,faceMarker_1]=splitCurveSetMesh(V_cell,ns,patchType,smoothPar,splitMethod);

smoothPar.Method='LAP';
smoothPar.n=250;
smoothPar.Tolerance=0.001;
switch smoothPar.Method
case 'HC'
smoothPar.Alpa=0.1; %Alpha scale factor to push points back to original
smoothPar.Beta=0.5; %Beta
case 'LAP'
smoothPar.LambdaSmooth=0.25;
end
[F_2,V_2,curveIndices_2,faceMarker_2]=splitCurveSetMesh(V_cell,ns,patchType,smoothPar,splitMethod);
```
```% Plotting results

% Plotting results
cFigure;
subplot(1,2,1); hold on;
title('HC smoothed','FontSize',fontSize);
gpatch(F_1,V_1,faceMarker_1);
plotV(V_1(curveIndices_1{1},:),'r.-','MarkerSize',25);
plotV(V_1(curveIndices_1{2},:),'g.-','MarkerSize',25);
plotV(V_1(curveIndices_1{3},:),'b.-','MarkerSize',25);
axisGeom(gca,fontSize);
colormap(gca,gjet(2)); icolorbar;

subplot(1,2,2); hold on;
title('LAP smoothed (shrinkage/growth not prevented)','FontSize',fontSize);
gpatch(F_2,V_2,faceMarker_2);
plotV(V_2(curveIndices_2{1},:),'r.-','MarkerSize',25);
plotV(V_2(curveIndices_2{2},:),'g.-','MarkerSize',25);
plotV(V_2(curveIndices_2{3},:),'b.-','MarkerSize',25);
axisGeom(gca,fontSize);
colormap(gca,gjet(2)); icolorbar;
drawnow;
```

GIBBON www.gibboncode.org

Kevin Mattheus Moerman, [email protected]

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GIBBON: The Geometry and Image-based Bioengineering add-On. A toolbox for image segmentation, image-based modeling, meshing, and finite element analysis.

Copyright (C) 2019 Kevin Mattheus Moerman

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