# subTriCentre

Below is a demonstration of the features of the subTriCentre function

## Syntax

[Fn,Vn]=subTriCentre(F,V,L);

## Description

The subTriCentre function splits the faces defined by L up into three by introducing a central node.

## Examples

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

Plot settings

```fontSize=10;
faceAlpha=1;
edgeColor=0.3*ones(1,3);
edgeWidth=1.5;
```

## Example: Splitting a selection of triangles

Building example patch data

```[V,F]=platonic_solid(4,1);
```

Create logic for faces to split

```L=false(size(F,1),1);
L(6:8)=1; %e.g. the first 3 faces
```

Splitting selected triangles

```[Fn,Vn]=subTriCentre(F,V,L);
```

Plotting results

```C=[ones(size(F,1),1) zeros(size(F,1),1) zeros(size(F,1),1)];
C(L,1)=0;
C(L,2)=1;

hf=cFigure;
subplot(1,2,1);
title('The original surface. Green faces need splitting','FontSize',fontSize);
xlabel('X','FontSize',fontSize); ylabel('Y','FontSize',fontSize); zlabel('Z','FontSize',fontSize);
hp=patch('Faces',F,'Vertices',V,'FaceColor','flat','FaceVertexCData',C,'FaceAlpha',faceAlpha,'lineWidth',edgeWidth,'edgeColor',edgeColor);

set(gca,'FontSize',fontSize);
view(3); axis tight;  axis equal;
axis off;
drawnow;

C=[ones(size(Fn,1),1) zeros(size(Fn,1),1) zeros(size(Fn,1),1)];
C(end-(3*nnz(L)-1):end,1)=0;
C(end-(3*nnz(L)-1):end,2)=1;

subplot(1,2,2);
title('The new surface with split faces shown in green','FontSize',fontSize);
xlabel('X','FontSize',fontSize); ylabel('Y','FontSize',fontSize); zlabel('Z','FontSize',fontSize);
hp=patch('Faces',Fn,'Vertices',Vn,'FaceColor','flat','FaceVertexCData',C,'FaceAlpha',faceAlpha,'lineWidth',edgeWidth,'edgeColor',edgeColor);
% [hp]=patchNormPlot(F,V,0.25);
set(gca,'FontSize',fontSize);
view(3); axis tight;  axis equal;
axis off;
drawnow;
```

## EXAMPLE SURFACE AREA BASED RESAMPLING

```[F,V]=parasaurolophus;
```

Split large triangles according to area threshold

```[A]=patch_area(F,V); % Calculate triangle surface areas
max_A=mean(A(:))+2*std(A(:)); %Set a max treshold

%Loop until all are within treshold
An=A;
Vn=V;
Fn=F;
Ln=false(size(Fn,1),1);
while 1
L=An>max_A;
Ln(L)=1;
if nnz(L)>0
[Fn,Vn]=subTriCentre(Fn,Vn,L);
[An]=patch_area(Fn,Vn);
else
break
end
end
```

Plotting results

```C=[ones(size(F,1),1) zeros(size(F,1),1) zeros(size(F,1),1)];
C(Ln,1)=0;
C(Ln,2)=1;

hf=cFigure;
subplot(1,2,1);
title('The original surface. Green faces need splitting','FontSize',fontSize);
xlabel('X','FontSize',fontSize); ylabel('Y','FontSize',fontSize); zlabel('Z','FontSize',fontSize);
hp=patch('Faces',F,'Vertices',V,'FaceColor','flat','FaceVertexCData',C,'FaceAlpha',faceAlpha,'lineWidth',edgeWidth,'edgeColor',edgeColor);

set(gca,'FontSize',fontSize);
view(3); axis tight;  axis equal;
axis off;
drawnow;

C=[ones(size(Fn,1),1) zeros(size(Fn,1),1) zeros(size(Fn,1),1)];
C(end-(3*nnz(Ln)-1):end,1)=0;
C(end-(3*nnz(Ln)-1):end,2)=1;

subplot(1,2,2);
title('The new surface with split faces shown in green','FontSize',fontSize);
xlabel('X','FontSize',fontSize); ylabel('Y','FontSize',fontSize); zlabel('Z','FontSize',fontSize);
hp=patch('Faces',Fn,'Vertices',Vn,'FaceColor','flat','FaceVertexCData',C,'FaceAlpha',faceAlpha,'lineWidth',edgeWidth,'edgeColor',edgeColor);
% [hp]=patchNormPlot(F,V,0.25);
set(gca,'FontSize',fontSize);
view(3); axis tight;  axis equal;
axis off;
drawnow;
```

Calculate new surface areas

```[An]=patch_area(Fn,Vn);
```

Plotting model

```hf=cFigure;
subplot(1,2,1);
title('The original surface and its surface area distribution','FontSize',fontSize);
xlabel('X','FontSize',fontSize); ylabel('Y','FontSize',fontSize); zlabel('Z','FontSize',fontSize);
hp=patch('Faces',F,'Vertices',V,'FaceColor','flat','CData',A,'FaceAlpha',faceAlpha,'edgeColor','none');
colormap jet; colorbar; caxis([0 max(A(:))]);
set(gca,'FontSize',fontSize);
view(3); axis tight;  axis equal;
axis off;
drawnow;

subplot(1,2,2);
title('The new model and surface area distribution','FontSize',fontSize);
xlabel('X','FontSize',fontSize); ylabel('Y','FontSize',fontSize); zlabel('Z','FontSize',fontSize);
hp=patch('Faces',Fn,'Vertices',Vn,'FaceColor','flat','CData',An,'FaceAlpha',faceAlpha,'edgeColor','none');

colormap jet; colorbar; caxis([0 max(A(:))]);
set(gca,'FontSize',fontSize);
view(3); axis tight;  axis equal;
axis off;
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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