# tetVol

Below is a demonstration of the features of the tetVol function

## Contents

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

## Syntax

[VE,L]=tetVol(E,V);

## Description

This function computes tetrahedral element volumes. The input is the element description (E) and the nodes (V). The output is the element volumes (always positive) and a logic denoting wheter the element appears to be valid (1) or inverted (0).

## Examples

Plot settings

```cMap=gjet(250);
faceAlpha1=1;
faceAlpha2=0.65;
edgeColor1='none';
edgeColor2='none';
fontSize=15;
```

## Example: Computing the volume of tetrahedral elements

Create example geometry

```%Creating a hexahedron
X=[-1;  1; 1; -1; -1;  1; 1; -1;];
Y=[-1; -1; 1;  1; -1; -1; 1;  1;];
Z=[-1; -1;-1; -1;  1;  1; 1;  1;];
Vh=[X(:) Y(:) Z(:)];
Eh=1:8; %The hexahedral element

%Convert to a tetrahedron.
[E,V]=hex2tet(Eh,Vh,[],2);

%Create faces data for plotting
[F,C]=element2patch(E);
```

Computing the volume

```[VE,logicValid]=tetVol(E,V)
```
```VE =

1.3333
1.3333
1.3333
1.3333
1.3333
1.3333

logicValid =

6×1 logical array

1
1
1
1
1
1

```

The summed volume should be 8 for this cube

```sum(VE)
```
```ans =

8.0000

```

## Visualize mesh and face normals

```cFigure; hold on;
gpatch(F,V,'kw','k',0.5);
patchNormPlot(F,V);
axisGeom;
drawnow;
```

Volumes are always positive but inverted elements have a 0 in the inverted logic. In the example below the first element is inverted which changes the logic to return a 0 for this element.

```E_inverted=E;
E_inverted(1,:)=E_inverted(1,[4 1 2 3]);
[VE,logicValid]=tetVol(E_inverted,V)
```
```VE =

1.3333
1.3333
1.3333
1.3333
1.3333
1.3333

logicValid =

6×1 logical array

0
1
1
1
1
1

```

GIBBON www.gibboncode.org

Kevin Mattheus Moerman, gibbon.toolbox@gmail.com

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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

This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses/.