# patchVolumepatchVolume

Below is a demonstration of the features of the `patchVolume` function

## Contents

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

## Syntax

`[volEst]=patchVolume(F,V);`

## Description

The patchVolume function computes the volume enclosed by the patch elements defined by the faces F and vertices V.

## Examples

```
makeAbsolute=0;
for testCase=1:9
```

switch testCase case 1 %Trianglulated sphere r=2; ns=5; [F,V]=geoSphere(ns,r); volTotalTrue=4/3*pi*r^3; %True theoretical volume case 2 %Trianglulated sphere r=2; ns=6; [F,V]=quadSphere(ns,r); volTotalTrue=4/3*pi*r^3; %True theoretical volume %Shift randomly to create non-zero centred patch data V=V+10.*randn(1,3); case 3 % %Torus parameters r=1; %Sphere radius R=2; %Central radius nr=76; nc=150; [F,V]=patchTorus(r,nr,R,nc,'tri'); volTotalTrue=2*pi^2*r*R; %True theoretical volume case 4 % %Torus parameters r=1; %Sphere radius R=2; %Central radius nr=76; nc=150; [F,V]=patchTorus(r,nr,R,nc,'quad'); volTotalTrue=2*pi^2*r*R; %True theoretical volume case 5 % %Torus parameters r=1; %Sphere radius R=2; %Central radius nr=76; nc=150; [F,V]=patchTorus(r,nr,R,nc,'honey'); volTotalTrue=2*pi^2*r*R; %True theoretical volume case 6 % triangulated box boxDim=[5 2 1]; pointSpacing=1; [F,V]=triBox(boxDim,pointSpacing); volTotalTrue=prod(boxDim); %True theoretical volume case 7 % quadrangulated box boxDim=[5 2 1]; [F,V]=quadBox(boxDim,[5 2 1]); volTotalTrue=prod(boxDim); %True theoretical volume case 8 % A mixed mesh consisting of pentahedra and hexahedra r=2; ns=5; [Ft,Vt]=geoSphere(ns,r); [V,F]=patch_dual(Vt,Ft); volTotalTrue=4/3*pi*r^3; %True theoretical volume case 9 %Trianglulated sphere r=2; ns=5; [F,V]=geoSphere(ns,r); F=fliplr(F); volTotalTrue=-4/3*pi*r^3; %True theoretical volume end

```
%Compute volume for the patch surface
volEst=patchVolume(F,V,makeAbsolute)
volTotalTrue
```

volEst = 33.4922 volTotalTrue = 33.5103

volEst = 33.5015 volTotalTrue = 33.5103

volEst = 39.4248 volTotalTrue = 39.4784

volEst = 39.4219 volTotalTrue = 39.4784

volEst = 39.3592 volTotalTrue = 39.4784

volEst = 10 volTotalTrue = 10

volEst = 10 volTotalTrue = 10

volEst = 33.4456 volTotalTrue = 33.5103

volEst = -33.4922 volTotalTrue = -33.5103

Visualization

cFigure; gpatch(F,V,'w'); axisGeom; camlight headlight; gdrawnow;

```
end
```

* GIBBON* www.gibboncode.org

*Kevin Mattheus Moerman*, [email protected]

**GIBBON footer text**

License: https://github.com/gibbonCode/GIBBON/blob/master/LICENSE

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

Copyright (C) 2006-2021 Kevin Mattheus Moerman and the GIBBON contributors

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/.

**GIBBON footer text**

License: https://github.com/gibbonCode/GIBBON/blob/master/LICENSE

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

Copyright (C) 2006-2023 Kevin Mattheus Moerman and the GIBBON contributors

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/.