# hexVol

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

## Contents

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

## Syntax

`[VE,L]=hexVol(E,V);`

## Description

This function computes hexahedral 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).

## Example: Computing the volume of hexahedral elements

Create example geometry

%Creating a single 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 %Subdevided into 8 smaller elements [E,V]=subHex(Eh,Vh,1); %Create faces data for plotting [F,C]=element2patch(E);

Computing the volume

[VE,logicValid]=hexVol(E,V)

VE = 1 1 1 1 1 1 1 1 logicValid = 8×1 logical array 1 1 1 1 1 1 1 1

The summed volume should be 8 for this cube

sum(VE)

ans = 8

## Visualize mesh and face normals

cFigure; hold on; gpatch(F,V,'kw','k',0.5); patchNormPlot(F,V); axisGeom; camlight headlight; 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,[5:8 1:4]); [VE,logicValid]=hexVol(E_inverted,V)

VE = 1 1 1 1 1 1 1 1 logicValid = 8×1 logical array 0 1 1 1 1 1 1 1

* GIBBON* www.gibboncode.org

*Kevin Mattheus Moerman*, gibbon.toolbox@gmail.com

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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) 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.

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