# hexVol

Below is a demonstration of the features of the hexVol function

## Contents

clear; close all; clc;

## Syntax

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

## 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

Creating example geometry for a beam

boxDim=[6 4 4]; %Box dimensions
boxEl=[5 3 3]; %Number of elements in each direction
[meshStruct]=hexMeshBox(boxDim,boxEl);

E=meshStruct.E;
V=meshStruct.V;
F=meshStruct.F;
Fb=meshStruct.Fb;

Computing the volume

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

2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333

The summed volume should match the theoretical

volume_theoretical=prod(boxDim);
volume_total=sum(VE);

disp(['Theoretical volume:',sprintf('%f',volume_theoretical)]);
disp(['Total volume computed:',sprintf('%f',volume_total)]);
Theoretical volume:96.000000
Total volume computed:96.000000

Visualize mesh and face normals

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

cFigure; hold on;
title('The elements colored based on volume, with face normals shown')
gpatch(F,V,C,'k',1);
patchNormPlot(F,V);
colormap spectral; colorbar;
caxis([0 max(VE)]);
drawnow;

## Example: Handling negative volumes

Volumes are made absolute by default. To help detect inverted elements the optional input absOpt can be set to 0 to allow for negative volume output. In addition an output logicPositive can be requested which is true for postive volumes and false for negative volumes.

E_inverted=E; %Copy element set
E_inverted(1,:)=E_inverted(1,[5:8 1:4]); %Invert first element

%Inspect element volumes and logic
absOpt=1 %Output absolute volumes
[VE,logicPositive]=hexVol(E_inverted,V,absOpt)

absOpt=0 %Output may include negative volumes
[VE,logicPositive]=hexVol(E_inverted,V,absOpt)
absOpt =

1

VE =

2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333

logicPositive =

45×1 logical array

0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1

absOpt =

0

VE =

-2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333
2.1333

logicPositive =

45×1 logical array

0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1

Visualize mesh and face normals

%Create patch data for plotting
[F,C]=element2patch(E_inverted,VE);

cFigure; hold on;
title('The elements colored based on volume, with face normals shown')
gpatch(F,V,C,'k',0.5);
patchNormPlot(F,V);
colormap spectral; colorbar;
caxis([min(VE) max(VE)]);
drawnow;

## Example: A more complex hex mesh

%Control settings
optionStruct.numElementsMantel=5;
optionStruct.numElementsCore=8;
optionStruct.makeHollow=0;
optionStruct.outputStructType=2;

%Creating sphere
[meshStruct]=hexMeshSphere(optionStruct);

% Access model element and patch data
Fb=meshStruct.facesBoundary;
Cb=meshStruct.boundaryMarker;
V=meshStruct.nodes;
E=meshStruct.elements;

absOpt=0; %Output may include negative volumes
VE=hexVol(E,V,absOpt);

Visualize mesh and face normals

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

cFigure; hold on;
title('The elements colored based on volume')
gpatch(F,V,C,'k',1);
colormap spectral; colorbar;
drawnow;

3D cut view

meshStruct.elementData=VE;
meshView(meshStruct,[]);

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) 2006-2022 Kevin Mattheus Moerman and the GIBBON contributors

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