hexVol

Below is a demonstration of the features of the hexVol function

Syntax
Description
Example: Computing the volume of hexahedral elements
Example: Handling negative volumes
Example: A more complex hex mesh

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)

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);
axisGeom; camlight headlight;
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);
axisGeom; camlight headlight;
colormap spectral; colorbar;
caxis([min(VE) max(VE)]);
drawnow;

Example: A more complex hex mesh

%Control settings
optionStruct.sphereRadius=10;
optionStruct.coreRadius=5;
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);
axisGeom; camlight headlight;
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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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.

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.

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hexVol

Contents

Syntax

Description

Example: Computing the volume of hexahedral elements

Example: Handling negative volumes

Example: A more complex hex mesh