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;
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,[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, [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.

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/.