Below is a demonstration of the features of the hexVol function
clear; close all; clc;
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 = 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
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
Kevin Mattheus Moerman, email@example.com
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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) 2019 Kevin Mattheus Moerman
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