patchVolumepatchVolume

Below is a demonstration of the features of the patchVolume function

Syntax
Description
Examples

clear; close all; clc;

Syntax

[volEst]=patchVolume(F,V);

Description

The patchVolume function computes the volume enclosed by the patch elements defined by the faces F and vertices V.

Examples

makeAbsolute=0;
for testCase=1:9

switch testCase
    case 1 %Trianglulated sphere
        r=2;
        ns=5;
        [F,V]=geoSphere(ns,r);
        volTotalTrue=4/3*pi*r^3; %True theoretical volume
    case 2 %Trianglulated sphere
        r=2;
        ns=6;
        [F,V]=quadSphere(ns,r);
        volTotalTrue=4/3*pi*r^3; %True theoretical volume

        %Shift randomly to create non-zero centred patch data
        V=V+10.*randn(1,3);
    case 3 %
        %Torus parameters
        r=1; %Sphere radius
        R=2; %Central radius
        nr=76;
        nc=150;
        [F,V]=patchTorus(r,nr,R,nc,'tri');
        volTotalTrue=2*pi^2*r*R; %True theoretical volume
    case 4 %
        %Torus parameters
        r=1; %Sphere radius
        R=2; %Central radius
        nr=76;
        nc=150;
        [F,V]=patchTorus(r,nr,R,nc,'quad');
        volTotalTrue=2*pi^2*r*R; %True theoretical volume
    case 5 %
        %Torus parameters
        r=1; %Sphere radius
        R=2; %Central radius
        nr=76;
        nc=150;
        [F,V]=patchTorus(r,nr,R,nc,'honey');
        volTotalTrue=2*pi^2*r*R; %True theoretical volume
    case 6 % triangulated box
        boxDim=[5 2 1];
        pointSpacing=1;
        [F,V]=triBox(boxDim,pointSpacing);
        volTotalTrue=prod(boxDim); %True theoretical volume
    case 7 % quadrangulated box
        boxDim=[5 2 1];
        [F,V]=quadBox(boxDim,[5 2 1]);
        volTotalTrue=prod(boxDim); %True theoretical volume
    case 8 % A mixed mesh consisting of pentahedra and hexahedra
        r=2;
        ns=5;
        [Ft,Vt]=geoSphere(ns,r);
        [V,F]=patch_dual(Vt,Ft);
        volTotalTrue=4/3*pi*r^3; %True theoretical volume
    case 9 %Trianglulated sphere
        r=2;
        ns=5;
        [F,V]=geoSphere(ns,r);
        F=fliplr(F);
        volTotalTrue=-4/3*pi*r^3; %True theoretical volume
end

%Compute volume for the patch surface
volEst=patchVolume(F,V,makeAbsolute)

volTotalTrue

volEst =

   33.4922


volTotalTrue =

   33.5103

volEst =

   33.5015


volTotalTrue =

   33.5103

volEst =

   39.4248


volTotalTrue =

   39.4784

volEst =

   39.4219


volTotalTrue =

   39.4784

volEst =

   39.3592


volTotalTrue =

   39.4784

volEst =

    10


volTotalTrue =

    10

volEst =

    10


volTotalTrue =

    10

volEst =

   33.4456


volTotalTrue =

   33.5103

volEst =

  -33.4922


volTotalTrue =

  -33.5103

Visualization

cFigure;
gpatch(F,V,'w');
axisGeom; camlight headlight;
gdrawnow;

end

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.

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