patchArea

Below is a demonstration of the features of the patchArea function

Contents

clear; close all; clc;

Syntax

[A]=patchArea(F,V);

Description

The patchArea function computes the surface area of the patch elements defined by the faces F and vertices V.

Examples

testCase=5;
switch testCase
    case 1 %Circle
        r=1;
        n=250;
        t=linspace(-pi,pi,n)'; t=t(1:end-1);
        V=[r*cos(t) r*sin(t) zeros(size(t))];
        F=[1:size(V,1)];
        aTotalTrue=pi*r^2 %True theoretical area
    case 2 %Single element square 1x1
        V=[0 0 0; 1 0 0; 0 1 0; 1 1 0];
        F=[1 2 4 3];
        aTotalTrue=1 %True theoretical area
    case 3 %Multi element square rotated 1x1
        V1=0.5*[-1 -1; -1 1; 1 1; 1 -1];
        regionCell={V1}; %A region between V1 and V2 (V2 forms a hole inside V1)
        plotOn=0; %This turns on/off plotting
        pointSpacing=0.1; %Desired point spacing
        resampleCurveOpt=1; %Option to turn on/off resampling of input boundary curves
        [F,V]=regionTriMesh2D(regionCell,pointSpacing,resampleCurveOpt,plotOn);
        V(:,3)=0;
        aTotalTrue=1 %True theoretical area
        R=euler2DCM([-0.25*pi 0.25*pi 0]);
        V=V*R;
    case 4 %Cube
        [V,F]=platonic_solid(2);
        V=V./max(V(:))/2;
        aTotalTrue=6 %True theoretical area
    case 5 %Sphere quads
        r=1;
        n=4;
        % [F,V]=geoSphere(n,r);
        [F,V]=quadSphere(n,r,2);
        aTotalTrue=4*pi*r^2 %True theoretical area
    case 6 %Sphere triangles
        r=1;
        n=4;
        [F,V]=geoSphere(n,r);
        aTotalTrue=4*pi*r^2 %True theoretical area
end

aTotalTrue =

   12.5664

%Compute areas for each patch/face
[A]=patchArea(F,V);

%Checking sum with theoretical (not changes due to discrete nature are
%possible).
aTotalEstimate=sum(A(:)) %Summed area check

aTotalEstimate =

   12.5400

Visualization

cFigure;
gpatch(F,V,A);
axisGeom; camlight headlight;
colormap parula; colorbar;
gdrawnow;

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) 2006-2021 Kevin Mattheus Moerman and the GIBBON contributors

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Published with MATLAB® R2021a