How do i find geometry properties of triangles?

I want to write a code to find the polar moment of inertia of an airfoil. Being a complex shape, a friend suggested a numerical estimate. I wrote a code to create the airfoil geometry and split it up into triangles using delaunay. I now need to find the moment of inertia about x and y for each triangle and use the parallel axis theorem to relate those to the centroid.

I have the delaunay triangulation complete but how can i find the Ix and Iy of each triangle? I don't even know where to start.

here's the code i have:

 chord = 0.25; %chord of airfoil
nacanum = 12; % NACA XX## number for the airfoil
t = nacanum/100; %max thickness of airfoil
x=0:0.005:chord; %points along x axis from 0 to chord length
distratio = x/chord; %ratio of points along x to the chord
% function generating top half of airfoil
yt = 5*t*(0.2969*sqrt(distratio)-0.126*distratio-0.3516*distratio.^2+0.2843*distratio.^3-0.1015*distratio.^4);
ytneg=yt*-1; %generatingg bottom half of airfoil
yfull= [yt ytneg]; % full points for y axis of airfoil
y=yfull';
x2=flipud(x);
xfull=[x x2];%full points for x axis of airfoil
x=xfull'; 
TR=delaunayTriangulation(x,y); %triangulation of the airfoil
triplot(TR,x,y) %plotting the triangulation

Answer 1

[KSSV]

You can access x,y coordinates of each triangle like below:

nodes = TR.ConnectivityList ;   % nodal connectivity matrix 
coor = TR.Points ;              % coordinates 
ntri = size(nodes,1) ;          % number of triangles 
% loop for each triangle 
for i = 1:ntri
    xi = coor(nodes(i,:),1) ;   % x coordinates of i'th rriangle 
    yi = coor(nodes(i,:),2) ;   % y coordinates of i'th triangle 
    % do what you want
end

But let me tell you, your mesh of air foil is very bad. I suggest you to go through the following meshing package: https://in.mathworks.com/matlabcentral/fileexchange/25555-mesh2d-automatic-mesh-generation

[Nasser Ramsis]

I've been trying to use the Mesh2d package you recommended. I get the following error:

Undefined function or variable 'tsearch'.

Error in meshfaces>boundarynodes (line 199) i = tsearch(ph(:,1),ph(:,2),th,p(:,1),p(:,2));

Error in meshfaces (line 140) pbnd = boundarynodes(qtree.p,qtree.t,qtree.h,node,edge,options.output);

Error in mesh2d (line 102) [p,t,junk,stats] = meshfaces(node,edge,[],hdata,options);

[KSSV]

that is a version problem...the same error is discussed there in the link, you can correct it.

[Nasser Ramsis]

yeah that was me who posted. unfortunately I'm not good enough at matlab to do so.

[KSSV]

Check with this link: http://people.sc.fsu.edu/~jburkardt/m_src/mesh2d/mesh2d.html

tsearch problem, can be sorted by minor editing the code. I have done it very long ago, if I get time I will check it. Mean while go through the above link.