Create a mesh within a triangle and interpolate within this mesh

Hi folks,

I have a 2D triangle and corrosponding data values at each vertices. I want to generate a mesh within the triangle, interpolate my data across that mesh, then average out all the values to get a mean across the triangles surface. I have a fairly clunky solution and was wondering if there was something more streamlined available. Here's what I have:

coord=[470590,7333138;470642,7333275;470643,7333214]; % coordinates of the triangle (these are eastings and northings)
v=[1 2 3] ; % data values at each vertices of the triangle
x=coords(:,1);
y=coords(:,2);
F=scatteredInterpolant(x,y,v);
% now I generate the query coordinates using a function from exchange called "generate triangle mesh" where X and Y are the coordinates of the new points
n=10 % number of interpolant points I want to generate in the triangle
[X,Y]=Triangle_Mesh(coords(1,:),coords(2,:),coords(3,:),n); % the function
vq=F(X,Y); % interpolates in the triangle which I can then average out

Thanks

Dirk

[KSSV]

Share the link for the fileexchange function.

[Dirk]

https://au.mathworks.com/matlabcentral/fileexchange/93425-generate-triangle-mesh

Note that I put [X Y] as the coordinates but the coordinates are actually contained in X only

Answer 1

[Bruno Luong]

coords=[470590,7333138;470642,7333275;470643,7333214];
v=[1 2 3] ; % data values at each vertices of the triangle
x=coords(:,1);
y=coords(:,2);

% Replace your mesh data
[X,Y]=meshgrid(linspace(min(x),max(x),10),linspace(min(y),max(y),10));

F=scatteredInterpolant(x,y,v(:));
vq=F(X,Y) % interpolates in the triangle which I can then average out

vq = 10×10

1.0000 1.3524 1.7047 2.0571 2.4095 2.7619 3.1142 3.4666 3.8190 4.1714 0.7654 1.1178 1.4701 1.8225 2.1749 2.5272 2.8796 3.2320 3.5844 3.9367 0.5308 0.8831 1.2355 1.5879 1.9403 2.2926 2.6450 2.9974 3.3498 3.7021 0.2962 0.6485 1.0009 1.3533 1.7057 2.0580 2.4104 2.7628 3.1151 3.4675 0.0615 0.4139 0.7663 1.1187 1.4710 1.8234 2.1758 2.5282 2.8805 3.2329 -0.1731 0.1793 0.5317 0.8841 1.2364 1.5888 1.9412 2.2935 2.6459 2.9983 -0.4077 -0.0553 0.2971 0.6494 1.0018 1.3542 1.7066 2.0589 2.4113 2.7637 -0.6423 -0.2899 0.0625 0.4148 0.7672 1.1196 1.4719 1.8243 2.1767 2.5291 -0.8769 -0.5245 -0.1722 0.1802 0.5326 0.8850 1.2373 1.5897 1.9421 2.2944 -1.1115 -0.7591 -0.4068 -0.0544 0.2980 0.6503 1.0027 1.3551 1.7075 2.0598

% Compute vq directly without the need of scatteredInterpolant
vq = reshape((([X(:) Y(:) ones(numel(X),1)] / [coords, [1;1;1]]) * v(:)), size(X))

vq = 10×10

1.0000 1.3524 1.7047 2.0571 2.4095 2.7619 3.1142 3.4666 3.8190 4.1714 0.7654 1.1178 1.4701 1.8225 2.1749 2.5272 2.8796 3.2320 3.5844 3.9367 0.5308 0.8831 1.2355 1.5879 1.9403 2.2926 2.6450 2.9974 3.3498 3.7021 0.2962 0.6485 1.0009 1.3533 1.7057 2.0580 2.4104 2.7628 3.1151 3.4675 0.0615 0.4139 0.7663 1.1187 1.4710 1.8234 2.1758 2.5282 2.8805 3.2329 -0.1731 0.1793 0.5317 0.8841 1.2364 1.5888 1.9412 2.2935 2.6459 2.9983 -0.4077 -0.0553 0.2971 0.6494 1.0018 1.3542 1.7066 2.0589 2.4113 2.7637 -0.6423 -0.2899 0.0625 0.4148 0.7672 1.1196 1.4719 1.8243 2.1767 2.5291 -0.8769 -0.5245 -0.1722 0.1802 0.5326 0.8850 1.2373 1.5897 1.9421 2.2944 -1.1115 -0.7591 -0.4068 -0.0544 0.2980 0.6503 1.0027 1.3551 1.7075 2.0598

[Bruno Luong]

Alternative way

% Compute vq directly without the need of scatteredInterpolant
c =  [coords, ones(3,1)] \ v(:);
vq = c(1)*X + c(2)*Y + c(3)