# How can I connect two 2D triangulated surfaces?

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Radu Andrei Matei on 21 Jun 2022
Edited: Radu Andrei Matei on 22 Jun 2022
Hi, I have the following surfaces created using the delaunayTriangulation function with the points in the attached .txt file (the yellow one has modified z coordinates): How can I connect those two surfaces with a third triangulated one so that I get a volume similar to the one below (without center hole)? The triangulation is very important, I dont want to just plot a surface between the points, I need a triangulated surface that connects the two. Thank you in advance guys :)
This is the code that generates the two surfaces:
nump = numel(app.pointsPinion(:,1));
C = [(1:(nump-1))' (2:nump)'; nump 1];
dt = delaunayTriangulation(app.pointsPinion(:,1),app.pointsPinion(:,2),C);
io = isInterior(dt); % Filter out the points outside the profile defined by the points
figure
h(1) = trisurf(dt.ConnectivityList(io,:),app.pointsPinion(:,1),app.pointsPinion(:,2),app.pointsPinion(:,3));
hold on
h(2) = trisurf(dt.ConnectivityList(io,:),app.pointsPinion(:,1),app.pointsPinion(:,2),app.pointsPinion(:,3)+app.optiTrans.b);
axis tight
pbaspect([1 1 1])

Radu Andrei Matei on 22 Jun 2022
Edited: Radu Andrei Matei on 22 Jun 2022
Hi, I've solved it. What I did is the following: points 1, 2, 3 and 4 are points from the top surface and 5,6,7 and 8 are points from the bottom surface. I need two triangles to connect 4 points together, which means 2 rows in the connectivity matrix. I created the ConnectSurfaces function, which generates a connectivity matrix given a certain number of points, which will be the nº of rows in the vector with coordinates:
% Delaunay constraints for 2D top and bottom surfaces
nump = numel(app.pointsPinion(:,1));
C = [(1:(nump-1))' (2:nump)'; nump 1];
% Triangulation
dt = delaunayTriangulation(app.pointsPinion(:,1),app.pointsPinion(:,2),C);
% For filtering triangles outside profile defined by the original points
io = isInterior(dt);
figure
h(1) = trisurf(dt.ConnectivityList(io,:),app.pointsPinion(:,1),app.pointsPinion(:,2),app.pointsPinion(:,3),'FaceColor','r','EdgeColor','k');
hold on
h(2) = trisurf(dt.ConnectivityList(io,:),app.pointsPinion(:,1),app.pointsPinion(:,2),app.pointsPinion(:,3)+app.optiTrans.b,'FaceColor','r','EdgeColor','k');
n_points = size(app.pointsPinion,1);
ConMat = ConnectSurfaces(n_points);
trisurf(ConMat,[app.pointsPinion(:,1);app.pointsPinion(:,1)],[app.pointsPinion(:,2);app.pointsPinion(:,2)],[app.pointsPinion(:,3);app.pointsPinion(:,3)+app.optiTrans.b],'FaceColor','r','EdgeColor','k')
axis tight
pbaspect([1 1 1])
function ConnectivityMatrix = ConnectSurfaces(n_points)
for j = 1:1:n_points-1
k = 2*j;
ConnectivityMatrix(k-1,1) = j;
ConnectivityMatrix(k-1,2) = j+1;
ConnectivityMatrix(k-1,3) = j+n_points;
ConnectivityMatrix(k,1) = j+n_points;
ConnectivityMatrix(k,2) = j+n_points+1;
ConnectivityMatrix(k,3) = j+1;
end
% The following is for connecting the last pair of points with the first to get a closed donut-like surface
ConnectivityMatrix = [ConnectivityMatrix;[n_points 1 n_points*2];[n_points*2 n_points+1 1]];
end
The above solution yields the following result, which is what I was looking for: R2020a

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