How can I calculate the perimeters of Delaunay triangles?

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Hello,
Assume I have a set of point coordinates in a 2D plane. x = [ 16 16 16 17 18 19 19 20 21 21 23 23 23 ] y = [ 151 369 397 208 84 93 177 326 112 243 164 213 390 ]
Then, I use these points to obtain the Delaunay triangles. I found in a thread which asked about the calculation of area of each triangle. But if I want to calculate the perimeter of each triangle, how can I do for that? If possible, I also want to know the vertices (coordiantes) of each triangle.
Thanks.

Answers (1)

Sven
Sven on 14 Apr 2014
Hi ZhG,
Here is some code that shows a few different ways of getting the perimeter of triangles. It first just shows the lengths of each edge in the Delaunay Triangulation. Then it sums up the perimeter of the boundary of the triangulation. Then it shows the perimeter of each face (displayed in red).
x = [ 16 16 16 17 18 19 19 20 21 21 23 23 23 ]
y = [ 151 369 397 208 84 93 177 326 112 243 164 213 390 ]
DT = delaunayTriangulation(x',y')
figure, triplot(DT), hold on
edges = DT.edges;
edgeLens = zeros(size(edges,1),1);
for i = 1:size(edges,1)
thisEdgePts = DT.Points(edges(i,:),:);
edgeCpt = mean(thisEdgePts,1);
edgeLen = sqrt(sum(diff(thisEdgePts,[],1).^2));
edgeLens(i) = edgeLen;
text(edgeCpt(1),edgeCpt(2),sprintf('%0.1f',edgeLen),'HorizontalAlignment','center')
end
outerBoundaryPerim = sum(edgeLens(ismember(DT.edges, DT.freeBoundary,'rows')))
for i = 1:size(DT.ConnectivityList,1)
thisVerts = DT.Points(DT.ConnectivityList(i,:),:);
faceEdgeLens = sqrt(sum(diff(thisVerts([1:end 1],:),[],1).^2,2));
facePerim = sum(faceEdgeLens);
faceCpt = mean(thisVerts,1);
text(faceCpt(1),faceCpt(2), sprintf('%0.1f',facePerim),'Color','r')
end
Did that help you out and answer your question?
  3 Comments
Sven
Sven on 15 Apr 2014
Edited: Sven on 15 Apr 2014
Oh, that's ok, you can still use the "DelaunayTri" class in 2011a.
There will be some minor differences:
  1. DT = delaunayTriangulation should be replaced with DT = DelaunayTri
  2. DT.Points should be replaced with DT.X
  3. DT.ConnectivityList should be replaced with DT.Triangulation
Everything else will work just the same.
Subrata Bhatacharjee
Subrata Bhatacharjee on 10 Mar 2019
yes, I can see the perimeter in red color. But I want to save all triangle's perimeter and calculater sum and average. Can you please solve this problem?

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