How can I calculate the perimeters of Delaunay triangles?

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.

Answer 1

[Sven]

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?

[ZhG]

Thanks Sven. I am using Matlab 2011a. This version does not provide function delaunayTriangulation(x',y'). Anyway, thanks again.

[Sven]

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]

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?