How can I calculate the perimeters of Delaunay triangles?

Question

ZhG 2014-4-14

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/125716-how-can-i-calculate-the-perimeters-of-delaunay-triangles

评论： Subrata Bhatacharjee 2019-3-10

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.

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Sven 2014-4-14

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/125716-how-can-i-calculate-the-perimeters-of-delaunay-triangles#answer_133353

在 MATLAB Online 中打开

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 个评论
显示 1更早的评论隐藏 1更早的评论

Sven 2014-4-15

编辑：Sven 2014-4-15

Oh, that's ok, you can still use the "DelaunayTri" class in 2011a.

There will be some minor differences:

DT = delaunayTriangulation should be replaced with DT = DelaunayTri
DT.Points should be replaced with DT.X
DT.ConnectivityList should be replaced with DT.Triangulation

Everything else will work just the same.

Subrata Bhatacharjee 2019-3-10

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?

请先登录，再进行评论。