how to find the area of the triangles formed as a result of delaunay triangulation
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I have applied delaunay triangulation to my image. i have got 160 triangles. i need to find area of each triangle. Kindly help me with code. only after i can proceed with my prooj.i am new to matlab.
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Roger Stafford
2014년 3월 3일
If a triangle is in two dimensional space with vertices at (x1,y1), (x2,y2), and (x3,y3), its area is given by:
area = 1/2*abs((x2-x1)*(y3-y1)-(x3-x1)*(y2-y1));
or
area = 1/2*abs(det([x1,y1,1;x2,y2,1;x3,y3,1]));
If it is in three dimensions with vertices at P1 = [x1,y1,z1], P2 = [x2,y2,z2], P3 = [x3,y3,z3], its area is:
area = 1/2*norm(cross(P2-P1,P3-P1));
These formulas are more accurate for numerical computation than those which depend on the lengths of the three sides of the triangle.
Of course you must adapt these formulas for use with your 160 triangles, either using the necessary for-loop or possibly a vectorized expression.
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Valerio Ficcadenti
2022년 8월 14일
Hi
How did you manage the polygons that are not closed? Namely, those with vertexes to infinite?
Valerio
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Christopher Rock
2018년 8월 2일
Vectorised code based off Roger Stafford's answer.
function A = triarea(t, p)
% A = TRIAREA(t, p) area of triangles in triangulation
Xt = reshape(p(t, 1), size(t)); % X coordinates of vertices in triangulation
Yt = reshape(p(t, 2), size(t)); % Y coordinates of vertices in triangulation
A = 0.5 * abs((Xt(:, 2) - Xt(:, 1)) .* (Yt(:, 3) - Yt(:, 1)) - ...
(Xt(:, 3) - Xt(:, 1)) .* (Yt(:, 2) - Yt(:, 1)));
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Diego Andrés Alvarez Marín
2021년 4월 23일
T is the output of delaunay()
P = [X Y]; % array with two columns that contains the coordinates of the nodes
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