MATLAB: 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.

Best Answer

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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