I have simplex surface and I need to calculate centroid of different parts of the simplex? The edges are not similar in every side. Screenshots attached.
For a closed volume part, one way to do it is to:
- pick a random point as guessed center
- calculate volume of each tetrahedron formed by the point and the triangles of the part
- keep a sum of the multiples of small tetrahedons’ volume and center
- divide the sum by the total volume
Here is an example code.
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This is simplex mesh. If I would say, may be all of the simplex cells will not have the same number of edges like 6 or 8. Still is it gonna work with your steps?
Calculating volume of a single cell formed by a single face and arbitrary center will be more complicated than a simple vector cross product, but it should still work.