Center of a irregular hexahedra given the vertices

[pyroknife]

I am trying to compute the center of irregular convex hexahedras (6 faced volume).

I have the 8 indices that define the hexahedra. I was reading that the center is simply the sum of the indices divided by the number of indices and this is true for all polygons and polyhedras. Is this true?

 

[mfb]

How do you define "center" in an irregular shape?

 

[pyroknife]

I am asking myself that same question. I believe I am referring to the geometrical/spatial center, but I am not positive.

Basically I have a 3-D structured mesh grid, with cells. And I am trying to find the "center" of that cell.
I believe it is a volume-based center?

Hmmmm, if it is a volume based center, then an averaging of the vertices would not yield the center of volume.

 

[mfb]

What do you mean by "geometrical/spatial center"?

There is a center of mass with a clear definition, for example. There might be other well-defined points, but you have to decide what you are actually looking for. "The center" is too unclear.

 

[pyroknife]

I will look into this and figure out what it is that I actually want.What "type of center" does an averaging of all the nodal points provide?

 

[mfb]

I'm not sure if that point has any special meaning.

 

[HallsofIvy]

The "centroid" of a triangle has coordinates equal to the average of the coordinates of the vertices. Other figures, such as a hexagon, can be divided into triangles. The coordinates of the centroid of such a figure is the weighted average of the coordinates of the centroids of the triangles, weighted by area.

 

[stedwards]

I am trying to compute the center of irregular convex hexahedras (6 faced volume).

I have the 8 indices that define the hexahedra. I was reading that the center is simply the sum of the indices divided by the number of indices and this is true for all polygons and polyhedras. Is this true?

Start with a cube. Take four of the corners and bring them close together so that the cube becomes something close to a four sided pyramid in shape. The average of the eight corner z coordinates is one 1/2 half of the height, but the center of mass is only 1/4 the height.