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A Formula for 3D Unstructured Grids wanted

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Old   February 25, 2000, 00:59
Default A Formula for 3D Unstructured Grids wanted
  #1
Yoshikiyo
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Hello all,

I want a formula for 3D grids which relates the # of nodes to the # of tetrahedra, i.e.

Nt = fnc(Nv)

where Nv is the # of vertices(nodes) and Nt is the # of tetrahedra.

Also, the # of triangles on boundaries may be involved.

Does anybody know whether or not it is possible to get such a formula? (even an approximation)

Thank you,

Yoshikiyo
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Old   February 25, 2000, 05:17
Default Re: A Formula for 3D Unstructured Grids wanted
  #2
Robert Schneiders
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Hi,

let V = number of nodes,

E = number of edges,

F = number of faces

T = number of tets

_i : inner

_a : boundary

Then (for a geometry without holes):

V + F = E + H + 1

4 * T = 2 * F_i + F_a

F_a + V_a = E_a + 2

4 * F_a = 2 * E_a

On the average, each internal node has 24 tets adjacent.

Regards,

Robert

Dr. Robert Schneiders MAGMA Giessereitechnologie GmbH D-52072 Aachen Kackertstr. 11 Germany Tel.: +49-241-88901-13 email: R.Schneiders@magmasoft.de www: http://www-users.informatik.rwth-aachen.de/~roberts/

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Old   February 25, 2000, 13:05
Default Re: A Formula for 3D Unstructured Grids wanted
  #3
Yoshikiyo
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Thank you for your information, Dr. Schneiders.

I understand the four formulas, but it seems impossible to eliminate both E_i and F_i in the first formula so that I have V=fnc(T,Va).

How did you deduce that each internal node has 24 tets adjacent on average?

Thank you
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Old   February 25, 2000, 13:16
Default Re: A Formula for 3D Unstructured Grids wanted
  #4
Robert Schneiders
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Dear Mr. Yoshikiyo,

I don't know whether it's possble to get the kind of formula that you want.

Your second question: A heuristic argument is:

- 1D: Each node has 2 = 1*2 edges adjacent - 2D: Each node has 6 = 1*2*3 triangles adjacent ==> 3D: Each node has 24 = 1*2*3*4 tets adjacent.

Best regards,

Robert Schneiders
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Old   February 25, 2000, 14:07
Default Re: A Formula for 3D Unstructured Grids wanted
  #5
clifford bradford
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in your formulae what is 'H'?
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Old   February 25, 2000, 14:12
Default Re: A Formula for 3D Unstructured Grids wanted
  #6
Robert Schneiders
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"H" should be "T", sorry.

Regards,

Robert
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Old   February 25, 2000, 23:17
Default Re: A Formula for 3D Unstructured Grids wanted
  #7
MLJ
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For a good Delaunay mesh, T approx=6*V
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