# A Formula for 3D Unstructured Grids wanted

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 February 25, 2000, 00:59 A Formula for 3D Unstructured Grids wanted #1 Yoshikiyo Guest   Posts: n/a 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

 February 25, 2000, 05:17 Re: A Formula for 3D Unstructured Grids wanted #2 Robert Schneiders Guest   Posts: n/a 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/

 February 25, 2000, 13:05 Re: A Formula for 3D Unstructured Grids wanted #3 Yoshikiyo Guest   Posts: n/a 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

 February 25, 2000, 13:16 Re: A Formula for 3D Unstructured Grids wanted #4 Robert Schneiders Guest   Posts: n/a 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

 February 25, 2000, 14:07 Re: A Formula for 3D Unstructured Grids wanted #5 clifford bradford Guest   Posts: n/a in your formulae what is 'H'?

 February 25, 2000, 14:12 Re: A Formula for 3D Unstructured Grids wanted #6 Robert Schneiders Guest   Posts: n/a "H" should be "T", sorry. Regards, Robert

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

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