Porosity calculation of complex three-dimensional model

[2641842777 (扬 崔)]

I now generate a three-dimensional model, using two methods to calculate the porosity, the first method is generated by the volume function, the second is calculated by the method of discrete mathematics, but I did not understand, the two results are not the same, is not my which method has a problem，
L = 2 [Pi]; d = 0.1;
point = Table[{x, y, z}, {x, -L, L, d}, {y, -L, L, d}, {z, -L, L,
d}];
point = Flatten[point, 3];
condition = -0.5 < (Cos[#1] Sin[#2] + Cos[#2] Sin[#3] +
Cos[#3] Sin[#1] &) @@ # < 0.5 &;
point1 = Select[point, condition];
1 - N@(Length[point1]/Length[point])

tpmsG := Cos[x] Sin[y] + Cos[y] Sin[z] + Cos[z] Sin[x]
porosity[formula_, neg_, pos_] :=
Module[{},
1 - Volume[
ImplicitRegion[-neg < formula <
pos, {{x, -2 [Pi], 2 [Pi]}, {y, -2 [Pi],
2 [Pi]}, {z, -2 [Pi], [Pi]}}]]/(4 [Pi])^3]
porosity[tpmsG, 0.5, 0.5]

Now, I have a more complex three-dimensional model of radial variation, how do I calculate its porosity

[gianlucagorni]

On my system this gives a nonempty plot:

tpmsI[a_] := 
  2 Cos[a x] Cos[a y] + 2 Cos[a x] Cos[a z] + 2 Cos[a y] Cos[a z] - 
   Cos[a 2 x] - Cos[a 2 y] - Cos[a  2 z];
RegionPlot3D[(-0.5 < tpmsI[1.7 - 0.2*(1 - Exp[-Norm[{x, y}]/3])] < 
    0.5) && Norm[{x, y}] < 10,
 {x, -10, 10}, {y, -10, 10}, {z, 0, 5}, PlotPoints -> 50]

It is probably not accurate, because PlotPoints should be much higher, but it would take longer computation time.

[gianlucagorni]

In your first example you have evaluated the plot without entering the definition of tpmsI.

[2641842777 (扬 崔)]

thanks,that is reason

[2641842777 (扬 崔)]

I now generate a three-dimensional model, using two methods to calculate the porosity, the first method is generated by the volume function, the second is calculated by the method of discrete mathematics, but I did not understand, the two results are not the same, is not my which method has a problem，

L = 2 \[Pi]; d = 0.1;
point = Table[{x, y, z}, {x, -L, L, d}, {y, -L, L, d}, {z, -L, L, 
    d}];
point = Flatten[point, 3];
condition = -0.5 < (Cos[#1] Sin[#2] + Cos[#2] Sin[#3] + 
        Cos[#3] Sin[#1] &) @@ # < 0.5 &;
point1 = Select[point, condition];
1 - N@(Length[point1]/Length[point])

tpmsG := Cos[x] Sin[y] + Cos[y] Sin[z] + Cos[z] Sin[x]
porosity[formula_, neg_, pos_] := 
 Module[{}, 
  1 - Volume[
     ImplicitRegion[-neg < formula < 
       pos, {{x, -2 \[Pi], 2 \[Pi]}, {y, -2 \[Pi], 
        2 \[Pi]}, {z, -2 \[Pi], \[Pi]}}]]/(4 \[Pi])^3]
porosity[tpmsG, 0.5, 0.5]

After that, I generated a model of radial variation, which is its code. How can I calculate its porosity？