Gyroid Sphere

In this tutorial, we will generate gyroid scaffold from sphere.stl whose bounding box is \(2 \times 2 \times 2\). In order to generate porous mesh, the implicit function (gyroid for this case), angular frequency (\(w\)), and isolevel (\(t\)) are required (See Command line).

Angular frequency

According to prior study, \(w\) is inversely proportational to the pore size (see Tips). That is, when \(w\) increases, the pore size will be decreased. For gyroid, \(w \approx \pi/\text{pore size}\). If we want pore size of 0.25 (unit as same as sphere.stl), we try to initially set \(w = \pi/0.25 \approx 12\)

Isolevel

\(t\) is directly proportional to the porosity. In the other word, if we want to increase porosity, we have to increase \(t\)!. However, some values of \(t\) are probably lead to the problematic 3D mesh. Thus we initially leave this value to the default (\(t=0\)).

Grid size

Grid size is a resolution of the output 3D mesh. Unless we generate a 3D mesh for FEA, this parameter is leave as a default value of 100.

Parameters summary

input file = sphere.stl, surface = gyroid, coff (\(w\)) = 12, isolevel (\(t\)) = 0, grid size = 100

Command line

Scaffolder sphere.stl out.stl gyroid,12,0,100 -m

We add -m or --microstructure to enable the pore size evaluation. Then the console output is reported as the following:

[Scaffolder v1.5.1]
-- Input file: .\sphere.stl
-- Output file: out.stl
-- Surface (-n): gyroid
-- Coff (-c): 12
-- Isolevel (-t): 0 
-- Grid size (-g): 100
--   Grid offset: 3
--   Shell: 0
-- Autoclean: True
--   Minimum diameter: 25%
--   Smooth step: 5
--   Fix self-intersect: False
--   Quadric Simplification (-z): 0
-- Analysis microstructure (-m): True
--   Slice grid (k_slice): 100
--   Nearest outer contours (k_polygon): 4
--   Export microstructure: False
--   Mean curvature: False
-- Export JPEG: No
--   Axis: X
-- Build: Yes(Intersect)
-- Bounding Box: [-0.9995, -0.9995, -0.9995] [0.9995, 0.9995, 0.9995]
-- Length: [1.999, 1.999, 1.999]
-- Grid delta: 0.01999
[Generating grid] OK
-- Grid size: 1191016 [106, 106, 106]
[Calculating Winding number] OK
-- Sign Distance: [ -0.834758, 0.998785]  Wind: [ -0.00238368, 1.00151]
[Generating isosurface Fxyz] OK
[Marching Cube]
[========================================] 100% 0.194s
-- Info: 118708 vertices 237636 faces
[libVCG Cleaning] OK
-- is_manifold: 1
[Topology Measurement]
-- Mesh is composed by 1 connected component(s)
-- border edge: 0
-- non-manifold edge: 0
-- non-manifold vertex: 0
-- self-intersect faces: 1831
-- Mesh is two-manifold
-- Mesh has 0 holes
-- Genus is 107
[=======================================>] 98% 2.1s7s
[Microstructure]
-- Avg Min Feret: 0.0893954
-- Avg Max Feret: 0.606401
-- Min Feret: [0.00073122 0.033939 0.105832 0.131947 0.615222]
-- Max Feret: [0.00132485 0.243246 0.630859 0.723238 1.91447]
-- Square Similarity: [0 0 0 0 0]
-- Circle Similarity: [0 0 0 0 0]
-- Triangle Similarity: [0 0 0 0 0]
-- Ellipse Similarity: [0 0 0 0 0]
-- Elongation Similarity: [0 0 0 0 0]
[Scaffold properties]
-- Volume: 2.04856
-- Surface Area: 29.5085
-- Porosity: 0.508139
-- Surface Area ratio: 2.35532
[Writing file] OK
[Finished]

Adjust isolevel for 60% porosity

Suppose that the target porosity is 60%. Then we increase \(t\) to 1 and generate 3D mesh again

Scaffolder sphere.stl out.stl gyroid,12,1,100 -m -q

This time, we add -q or --quite to prevent the verbose output. The program will save the report in a file (<output_name>_<surface><timestamp>.txt) instead. We use binary search to adjust the new value of \(t\) to find the optimal value with the 60% porosity.

\(t\)	0	1	0.5	0.25	0.375	0.3125	0.28	0.265
Porosity	0.508	0.85	0.67	0.59	0.634	0.613	0.602	0.597

We can also use the classical numerical method called Secant method to find the optimal \(t\) for the target porosity.

\[ F(t) = Porosity(t) - 0.6 = 0 \]

\[ t_{next} = t_{current} - F(t_{current})\frac{t_{current} - t_{old}}{F(t_{current}) - F(t_{old})} \]

\[ t_{next} = t_{current} - (\text{Porosity}_{current} - 0.6)\frac{t_{current} - t_{old}}{\text{Porosity}_{current} - \text{Porosity}_{old}} \]

\(t\)	0	1	0.27
Porosity	0.508	0.85	0.5989