Tips

What is the value of \(w\) used for pore size \(x\)?

The angular frequency (\(w\)) control the number of repetitive TPMS units:

\[ w = 2\pi / T = 2\pi N / L \]

where \(T\) = period or length of a unit cell, \(N\) = the number of unit cells, and \(L\) = the length of input 3D mesh.

For example, if we want \(N=2\) in cube20mm.stl (\(L=20mm\)), \(w\) will be \(2\pi*2/20 = \pi/5\) (the unit of \(L\) has the same dimension with the input mesh).

The image show the Gyroid (left) and Double-Gyroid (right) with \(w=\pi/5\) and \(t=0\). The pore size \(x \approx T/2\) for Gyroid and \(T/4\) for Double-Gyroid. Then,

\[ w \approx \left\{ \begin{array}{l} \pi/x, & \text{for gyroid} \\ \pi/2x, & \text{for double-gyroid} \end{array} \right. \]

If we want a gyroid with \(x=5mm\), we will set \(w=\pi/5\).

Example:

./Scaffolder cube20mm.stl out.ply -c 3.14159 -g 100 -n tubulat_g_ab

Program will generate the scaffold from cube20mm.stl (\(L=20mm\)) with theoretical \(N=10\)

How to reduce the size of 3D mesh?

Scaffolder uses the Quadratic decimation from MeshLab to reduce the result 3D mesh with an option --size_optimize (-z). For example, the following command is used to generate a gyroid with 50% decimation, thus resulting the 50% less faces:

./Scaffolder input.stl out.stl gyroid,0.6283,0.61,200 -z 0.5

Note

You can manually reduce the size by using MeshLab: Filter > Remeshing, Simplification, and Reconstruction > Simplification: Quadric Edge Collapse Decimation

How to intrepret the output from console?

Suppose that the following command was used:

.\Scaffolder.exe .\cube20mm.stl out.stl gyroid,0.6283,0.61,100

Then this is an output generated by program with default options (--format default)

[Scaffolder v1.5.1]
-- Input file: .\cube20mm.stl
-- Output file: out.stl
-- Surface (-n): gyroid
-- Coff (-c): 0.6283
-- Isolevel (-t): 0.61
-- 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): False
--   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, 0, 0] [20, 20, 20]
-- Length: [20, 20, 20]
-- Grid delta: 0.2
[Generating grid] OK
-- Grid size: 1191016 [106, 106, 106]
[Calculating Winding number] OK
-- Sign Distance: [ -1.03923, 9.99999]  Wind: [ -2.86488e-06, 1]
[Generating isosurface Fxyz] OK
[Marching Cube]
[========================================] 100% 0.178s
-- Info: 105896 vertices 211896 faces
[libVCG Cleaning] OK
[Laplacian smoothing] 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: 840
-- Mesh is two-manifold
-- Mesh has 0 holes
-- Genus is 27
[Scaffold properties]
-- Volume: 2267.63
-- Surface Area: 2855.25
-- Porosity: 0.716547
-- Surface Area ratio: 1.18969
[Writing file] OK
[Finished]

Parameters summary (Lines 1-25)

Line	Parameter (value)	Detail	Refer to a process at
2	Input file (cube20mm.stl)	Path to input file	Line 26,Line 28
3	Output file (out.stl)	Path to output file	Line 51
4	Surface (gyroid)	TPMS types	Line 30
5	Coff (0.6283)	Angular frequency (\(w\))	Line 30
6	Isolevel (0.61)	Isolevel (\(t\))	Line 30
7	Grid size (100)	Grid Resolution	Line 26
8	Grid offset (3)	Padding size adding to grid	Line 26
9	Shell (0)	Depth of solid shell	Line 30
10	Autoclean (True)	Clean 3D Mesh	Line 34
11	Minimum diameter (25%)	Minimal diameter (% of diagonal length of bounding box) to classify the small components in cleaning process	Line 34
12	Smooth step (5)	Steps to Laplacian smoothing	Line 35
13	Fix self-intersect (False)	Whether the program should fix the self-intersect or not	Line 34
14	Quadric Simplification (0)	% triangles reduction	NA
15	Analysis microstructure (False)	Report the pore size	NA
16	Slice grid (100)	\(k_{slice}\) (the number of slice layers)	NA
17	Nearest outer contours (4)	\(k_{polygon}\)	NA
18	Export microstructure (False)	Export the SVG of sliced layers	NA
19	Mean curvature (False)	Calculate the mean curvature	NA
20	Export JPEG (No)	Export sliced layer	NA
21	Axis (X)	Axis to slice 3D Mesh	NA
22	Build (True)	Generate 3D Mesh	Line 51
23	Bounding Box ([0, 0, 0] [20, 20, 20])	Two points of bounding box	Line 26
24	Length ([20, 20, 20])	\(\text{Length}\) of bonding box in [x, y, z]	Line 26
25	Grid delta (0.2)	\(min(\text{Length})/\text{grid size}\)	Line 26

Grid Generation (Line 26)

The voxels were generated based on \(\text{Length}/\text{Grid delta} + 2(\text{Grid offset})\).
In this case, the grid size of (X, Y, Z) is \((20, 20, 20)/0.2 + 2(3) = (106, 106, 106)\)
and the total number of voxels is \(106\times106\times106=1191016\)

Winding number and SDF calculation (Line 28)

The winding number and SDF with \(106\times106\times106\) voxels was calculated based on vertices and faces from input file.

Surface Generation (Line 30)

By combining \(w\) (0.6283), \(t\) (0.61), implicit function (gyroid), and input SDF, the output SDF was constructed.

Surface visualization (Line 31)

The trigular mesh was generated from output SDF by dual marching cubes algorithm

Cleaning (Line 34)

If autoclean option is enabled, the trigular mesh was cleaned by VGClib.

Smoothing (Line 35)

The Laplacian smooth is used to fix the mis-shape faces from dual marching cube algorithm.

Topology properties (Line 37)

In order to fabricate with 3D printer, make sure that 3D mesh is watertight. Thus, the program asserts whether the 3D mesh is two-manifold or not. Moreover, the number non-manifold and border edges are reported, which should be zero to ensure the watertight property of the 3D mesh.

Scaffold properties (Line 46)

Finally, the scaffold property such as volume (\(\text{unit}^3\)), surface area (\(\text{unit}^2\)), porosity, and surface area ratio were reported.

\[ Porosity = 1 - \left|\frac{\text{Volume}_{output}}{\text{Volume}_{input}}\right| \]

\[ \text{Surface Area Ratio (SAR)} = \left|\frac{\text{Surface area}_{output}}{\text{Surface area}_{input}}\right| \]

How to intrepret the output from console? (2)

If the Analysis microstructure (-m) is added to the previous command:

.\Scaffolder.exe .\cube20mm.stl out.stl gyroid,0.6283,0.61,100 -m

an additional output from microstructure measurement will be reported (Line 47).

[Scaffolder v1.5.1]
-- Input file: .\cube20mm.stl
-- Output file: out.stl
-- Surface (-n): gyroid
-- Coff (-c): 0.6283
-- Isolevel (-t): 0.61
-- 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, 0, 0] [20, 20, 20]
-- Length: [20, 20, 20]
-- Grid delta: 0.2
[Generating grid] OK
-- Grid size: 1191016 [106, 106, 106]
[Calculating Winding number] OK
-- Sign Distance: [ -1.03923, 9.99999]  Wind: [ -2.86488e-06, 1]
[Generating isosurface Fxyz] OK
[Marching Cube]
[========================================] 100% 0.202s
-- Info: 105896 vertices 211896 faces
[libVCG Cleaning] OK
[Laplacian smoothing] 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: 840
-- Mesh is two-manifold
-- Mesh has 0 holes
-- Genus is 27
[=======================================>] 98% 1.939s
[Microstructure]
-- Avg Min Feret: 3.1344
-- Avg Max Feret: 8.62469
-- Min Feret: [1.05429 2.39338 3.18016 3.8397 9.99987]
-- Max Feret: [3.52792 5.91049 7.67635 11.9059 14.8046]
-- 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: 2267.63
-- Surface Area: 2855.25
-- Porosity: 0.716547
-- Surface Area ratio: 1.18969
[Writing file] OK
[Finished]

Feret Diameter

Feret diameter, or caliper diameter, is a diameter of an object measured with a caliper. According to the above image, \(\upvarphi\) and \(\Phi\) are the minimum and maximum Feret diameter, respectively.

The minimum and maximum of Feret diameters are collected. The interquartile ranges (IQR) reported in Line 50-51 are formatted as [Min, Q1, Median, Q3, Max].