Alberaic Framework for Generating Infinite Polyhdral Frames Using Nonwoven Fabric Patterns

1. Installation
2. Shape Generation Controls
3. Rendering
4. Citation

In this repository you can find the implementation of the framework described in "Volumetric nonwoven structures: An algebraic framework for systematic design of infinite polyhedral frames using nonwoven fabric patterns"

Installation

To use these blender files you need to have a stable release of blender 4.3+, which can be found here.

Shape Generation Controls

Shape generator can be controlled through the Geometry Nodes modifier inputs that can be accessed through the Blender interface:

There are in total 9 shape generators, each input is explained within the files through a README text embedded inside the file. It should be visible with main workspace, if not open up the text editor and choose it to view controls for the shapes.

All the description for the controls are given below

volumetric_nonwoven_NSD INPUTS:

N: Base 10 representation of the binary string {0,1}^k represents, the base size of a column is determined by log2(N)

S: shift amount for each row

D: shift amound in X direction for each layer

Z: number of dual layers since all layers should have a warp and weft pair, total number of layers is N*2

Thickness: Controlls the thickness of the connections

Single/Tiled: Tiles the structure to a 3x3x3 domain

Subdivision Level: Subdivision iterations applied after construction

Wall Thickness: Controlls the wall thickness of the connections

volumetric_nonwoven_ABCD INPUTS:

X: number of elements in X direction for the fundamental domain

Y: number of elements in Y direction for the fundamental domain

Z: number of elements in Z direction for the fundamental domain

A: Number of consecutive no connections for a single column

B: Number of consecutive connections for a single column

C: Shift amount for next row

D1: Shift amount for layers in X direction

Pipe Width: Width of the pipes

Shell Thickness: Controls the thickness of walls

Tile 3x3: Tiles the structure to 3x3x3 cube lattice

CC Subdivision Level: Subdivision iterations applied after construction

Skeleton Switch: Adds the skeletal structure to the model

handlebody_surface_volumetric_nonwoven_ABCD INPUTS:

X: number of elements in X direction for the fundamental domain

Y: number of elements in Y direction for the fundamental domain

Z: number of elements in Z direction for the fundamental domain

A: Number of consecutive no connections for a single column

B: Number of consecutive connections for a single column

C: Shift amount for next row

D1: Shift amount for layers in X direction

grunbaum_shephard_matrix INPUTS:

x: number of elements in X direction

y: number of elements in Y direction

z: number of elements in Z direction

A: Number of consecutive 0s

B: Number of consecutive 1s

C: Shift amount for next row

Y: Scale of the structure

D1: Shift amount for layers in X direction

D2: Shift amount for layers in Y direction

abc_nonwoven INPUTS:

x: number of elements in X direction

y: number of elements in Y direction

A: Number of consecutive free elements

B: Number of consecutive connected elements

C: Shift amount for next row

Y: Scale of the structure

abc_woven INPUTS:

x: number of elements in X direction

y: number of elements in Y direction

A: Number of consecutive up crossings

B: Number of consecutive down crossings

C: Shift amount for next row

Z: Z-Scale of the weave

Y: Scale of the structure

adic_shift_random_nonwoven INPUTS:

NX: number of elements in X direction for the fundamental domain

NY: number of elements in Y direction for the fundamental domain

NZ: number of elements in Z direction for the fundamental domain

Thickness: Controlls the thickness of the connections

Subdivision Level: Subdivision iterations applied after construction

Seed: seed used for the random number

adic_shift_nonwoven INPUTS:

NX: number of elements in X direction for the fundamental domain

NY: number of elements in Y direction for the fundamental domain

NZ: number of elements in Z direction for the fundamental domain

Adic Number: Adic number used for the first row. If the number is less than 10^(NX-1) then the number contains leading 0. If the number is greater then 10*NX then the only firts NX digits of the number is considered

Shift1: shift applied for each row

Shift2: shift applied for each layer

probabilistic_nonwoven INPUTS:

NX: number of elements in X direction for the fundamental domain

NY: number of elements in Y direction for the fundamental domain

NZ: number of elements in Z direction for the fundamental domain

P_X: Probability of not having connection for X direction

P_Y: Probability of not having connection for Y direction

P_Z: Probability of not having connection for Z direction

Thickness: Controlls the thickness of the connections

Subdivision Level: Subdivision iterations applied after construction

Disable X Connections: Disables X Connections

Disable Y Connections: Disables Y Connections

Disable Z Connections: Disables Z Connections

Seed: seed used for the random number

Rendering

To get different rendering of the shape you can use Blender's features which can be accessed through the viewport interface.

Citation

@article{yildiz2024adicVolumetricNonwovens,
    title = {Volumetric nonwoven structures: An algebraic framework for systematic design of infinite polyhedral frames using nonwoven fabric patterns},
    journal = {Computers & Graphics},
    volume = {122},
    pages = {103979},
    year = {2024},
    issn = {0097-8493},
    doi = {https://doi.org/10.1016/j.cag.2024.103979},
    url = {https://www.sciencedirect.com/science/article/pii/S0097849324001146},
    author = {Tolga Yildiz and Ergun Akleman},
    keywords = {Volumetric nonwoven structures, Shape algebra, Shape modeling and design, P-adic numbers}
}