A Modular Approach for Creation of Any Bi-Axial Woven Structure with Congruent Tiles

Within this repository Blender programs and Geometry Nodes feature is used to develop the congruent tiles.

models directory contains 3D printable .stl files of the shapes with slots.

shape_generator.blend is used for generating the congruent tiles

shape_generator_demo.blend contains a animation demo of the heightfields tiles

shape_foldings.blend contains animations for folding and unfolding of the congruent tiles

voronoi_partition_finding_2D.blend is used for finding voronoi partitions from the curved voronoi sites using a finite voxel data structure

Installation

To use these blender files you need to have a stable release of blender 3.5+, 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:

ABGeometry Controls

SUBDIV_LEVEL_SIMPLE: Controls the simple subdivision used for subdividing the bounday curve

SUBDIV_LEVEL_SMOOTH: Controls the catmull-clark subdivision used for subdividing the boundary curve

BOUNDARY_A: Controls the A parameter(i.e. height difference) of the boundary curve

BOUNDARY_B: Controls the B parameter(i.e. width difference) of the boundary curve

CUBE_VERTEX_AMOUNT: Controls the amound of verticec in the fundamental cube region, this might be needed for finer displacement of the shape later on if needed.

ABCStructure Controls

SLAB_THICKNESS: Controls the height of the fundamental tile

N: Number of warp and weft threads, single value creates a square fabric pattern

A: Number of warps before wefts

B: Number of wefts after warps

C: Shift amount at each different row

HIDE_WARP: Hides warp threads

HIDE_WEFT: Hides weft threads

SHOW_SINGLE_WARP_THREAD: Shows only a single warp thread defined by the WARP_THREAD_NUMBER=[0,N-1]

WARP_THREAD_NUMBER: Warp thread to be shown if SHOW_SINGLE_WARP_THREAD is selected

SHOW_SINGLE_WEFT_THREAD: Shows only a single weft thread defined by the WEFT_THREAD_NUMBER=[0,N-1]

WEFT_THREAD_NUMBER: Weft thread to be shown if SHOW_SINGLE_WEFT_THREAD is selected

Rendering

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

Citation

@article{yildiz2023congruentbiaxial,
	title = {A modular approach for creation of any bi-axial woven structure with congruent tiles},
	author = {Tolga Yildiz and Ergun Akleman and Vinayak Krishnamurthy and Matthew Ebert},
	journal = {Computers & Graphics},
	volume = {114},
	pages = {357-367},
	year = {2023},
	issn = {0097-8493},
	doi = {https://doi.org/10.1016/j.cag.2023.06.017},
	url = {https://www.sciencedirect.com/science/article/pii/S0097849323001127},
	keywords = {Spherical coordinates, Voronoi tessellation, Parametrization, 3D tiling}
}