From: bemfarmer
These objects should be constructable with MoI.
1. Voronoi Spaghetti & VoroNoodles. This movie version of the (unavailable?) paper is very interesting.
A helix spiral of line segments, (or curve segments), of variable progress length, (or points on them), converted to a plane of Voronoi closed curve(s), converted to thin slabs, and stacked up, form interlocking 3D shapes.
The Movie:
https://dl.acm.org/doi/abs/10.1145/3550340.3564229
This paper seems to be an evolved form of a few other papers using Voronoi shapes to build a 3D structure.
Patents pending...
Comparing and contrasting the 4 or so variations of papers, helps to understand what is being done. The progessive Voronoi shapes are created by changing point on the lines or curves, somehow.
*****
2. A precursor paper?:
Simple VoroNoodles using moving points on 2D fractals.
Each new points locations set, is for a new 3D layer.
Motion could be continous, or stepwise.
http://gallery.bridgesmathart.org/exhibitions/2022-bridges-conference-short-film-festival/cmullins7
The short movie of the simple VoroNoodles:
https://www.youtube.com/watch?v=3MB3P7AmiSY
*****
3. A (simpler?) precursor to the Voronoi Spaghetti?
LayerLock the movie:
https://www.youtube.com/watch?v=jSNbidsPiNI
The LayerLock paper will become publicly available Nov 1, 2023, according to:
https://par.nsf.gov/biblio/10353832-layerlock-layer-wise-collision-free-multi-robot-additive-manufacturing-using-topologically-interlocked-space-filling-shapes
4. This hard to understand paper uses 3D Voronoi decomposition of points on interwoven (2D) curves, arranged in 3D space:
file:///C:/Users/orcha/Downloads/Bi_Axial_Woven_Tiles_Interlocking_Space.pdf
- Brian
From: Frenchy Pilou (PILOU)
Cool research!
Another way! ;)
https://lexica.art/?q=Voronoi+Spaghetti+%26+Noodles
From: bemfarmer
The following paragraph is a Redundant explanation of how interlocking layers are produced for the VoroNoodles.
It is redundant to try and improve understanding of the Voronoodle movie, not to be confusing:-).
The paper linked to below is a "precursor" paper to the Voronoi Noodles paper. The paper explains the union of Voronoi made from points located on the same LINE. (The Voronoi Decomposition also makes sibling convex Voronoi because there are additional ruled surface lines in the (Bravais Lattice Array) (An array of parallel ribbons)). Each of said LINE(s) is a "ruled line" on the 3D ruled surface (Ribbon). For each layer, the Bravais lattice of lines containing points has Voronoi Decomposition applied to the points on all of the Lines, and each Line group of Voronoi are booleaned together. (So there are a lot of side by side closed (convex?) polygons, each of which is made up of the Boolean of Voronoi for each (Line with multiple points on it).) (See page 6 and 7 for algorithm outline.):
file:///C:/Users/orcha/Downloads/GeneralizedAbeilleTiles_Print.pdf
(The Lines can also be curved, provided they are Ruled.(?))
The LINES can rotate between layers. (The Ribbon ruled surface can spiral in a helix.)
This Abeille Tiles paper is of course different from the VoroNoodles paper, but the two papers share some of the layer by layer creation. (The Algorithms are similar, but also have portions which have differences.) (There is also a step for the simple extrusion for the polygons obtained by Boolean, for each layer.)
The polygons will progressively change for each layer, as the lines for the next layer rotate from the preceding layer.
The lines can change in length between layers(?)
- Brian
Voronoi Decomposition = Voronoi Tessellation.
Certain Voronoi are booleanized together.
Still have to read up on the Bravais Lattice. I think it is basically an array of unit cells, "without voids".
https://en.wikipedia.org/wiki/Bravais_lattice
"unit cell is defined as a space that, when translated through a subset of all vectors described by
.........., fills the lattice space without overlapping or voids."
"a lattice space is a multiple of a unit cell"
