Hey folks. I *really* like the geometric pattern found on the removable panels of this machine. What would you call the design, and how would you suggest I model it? This would be for producing similar panels for use on an unrelated real-world project.

See it in motion here: https://youtu.be/ue4AsQutgsM?si=muZ7hBDkDNgjDox5

Thanks!

Chris

Hi Chris,

The pattern resembles honeybee wax foundation.

The pattern also looks like cubes above and below a 90 degree angle iron.
Maybe a projected view of cubes?

It is hard to focus on the video.

- Brian

Edit: Google "stacked cube pattern"

Hi Chris,

To have this pattern you could begin with an hexagon (only with its lines)
Separate it by cutting from center.
You lift some points and lower some other points.
Then do plans with each 4 lines group.
Copy and move your surfaces to have your "stacked cubes pattern"

Have fun

Something like this




Stacked cube pattern, a 3dm file

Is this what you are looking for?

the second method was made by creating a 3d square, rotate to the view I wanted, scaled 1d to squish it but maintaining the top view, then boolean merge a line to cut it.

Hi Chris, I guess you'd call that a relief pattern? Maybe something like geometric relief pattern?

The main strategy would be probably something like build a 2D pattern first mostly by copying or mirroring an initial cell:

Then to get the relief element, turn on control points for all the lines and displace several in elevation, then select a region and use Construct > Planar (or Construct > Network) to form surfaces.

- Michael

Honey bee foundation is created by humans with three rhombi, which have a 3rd dimension, and which the bees draw out to form near hexagonal cells, with a slight slope/slant.

For naturally bee build honeycomb, starting from nothing, the bees create 2 different varieties of bases. One is with 3 rhombi, which gives the illusion of stacked cubes, which appear very similar to the TiniJet patterns.
The other base is with 2 hexagons, and two rhombi, and is theoretically slightly more efficient.

http://www.matematicasvisuales.com/english/html/geometry/rhombicdodecahedron/honeycombmin.html

The above link has some math formulas, to calculate the "energy" efficiency/ construction efficiency of theoretical honeycomb, with variable lengths and angles.

The hexagonal prism is an "extruded hexagon".

I still want to draw some of the papers designs in Moi!!! And the rhombicdodecahedron...
The paper's math takes some study...

- Brian

ps, I caught a swarm of honeybees at the end of August.

The "keel" can be constructed in Moi, from a Cube:
https://en.wikipedia.org/wiki/File:R1-cube.gif

The "corner" with 3 rhombi is the keel, the unit for the illusion of cubes.

The acute angle between faces seems to be wrong??? It is supposed to be 70.528779 degrees.
Not getting the Maraldi angle, 109 degrees, 28 minutes, 16 seconds ...
(I must have made some mistake?)

- Brian

Some of these papers are very hard to follow...

An old link with keel angles for bee honeycomb, of rhombi.
https://www.tandfonline.com/doi/abs/10.1080/14786447308640909

http://www.matematicasvisuales.com/english/html/geometry/rhombicdodecahedron/maraldi.html

See page 12 for cube illusion with rhombi:
https://www.jstage.jst.go.jp/article/forma/36/1/36_1/_pdf/-char/en
"Plane filling by the golden rhombus & the square-root-of-2 square rhombus" (Assumed 3d, not planar???)

A rhombic dodecahedron keel was created in Moi, using the formulas in the link in post 7.

The keel is the 3D combination of 3 rhombi. The keel for the rhombic dodecahedron has certain specific dimensions. Other "non-efficient" keels are possible.
R = (outer) radius of hexagon, (or hexagon prism). Set to value of 4 units.
height_min = R * sqrt(2) / 4 (This is the height above the top of the hexagon prism, and is half the height of the keel.) (sqrt(2) is the diagonal of a unit square.)
d is the diagonal of the hexagon, with one vertex in between. d = R*sqrt(3). d is also one of the diagonals of the rhombi.
For a_min, 2*a is the other diagonal of the rhombi. 2*a = R*sqrt(3) / sqrt(2)

The Maraldi angle is the obtuse angle of the rhombi_min. Angle is about 109.4712 degrees. (109degrees, 28 minutes, 16 seconds.)
I had to use Michael's old Angle script to measure the angle.

Have had trouble using the angle Dim command, in 3D view, with angles that are not orthogonal in other views...

The 3D keel gives the illusion of viewing a cube.

- Brian

Two planes through two of these rhombi, intersect at an angle of 120 degrees. (Used two lines perpendicular to the intersection edge, to measure angle.)

Hi Michael,
Wanted to ask for some help.

I believe the image is only 2d. Done in a vector program or something. So the "Model" would actually look a little different. I think others have already shown a result.

But I wanted to fool around a bit with this.

I couldnt figure out the "Projection" with regard to how to rotate the 3d object. Used a CPlane and got it but then was still confused on where I was in WCS...

So the hexagon with center connected "cube" projection. I want to rotate an actual cube to that projection

Like 30 and 60 and 30 degrees or something.

If I cut the cube in half, I get 54.74 and 35.26 to equal 90. But I think i have left my level.

Can you help me with that?

Here is my initial look.

I can get the top view going.

Angle C = 54.736 degrees approximately :

http://www.matematicasvisuales.com/english/html/geometry/rhombicdodecahedron/maraldi.html

Hi Burr, how about setting an isometric view and then use Make2D or export to DXF using the 3D view projection?

Script for setting isometric view here:
http://moi3d.com/forum/index.php?webtag=MOI&msg=1917.35

- Michael

Hi Michael,
I wanted to make it with actual 3d cubes and lay them out and cut the bottom flat.

Was trying to set the cube to be rotated like that per my top or front view

I have been able to get it done also by rotating, though i loose my train of thought. I was looking for an explanation or method from you

Hi Burr, so starting with a cube centered at the origin, first rotate it in the Top view by 45 degrees then rotate in the Right view by 54.736 like Brian writes above, or also you can snap the rotation onto the cube's corner with the first pick and then straight up with the 2nd pick.

Looks like this:



- Michael

Ok, much clearer than i was doing.

Thank you.

The solution, I gave before, seems easy and fast.
It's as Michael explained, to begin with an cutted hexagon and displacement of key points.
No theory, only practice.

I posted the file too if you want to see it.

Have an happy modeling !