Difference between revisions of "Visualization methods for gemstone metamaterial factories"

Latest revision as of 11:30, 6 February 2024

There are at least two major challenges.

• structures reach over a vast range of size scales that one wants do display simultaneously and in intuitively graspable relation to each other.
• getting a smooth seamless cross-zoomable transition from atomic detail to larger scale homogebeouseness.

Displaying many scales and their relation simultaneously

This can be done by generalizing log polar mapping to 3D like so:

• x'(x,y,z) = pi/2 - atan2( z, sqrt(pow(x,2) + pow(y,2)) ) * cos(atan2(y,x)))
• y'(x,y,z) = pi/2 - atan2( z, sqrt(pow(x,2) + pow(y,2)) ) * sin(atan2(y,x)))
• z'(x,y,z) = log( sqrt(pow(x,2) + pow(y,2) + pow(z,2)) ) / log(base)

See main articles:

• Distorted visualization methods for convergent assembly
• Log polar mapping

Idea: tracing the winding path of a moiety as the reference axis for a visualization

One may want to map the z-axis to a winded path the (roughly) follows the trajectory
moiety from its entrance into machine phase to its final resting place in the final fully assembled product.
To avoid sharp kinks in the path the tracing path where one wants to map the z axis onto
could be somewhat spacially low pass filtered in an scale dependent way.

Due to complexly changing of physics with size scales it is very likely that all of the convergent assembly process won't go strait up through the chip (across idealized assembly layers) in a almost straight line. Instead it's expectable that a considerable amount of horizontal transport and re- routing will take place.

Like when zooming in a fractal like the Mandlelbot set there are uninteresting structureless bland areas.
Just like that there may be areas of the nanofactory that are rather uninteresting homogeneous at the lowest scales.

• One would not want to center the log polar view is an area like that. Also ...
• One would not want to cross cross vast "areas" of uninteresting space before finally reaching an interesting space.

Like e.g.

• The homogeneous structural gem-gum walls of the nanofactory where they are not filled with other interesting stuff like data, energy, thermal, or other subysstems.
• Bigger hinges in the robotics of the further up assembly levels.
  For big macroscopic robotics even the already bland and homogeneous infinitesimal bearings might make up only a thin sliver of the hinges volume. The bulk possibly being made out of purely structural (meta)material. Maybe emulating flexibility and exotic anisotropic mechanical properties at best.

Atomistic to continuum – smooth cross-zoomable transition

Having a smooth transition

• from where atoms are resolves as individual spheres
• to where they are only visible as a fine-grained pattern on the surface to where
• to where they completely blur out to a homogeneous representative color

• without producing moire effects
• without incurring bad compression artifacts from the confetti effect

Current image and video compression algorithms where not built for this kind of imagery. An AI based compression algorithm might likely do better, but there are no standards for that.

New volume-plane-line triangulation shrink-wrap vizualisation

One interesting visualization that maybe especially suitable for gemstone like compounds and diamondoids
is the the lines molecular visualization generalized to more densely meshed covalent networks giving planes and volumes
(with the vertices sitting at the locations of the nuclei) too.

Generating that visualization:

• Take only the positions of all the the atomic nuclei and the nucleus to nucleus lines representing bonds of a crystolecule.
• Suck-shrink-wrap (concave fill-in) a triangulation around that point-and-line-aggregations such that it can (but need not) collapse to 2D or even 1D.

The result and eventual benefits of that visualization:

• The densely connected inner parts of gemstone-like compounds become represented as solid volumes atom radius smaller than the real parts
• Off stating sulfur and disulfur-bridges make 2D planes
• Off standing OH groups, hydrogens and halogen atoms make "hair".

The latter two hint on areas where snapback could occur.

One can directly look into sliding interfaces while still getting a solid (albeit virtulal) surface as a reference
that is of low computational effort to calculate. Maybe one can build better intuition with that sort of visualization.
Judging the not directly displayed radii of the atoms can be done from the lateral bond distances and maybe the classical color coding.

(wiki-TODO: add a sketch of volume-plane-line shrinkwrap vizualisation)

Related here:

• Vacuum lockout – interfaces where no gas shall be able to seep through (atomically precise positive displacement PPV pump)
• Superlubricity – interfaces that need the right distance – tuning crystolecule bearings for the right thightness

Related

• More concretely: Distorted visualization methods for convergent assembly & Log polar mapping
• Challenges in the visualization of gem-gum factories
• Design levels#Lower bulk limit design
• Gemstone metamaterial factory