Challenges in the visualization of gem-gum factories

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Static non-animated visualization

Visualizing the internal workings of a gem-gum factory over all the involved size scales
in just one picture is hard. Especially when there shall no be discontinuous jumps in scale.
The natural solution to that problem seems to be a log polar mapping generalized to 3D
See: Visualization methods for gemstone metamaterial factories
Whether such a depiction can helps for building an intuitive understanding remains to be seen.

dynamic animated visualization

  • Challenges in speed visualization – stroboscopic illusion
  • Acceleratingly racing along long assembly lines to give a feeling of relative length

3D was never build for modelling over so many size scales
Modelling everything on the same scale can leads to

  • running out of floating point precision
  • running into size scales where the 3D software rounds to
  • other weird stuff

So one needs to hack around this and model on different size scales
A continuous cut-less animation over many size scales then faces the problem of plumbing several sequences
of scenes shot at different scalings (different scalings that making different scales the same scale) mathchingly.
This is super annoying, tedious and productivity quenching.

Texturing and rendering choices

How to visualize a gem-gum factory at different size scales physically as accurate as possible,
but still visually appealing and helpful?

Rendering gemstones as transparent optical gemstones makes only sense for the macroscale.
See: Visible wavelength light at the nanoscale

Mimicking a real physical microscopes contrast mechanism

Tho show something physically more accurate the the contrast should go down and things become blurry
leaving only the overall homogenous monochomous color.
To still see things really well despite all that optical blurring
an other non optical contrast mechanism must be added.

Emulating electron microscopy is not such a good idea since

  • especially at the lowest scales everything becomes quite transparent (like in TEM images)
  • practically this would be hard on the sample – well gem-gum sytems might cope

A really good contrast mechanism is what (cold neutral helium) matter wave microscopy would give.
This is extrelmely surfece sensitive. Pretty much no penetration into the material that is being imaged at at all.
This technology currently (2021) is still far from atomic resolution, but eventually shoud be able to achive that someday.
And then it should be an exceptionally useful tool.

In effect choosing to emulate a matter wave microscopes images look would
roughly mean keeping a scanning microscope like look all the way down to the smallest scales.

Downsides of the contrast mechanism mimicking approach:

  • Can come over as bland and ugly.
  • If not colorizes hard but just grayscale then can be hard for the viewer to decypher what is seen.
  • Annoyingly the atomic precision of these sytems disallows for any artistic scratches and such.
    All the stuff that makes things pleasing to look at is out.

Atomistic texturing

As for when atomic details become visible several more challenges present themselves:

  • The (crappy) compression algorithms of our time like to make a mess out of huge high spacial frequency patterns – confetti effect – moire effect
  • Modelling all the atoms individually as highly resolved spheres is infeasible
  • "displacement maps" introduce the same load but only at the final rendering
  • bump-maps are cheap but one can see that it's fake

In case of diamond three textures for the different faces are needed

  • 111 (3fold symmetry)
  • 110 (2fold symmetry)
  • 100 (4fold symmetry)

And they somehow need to be slapped on the right faces.

True atomistic modelling

Approximating atoms by spheres

For the tooltips modelling individual atoms as highly resolved spheres is feasible.
Here even a completely fake pretty metallic and colorful rendering is ok (and useful) since it's obvious that its not mimicking a microscopes contrast mechanism.

Note that the sum of all orbitals of a free unbound atom (full shells) is actually perfectly spherically symmetrical and a equi-electron-density surface (the shape of the atom) is really a perfect sphere.
Ignoring here that free unbound atoms alone in a vacuum disperse quantum mechanically as a matter wave. But what interests us here is bound atoms in machine phase anyway.

Modelling the actual shapes of atoms

Modelling atoms more accurately than just by spheres requires modelling atomic orbitals.

Difficulties in determining the shape of atoms (in the sense of equi-electron-density surfaces near the Van der Waals radii) are:

  • electron-electron interactions (even mean field ones) cause deviations from the ideal analytic solutions for one-electron hydrogen like atom
  • more than one nucleus being present causing deviations from ideal analytic solutions for a pure 1/r potential

When it is just for visualization purposes then using linear combinations of crude initial guesses for the orbitals orbitals can suffice though.

Difficulties in rendering such shapes:

  • Many 3D modelling programs provide by default no or limited means for rendering surfaces defined by implicit functions

Repetition

Visualizing huge numbers of the very same geometry (or worse slight variations) is difficult.

Cases where this occurs:

  • exact repetitions of atomic patterns on surfaces – Related: 2D wallpaper groups (and 2D quasi-crystal symmetries)
  • almost exact repetitions in molecular mill assembly lines
  • almost exact repetitions in 2D layer of larger robotic assembly cells. E.g. naked eye visible 1mm sized assembly cells that may form the last main assembly layer

Options to model this with limited computing resources:

  • pre-rendering on a 2D texture for a certain perspective of a 3D geometry (possibly at different scales aka mipmapping) an plastering that texture all over the place
  • Rendering by raymarching rather than triangles – a fundamental switch

Time scaling and motion blur

Giving an intuitive sense for the absolute speeds and frequencies might be impossible.
Giving an intuitive sense for the relative speeds and frequencies might be possible at least in some cases cases but is still hard.

Ways to visualize relative speeds and frequency transitions include:

  • gradual scaling of the flow of time
  • motion blur – actually that only visualizes that the point of last visualizability has already been crossed – like a binary flag

Concrete cases:

(1) Showing a small crystolecular element and sweeping frequency from thermal motion illustrating to machine motion illustrating.

Scaling the flow of time from thermal-motion-visualizing scales down to machine-motions-visualizing scales in a way that is intuitively comprehensible is not easy because (for proposed operation speeds) that time-scaling-sweep goes over several orders of decimal magnitude with no reference "points" in-between. Illustrating the this large of a frequency gap probably can be done best in an auditorily way since human hearing goes over quite a freqency range of (20Hz to 20kHz => ~x1000Hz)

This (optionally) poses the additional (interesting) challenge of determining the spectrum of phonons present on diamond surfaces or diamondoid crystolecule surfaces such that a physically accurate sound of atoms can be created.

A visual illustration of a frequency sweep is a bit more limited than an audio sweep (0.3Hz to 30Hz => ~x100Hz rather than ~x1000Hz for audio) Once the sweep is no longer visually illustratable the sweep can no longer be followed. It is beyond rendering capabilities (that where made for human senses) and would be beyond human senses.

Worse: Without a proper motion blur there might be confusing stroboscopic effects. It is highly advisable (but not necessarily easy) to add motion blur. Otherwise viewers may fall prey of the trapdoor of the stroboscopic illusion in crystolecule animations. Note that this blurring mixes up with the already present quantum blurriness of electrons in atoms. Quantum and thermal blurriness is only clearly separable by viewers when the quantum blurriness is replaced with a hard shell visualization with hard surface modelling of atoms (equi electron density surface of atoms near the typical Van der Waals radius – or just crude sphere approximations) Of course there is some quantum blurriness of the nuclear core positions in the crystal lattice too. This goes into a whole nother can of worms.

(2) Racing down a molecular mill assembly line getting increasingly faster.
(TODO: Find out how long will molecular mill assembly lines need to be typically? What would be their aspect ratio?)
Speedline like radial motion blur to visualize speed gives an emotionally intense visual effect far too good to pass up from a movie director poimt of view.
. This effect can only give an intuitive feeling of large distance (in relative terms) though. Not an intuitive feeling for actual distance (in relative terms).

(3) Crossing speed transition points:
At a speed change point: Stop the camera motion and softly slowly sweep the time-scaling factor down a bit such that the output speed becomes as slow as the input speed was at the sweeps start.

Related

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