Data decompression chain

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The "data decompression chain" is the sequence of expansion steps from

• very compact highest level abstract blueprints of technical systems to
• discrete and simple lowest level instances that are much larger in size.

3D modeling

Constructive solid geometry graph (CSG graph). Today (2017) often still at the top of the chain.

Programmatic high level 3D modelling representations with code can
considered to be a highly compressed data representation of the target product.

The principle rule of programming which is: "don't repeat yourself" does apply.

• Multiply occurring objects (including e.g. rigid body crystolecule parts) are specified only once plus the locations and orientations (poses) of their occurrences.
• Curves are specified in a not yet discretized (e.g. not yet triangulated) way. See: Non-destructive modelling
• Complex (and perhaps even dynamic) assemblies are also encoded such that they complexly unfold on code execution.
  Laying out gemstone based metamaterials in complex dynamically interdigitating/interlinking/interweaving ways.

Note: "Programmatic" does not necessarily mean purely textual and in: "good old classical text editors".
Structural editors might and (as to the believe of the author) eventually will take over
allowing for an optimal mixing of textual and graphical programmatic representation of target products in the "integrated deveuser interfaces".

The decompression chain in gem-gum factories (and 3D printers)

The list goes:

• from top high level small data footprint
• to bottom low level large data footprint

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• high language 1: functional, logical, connection to computer algebra system
• high language 2: imperative, functional
• Volume based modeling with "level set method" or even "signed distance fields"
  (organized in CSG graphs which reduce to the three operations: sign-flip, sum and maximum)
• Surface based modeling with parametric surfaces (organized in CSG graphs)
• quadric nets C¹ (rarely employed today 2017)
• triangle nets C⁰
• tool-paths
• Primitive signals: step-signals, rail-switch-states, clutch-states, ...

(TODO: add details to decompression chain points)

High level language

Batch processing style programmatic 3D modelling lends itself exceptionally nicely to
side effect free programmatic representation.
Side effect free means: Functions always give the same output when given the same explicit input.
There is no funny hidden implicit global variable passing business going on in the background.

Sticking to code that is by some means enforced to be free of side effects comes with great benefits like:

• mathematical substitutability
• irrelevance of order of code lines
• narrowing down errors predictably leading to the problem spot
  no horrid intractable errors that a excellent in refusing to be narrowed down
• ...

One side effect free system of today (2021) is OpenSCAD but
it lacks in many other regards (outlined on the linked page)
There are quite a few clones of OpenSCAD attempting to fix these other regards but
more often than not at the extremely high cost of abandoning the guaranteed lack of side effects.
In case of the case of embedded doman specific languages (EDSLs) this weakness is usually inherited from the the host language.
(Javascript, Python, your imperative side effect laden language of choice ...)

Another side effect free 3D modelling system of today (2021) is implicitCAD but
it lacks in many other regards (outlined on the linked page).
Perhaps even more so than OpenSCAD but in other areas.

All of today's (2021) graphical point and click 3D modelling systems seem hopelessly insufficient compared to
what would be desirable for modelling something as complex as a gemstone based on chip factory.
This is mostly because the visual-textual rift problem is still far (decades?) from being resolved yet.

Quadric nets

This is highly unusual but seems interesting (state 2021).
One could say that in some way quadric nets are an intermediary representation of 3D geometry lying between

• general arbitrary function representation and
• triangulated representation.

Piecewise defined quadric mesh surfaces can be made to be one time continuously differentiable (C¹).
See: Wikipedia Differentiability_classes)
(TODO: Find if pretty much all surfaces of practical interest van be "quadriculated" just as they can be "triangulated")

The second derivative of a function representation (in form of a scalar field) gives the Hesse matrix where

• it's eigenvectors give the principle curvatures and
• it's determinant giving the Gaussian curvature (smaller zero: saddle, equal zero: or valley/plane, bigger zero: or hill/through)

Side-note: Projections from 3D down to 2D form conic sections of same or lower degree.
These can be re-extrusion to 3D. It may be interesting to implement this functionality in programmatic 3D modelling tools.

It seems that calculating convex hulls is only possible for a few special cases.
This is different for triangle meshes where convex hulls are always possible.
Convex hulls can be quite useful in 3D modelling, but it seems they are only applicable quite far down the decompression chain.

Triangle nets

• There is an enormous mountain of theoretical work about them.
• Often it might be desirable to skip this step and go directly
  –– from some functional representation
  –– to toolpaths.
  Today's (2021) FDM/FFF 3D-printers pretty much all go through the intermediary representation of triangle-meshes.
• There are difficult since they offer a gazillion ways of bad geometries
  (degenerate triangles, more than two edges meeting, vertices on edges, mesh holes, flipped normals, ...)

Tool-paths

Related:

• Tracing trajectories of component in machine phase
• Sequence of zones
• Mechanosynthesis core

Primitive signals

The many places Where the control-subsystem finally comes together with the power-subsystem.
Signals are amplified to do the driving of motions but also possibly energy recuperation from the motions of the nano-robotics.
Related:

• Coumputation subsystem
• Energy subsystem – Drive subsystem of a gem-gum factory

(Compilation) Targets

Beside the actual physical product another desired product of the code is just a digital preview.
So there are several desired outputs for one and the same code.
Maybe useful for compiling the same code to different targets (as present in this context): Compiling to categories (Conal Elliott)

Possible desired outputs include but are not limited to:

• the actual physical target product object
• virtual simulation of the potential product (2D or some 3D format)
• approximation of output in form of utility fog?

3D modeling & functional programming

Modeling of static 3D models is purely declarative.

• example: OpenSCAD

...

Similar situations in today's computer architectures

• high level language ->
• compiler infrastructure (e.g. llvm) ->
• assembler language ->
• actual actions of the target data processing machine

Bootstrapping of the decompression chain

One of the concerns regarding the feasibility of advanced productive nanosystems is the worry that that all the necessary data cannot be fed to

• the mechanosynthesis cores and
• the crystolecule assembly robotics

The former are mostly hard coded and don't need much data by the way.

For example this size comparison in E. Drexlers TEDx talk (2015) 13:35 can (if taken to literally)
lead to the misjudgment that there is an fundamentally insurmountable data bottleneck.
Of course trying to feed yotabits per second over those few pins would be ridiculous and impossible, but that is not what is planned.
(wiki-TODO: move this topic to Data IO bottleneck)

We already know how to avoid such a bottleneck.
Albeit we program computers with our fingers delivering just a few bits per second
computers now perform petabit per second internally.

The goal is reachable by gradually building up a hierarchy of decompression steps.
The most low level most high volume data is generated internally and locally very near to where it's finally "consumed".

Related

• Control hierarchy
• mergement of GUI-IDE & code-IDE
• The reverse: while decompressing is a technique compressing is an art - (a vague analog to derivation and integration)
  See: the source of new axioms Warning! you are moving into more speculative areas.
• Why identical copying is unnecessary for foodsynthesis and Synthesis of food
  In the case of synthesis of food the vastly different decompression chain between biological systems and advanced diamondoid nanofactories leads to the situation that nanofactories cannot synthesize exact copies of food down to the placement of every atom. See Food structure irrelevancy gap for a viable alternative.
• constructive corecursion
• Data IO bottleneck
• Compiling to categories (Conal Elliott)

External Links

Wikipedia

• Solid_modeling, Computer_graphics_(computer_science)
• Constructive_solid_geometry
• Related to volume based modeling: Quadrics (in context of mathematical shapes) (in context of surface differential geometry)
• Related to volume based modeling: Level-set_method Signed_distance_function
• Avoidable in steps after volume based modeling: Triangulation_(geometry), Surface_triangulation

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• Boundary representation
• Function representation