Difference between revisions of "Distorted visualization methods for convergent assembly"
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{{wikitodo| add image [http://i.imgur.com/GFGJU.jpg] -- license?}} | {{wikitodo| add image [http://i.imgur.com/GFGJU.jpg] -- license?}} | ||
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| + | == Displaying many scales and their relation simultaneously == | ||
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| + | 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(pow(x,2) + pow(y,2) + pow(z,2)) / log(base) | ||
== Related == | == Related == | ||
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* [[assembly levels]] | * [[assembly levels]] | ||
* [[nanofactory layers]] | * [[nanofactory layers]] | ||
| + | * [[Visualization methods for gemstone metamaterial factories]] | ||
| + | * [[Challenges in the visualization of gem-gum factories]] | ||
== External Links == | == External Links == | ||
Revision as of 08:26, 2 June 2021
To get a complete picture of the physical layout of all the assembly levels of the convergent assembly in a nanofactory (which might be organized in a stack of coplanar layers) and see all of this in one single image at one glance one needs to project space in a nonlinear way.
Normal perspective (a linear projection) is unsuitable since it compresses most details towards the horizon.
Instead a nonlinear polar logarithmic mapping is the best fit.
An additional difficulty is that a nanofactory as opposed to a map is inherently three dimensional so some cross cut has to be chosen. Whether that cross cut can be simply planar or not depends on the exact design choices taken in a concrete nanofactories design.
(wiki-TODO: add image [1] -- license?)
Contents
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(pow(x,2) + pow(y,2) + pow(z,2)) / log(base)
Related
- This visualisation method may also be useful to keep oriented in spaces other than physical space like very lare software systems.
- The software interface principle of progressive disclosure
- general software issues
- assembly levels
- nanofactory layers
- Visualization methods for gemstone metamaterial factories
- Challenges in the visualization of gem-gum factories
External Links
- Wikipedia on log polar mapping [2]
- Wikipedia on the Mercator projection which becomes log polar near both poles [3]
- An interactive online map spanning a wide range of scales: mercator extreme
The mercator projection cut off much closer to the poles whichs location can be freely chosen.
- python scripts to generate log-polar maps from pixelgraphics [4]
- "Detail-In-Context Visualization for Satellite Imagery" [5]
"Complex Logarithmic Views for Small Details in Large Contexts" [6]
by Joachim Boettinger et. al.
Department of Computer and Information Science, University of Konstanz, Germany - Video showing a manual multi-scale zoom device [7] the "zoom-scope"
- square grid mapped to show details on all scales equally [8]
- More large scale map examples [9]
Keywords
distortion lens view; log-polar map; complex logarithmic map, complex logarithmic view, anamorphic mirror, anamorphosis
![[1]](http://i.imgur.com/GFGJU.jpg){kind=link}