Distorted visualization methods for convergent assembly - Revision history

Apm: Category:Surprising facts

2026-03-29T20:39:06Z

← Older revision		Revision as of 22:39, 29 March 2026
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	[[Category:Far term target]]		[[Category:Far term target]]
			[[Category:Surprising facts]]

Apm: Category:Far term target

2026-03-29T18:12:09Z

Category:Far term target

← Older revision		Revision as of 20:12, 29 March 2026
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	* [[Visualizations of gemstone metamaterial factories]]		* [[Visualizations of gemstone metamaterial factories]]
	* [[Log polar mapping]]		* [[Log polar mapping]]

			[[Category:Far term target]]

Apm: whichs => whose

2024-09-27T15:45:37Z

whichs => whose

← Older revision		Revision as of 17:45, 27 September 2024
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	* Wikipedia on the Mercator projection which becomes log polar near both poles: [https://en.wikipedia.org/wiki/Mercator_projection Mercator projection]		* Wikipedia on the Mercator projection which becomes log polar near both poles: [https://en.wikipedia.org/wiki/Mercator_projection Mercator projection]
	----		----
	* An interactive online map spanning a wide range of scales: [http://mrgris.com/projects/merc-extreme/ '''mercator extreme'''] <br> The mercator projection cut off much closer to the poles ~~whichs~~ location can be freely chosen.		* An interactive online map spanning a wide range of scales: [http://mrgris.com/projects/merc-extreme/ '''mercator extreme'''] <br> The mercator projection cut off much closer to the poles whose location can be freely chosen.
	----		----
	* python scripts to generate log-polar maps from pixelgraphics [https://github.com/dmishin/log-zoom]		* python scripts to generate log-polar maps from pixelgraphics [https://github.com/dmishin/log-zoom]

Apm: /* Related */ == Hyperbolic geometry and Escher disks ==

2024-02-06T11:09:29Z

Related: == Hyperbolic geometry and Escher disks ==

@@ Line 30: / Line 30: @@
 * Showing only what is needed at anyone time. Related: The software interface principle of "[[progressive disclosure]]".
 * Drifting off-topic: [[General software issues]]
 == External Links ==

Apm: Added second image showing two assembly levels

2024-02-06T10:27:46Z

Added second image showing two assembly levels

← Older revision		Revision as of 12:27, 6 February 2024
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	[[File:LogPolarMapping3DwithMolecularMills.jpg\|480px\|thumb\|right\|Here mapped is both a c coordinate grid and molecular mill rotors analog to the ones seen in: "Productive Nanosystems from Molecules to Superproducts". Note that in non-transformed coordinates the grey wall sits on xy-plane partly above partly below. Thus it gets curls both ways in the magnifying log polar coordinates. The wide bottom is a small cutout around (0,0,0) that's necessary as nearing zero everything gets exponentially magnified.]]		[[File:LogPolarMapping3DwithMolecularMills.jpg\|480px\|thumb\|right\|Here mapped is both a c coordinate grid and molecular mill rotors analog to the ones seen in: "Productive Nanosystems from Molecules to Superproducts". Note that in non-transformed coordinates the grey wall sits on xy-plane partly above partly below. Thus it gets curls both ways in the magnifying log polar coordinates. The wide bottom is a small cutout around (0,0,0) that's necessary as nearing zero everything gets exponentially magnified.]]

			[[File:LogPolarMapping3DacrossTwoAssemblyLayers.png\|200px\|thumb\|right\|Generalized log polar mapping across two assembly layers. This should be extendable to more. Big caveat here is that assembly layers need to be roughly same sub-layer number which is not at all the case for the lowermost assembly layers. Hard coded assembly lines makes for very many sub-layers.]]

	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 [[nanofactory layers\|layers]]) and see all of this in one single image at one glance one needs to project space in a nonlinear way. <br>		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 [[nanofactory layers\|layers]]) and see all of this in one single image at one glance one needs to project space in a nonlinear way. <br>

Apm: added image

2024-02-06T10:05:12Z

added image

← Older revision		Revision as of 12:05, 6 February 2024
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	~~{{stub}}~~		[[File:LogPolarMapping3DwithMolecularMills.jpg\|480px\|thumb\|right\|Here mapped is both a c coordinate grid and molecular mill rotors analog to the ones seen in: "Productive Nanosystems from Molecules to Superproducts". Note that in non-transformed coordinates the grey wall sits on xy-plane partly above partly below. Thus it gets curls both ways in the magnifying log polar coordinates. The wide bottom is a small cutout around (0,0,0) that's necessary as nearing zero everything gets exponentially magnified.]]

	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 [[nanofactory layers\|layers]]) and see all of this in one single image at one glance one needs to project space in a nonlinear way. <br>		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 [[nanofactory layers\|layers]]) and see all of this in one single image at one glance one needs to project space in a nonlinear way. <br>
	Normal perspective (a linear projection) is unsuitable since it compresses most details towards the horizon.		Normal perspective (a linear projection) is unsuitable since it compresses most details towards the horizon.

Apm: /* Displaying many scales and their relation simultaneously */ added missing sqrt

2024-02-06T09:01:51Z

Displaying many scales and their relation simultaneously: added missing sqrt

← Older revision		Revision as of 11:01, 6 February 2024
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	* x'(x,y,z) = pi/2 - atan2( z, sqrt(pow(x,2) + pow(y,2)) ) * cos(atan2(y,x)))		* 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)))		* 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)		* z'(x,y,z) = log( sqrt(pow(x,2) + pow(y,2) + pow(z,2)) ) / log(base)

	== Related ==		== Related ==

Apm: /* Related / Log polar mapping

2023-07-03T06:39:56Z

Related: * Log polar mapping

← Older revision		Revision as of 08:39, 3 July 2023
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	* [[Visualization methods for gemstone metamaterial factories]]		* [[Visualization methods for gemstone metamaterial factories]]
	* [[Visualizations of gemstone metamaterial factories]]		* [[Visualizations of gemstone metamaterial factories]]
			* [[Log polar mapping]]

Apm at 18:03, 27 June 2023

2023-06-27T18:03:34Z

← Older revision		Revision as of 20:03, 27 June 2023
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	== External Links ==		== External Links ==

	* Wikipedia on log polar mapping [https://en.wikipedia.org/wiki/Log-polar_coordinates]		* Wikipedia on log polar mapping: [https://en.wikipedia.org/wiki/Log-polar_coordinates Log-polar coordinates]
	* Wikipedia on the Mercator projection which becomes log polar near both poles [https://en.wikipedia.org/wiki/Mercator_projection]		* Wikipedia on the Mercator projection which becomes log polar near both poles: [https://en.wikipedia.org/wiki/Mercator_projection Mercator projection]
	----		----
	* An interactive online map spanning a wide range of scales: [http://mrgris.com/projects/merc-extreme/ '''mercator extreme'''] <br> The mercator projection cut off much closer to the poles whichs location can be freely chosen.		* An interactive online map spanning a wide range of scales: [http://mrgris.com/projects/merc-extreme/ '''mercator extreme'''] <br> The mercator projection cut off much closer to the poles whichs location can be freely chosen.

Apm: /* Displaying many scales and their relation simultaneously */

2021-11-21T21:03:09Z

Displaying many scales and their relation simultaneously

← Older revision		Revision as of 23:03, 21 November 2021
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	== Displaying many scales and their relation simultaneously ==		== Displaying many scales and their relation simultaneously ==

	This can be done by generalizing log polar mapping to 3D like so:		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)))		* 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)))		* y'(x,y,z) = pi/2 - atan2( z, sqrt(pow(x,2) + pow(y,2)) ) * sin(atan2(y,x)))

← Older revision		Revision as of 12:27, 6 February 2024
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	[[File:LogPolarMapping3DwithMolecularMills.jpg\|480px\|thumb\|right\|Here mapped is both a c coordinate grid and molecular mill rotors analog to the ones seen in: "Productive Nanosystems from Molecules to Superproducts". Note that in non-transformed coordinates the grey wall sits on xy-plane partly above partly below. Thus it gets curls both ways in the magnifying log polar coordinates. The wide bottom is a small cutout around (0,0,0) that's necessary as nearing zero everything gets exponentially magnified.]]		[[File:LogPolarMapping3DwithMolecularMills.jpg\|480px\|thumb\|right\|Here mapped is both a c coordinate grid and molecular mill rotors analog to the ones seen in: "Productive Nanosystems from Molecules to Superproducts". Note that in non-transformed coordinates the grey wall sits on xy-plane partly above partly below. Thus it gets curls both ways in the magnifying log polar coordinates. The wide bottom is a small cutout around (0,0,0) that's necessary as nearing zero everything gets exponentially magnified.]]

			[[File:LogPolarMapping3DacrossTwoAssemblyLayers.png\|200px\|thumb\|right\|Generalized log polar mapping across two assembly layers. This should be extendable to more. Big caveat here is that assembly layers need to be roughly same sub-layer number which is not at all the case for the lowermost assembly layers. Hard coded assembly lines makes for very many sub-layers.]]

	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 [[nanofactory layers\|layers]]) and see all of this in one single image at one glance one needs to project space in a nonlinear way. <br>		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 [[nanofactory layers\|layers]]) and see all of this in one single image at one glance one needs to project space in a nonlinear way. <br>