Log polar mapping

This page is about a generalization of log-polar mapping to 3D space.
Specifically usable as one of the visualization methods for gemstone metamaterial factories and
as one of the distorted visualization methods for convergent assembly.

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

• Distorted visualization methods for convergent assembly
• Visualization methods for gemstone metamaterial factories
• Challenges in the visualization of gem-gum factories

External links

• https://en.wikipedia.org/wiki/Log-polar_coordinates
• 1996 – An Introduction to the Log-Polar Mapping – Helder J. AraujoJorge Miranda DiasJorge Miranda Dias – ResearchGate

Not log polar mapping but mercator projection to the extreme.
This should be locally similar to log polar mapping in that math in the limit becomes identical.
https://mrgris.com/projects/merc-extreme/