
Show HN: Visualizing Maps in R^3 - slushy-chivalry
https://topovis.iambeef.com
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heinrichhartman
This is nice. Is the code on GitHub?

Might make sense to use two coordinate systems for source and target?

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the8472
An orthographic camera might be appropriate, at least for that particular
demo.

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axelsvensson
Bug: y seems to be undefined or 0 when evaluating the z part of the mapping

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quickthrower2
Nice retro nightclub feel

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tjs8rj
Nitpicky, but calling something R^3 outside of an academic context when '3D'
suffices leaves me feeling oversold and underdelivered. This is 3-dimensional,
and no further info is added with R^3 while only making it slightly less
approachable.

R^3 contains R^2 and R, but I can't change the view to just 2D or 1D, so why
call it R^3?

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slushy-chivalry
tldr: the original idea came to me while studying homeomorphisms of various
topological spaces embedded in R^3, thus the name.

My original goal was to visualize homeomorphisms in R^3 and verify closed
forms for some of them. I'm used to calling it R^3 because there are many
3-dimensional spaces (C^3, {0,1}^3, etc) and there are many embeddings into
R^3 that are homeomorphic (e.g. D^2 is 'z==A and x^2 + y^2 < 1' for every A).
So the context is a bit academic. Visualizing a continuous deformation ended
up being pretty cool -- I ended up "inventing" a traversal in a metric space
that is very similar to BFS, but works for metric spaces, by repeatedly
selecting a subset of it fitting in a progressively bigger open ball. You
might know a concept pretty similar to this as filtration.

