Show HN: Visualizing Maps in R^3

topovis.iambeef.com

45 points·slushy-chivalry··9 comments

This is nice. Is the code on GitHub?

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

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

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

Nice retro nightclub feel

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?

I disagree.

I would see "visualizing maps in 3D" and think "oh so like Google Earth?"

that is indeed nitpicky. why is calling something what it is a problem?

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.

It was completely clear to me, from the title alone, what "Maps in R^3" referred to. "Maps in 3D" doesn't describe the same thing.

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