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A comment on Why are 2D vector graphics so much harder than 3D?. Parent comment

Re:Why are 2D vector graphics so much harder than 3D? by gugagore on Thursday May 09, 2019 @07:19PM (#19873475)
I understand and appreciate striking a balance between precision and a good story.

But I thought in this case, perhaps this was a big deal. I thought one of the reasons why 2D graphics and 3D graphics are so different is because of ... is it topology? ... For any arbitrarily complex curve, I think I can give you a 1D parameterization for it. At least to some desired accuracy.

What condition is required of a surface so that you can do the same, with a 2D parameterization?

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Re:Why are 2D vector graphics so much harder than 3D? by stevesimmons on Friday May 10, 2019 @02:32AM (#19875541)
> For any arbitrarily complex curve, I think I can give you a 1D parameterization for it.

If you haven't see it already, read this paper by Laurent Boue: "Real numbers, data science and chaos: How to fit any dataset with a single parameter"

https://arxiv.org/abs/1904.12320

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