TranslationSurface equivalent for 2D?

Questions
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1

Hello everyone. I’m looking for something like this: https://resources.wolframcloud.com/FunctionRepository/resources/TranslationSurface but for 2D.

Does it exist?

Thanks for any help.

2

Do you mean something like this?

c1[v_] := {v, v^2}
c2[u_] := {2 + Sin[u], u}
f[u_, v_] := c1[v] - c2[0] + c2[u]

p1 = ParametricPlot[{c1[t], c2[t]}, {t, 0, 2}]
p2 = ParametricPlot[{c1[t], f[t, .5], f[t, 1], f[t, 1.5]}, {t, 0, 2}]
3

The output is similar to what I’m looking for, but the 3D function is way more elegant, and I hope a similar solution exists for 2D too.

4

If you prefer to not think yourself why don’t you try to use the elegant 3D stuff, but confining your curves to, say, the x-y-plane?

5

Honestly, I thought about that solution, but I don’t know how could I then export the result as a 2D plot, if is it possible at all.

It’s not I prefer not to think, but I’m not yet strong enough with math, and:

  1. I’m exploring Mathematica just for its artistic potential (I’m interested in generative art)

  2. I also am new to the Wolfram language, so peeking here and there in the documentation finding features I like and think are useful to me, and asking questions

That’s why I’m asking such stupid/weird (from a Wolfram user perspective) questions.

Thanks for your help anyhow, I appreciated you took some time for me.

6

Ok. I have a stone-age-old version of Mathematica, and I am afraid the 3D procedure won’t run on my system. What is returned by the 3D function? If these were 3D vectors (look at the output ), you might get 2 D vectors by

vecs3D = Flatten[ Table[{i, j, 0}, {i, 1, 3}, {j, 1, 3}], 1]
Drop[#, -1] & /@ vecs3D
7

Yes, exactly what I was looking for!

Thanks a lot!