Given a diagonal line which is taller than it is wide, how does one spin an S-curve through it so it is composed of 32 equally-spaced vertexes?

Diagonal Line and Desired Curves

I'm trying to achieve the thick bright green curve without using bezier curves (as these are inaccurate when trying to get them to correspond to span curves in the mesh).

The closest I've managed to get with spins is this...

Undesired Curves with Spins

I've also tried with Beziers but their curves don't match up to the curve of the arch. The control points on each Bezier point are halfway up the height of the arch (0.425 units). I guess the bezier curve may line up with the arch if these control points were moved further up but the problem is I don't know how much by to do it accurately!

Unmatching Curves with Beziers I believe I might be using the wrong tool for the job, but the question is: what is the right tool?

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    $\begingroup$ Hello and welcome. Is that really Blender 2.49? Do you normally work with that color theme? My eyes hurt just from the screenshots. Kidding asside what do you mean "spin", are you trying to make a revolution surface? $\endgroup$ – Duarte Farrajota Ramos Apr 20 at 2:26
  • $\begingroup$ Yeah, it's 2.49; I tried a later version and the UI was all messed-up (less text, lots of meaningless icons and no landscape panels). I also couldn't figure out how to get rid of all the grey in the UI (as I prefer a more colourful high-contrast UI to work with). I hadn't heard of the term "revolution surface" but based on a quick Google it's not what I'm after. I'm actually just trying to create this curve as a profile for a wheel arch: blender.stackexchange.com/questions/137496/… $\endgroup$ – Sphynx Apr 20 at 2:34
  • $\begingroup$ Not sure I understand what you are trying to achieve. Is that some type of mathematical type of curve function? Are the end tangents supposed to be vertical? how did you achieve the first example? Bezier curve objects do sound exactly like the right tool; you can even adjust subdivisions after the fact non destructively. $\endgroup$ – Duarte Farrajota Ramos Apr 20 at 2:44
  • $\begingroup$ It was a Bezier curve I made in Paintshop Pro over the top of the screenshot. I had control points coming from the start and end points directly up and down to the middle line. My concern about using Beziers again is that the last time I did, I found myself with a model where none of the vertexes from the Beziers lined up with curves generated on the model. It might not be an issue for the profile of the arch tbh, but for the arch itself in the other question, it would be. I think what you said about the end tangents being vertical is exactly what I need. $\endgroup$ – Sphynx Apr 20 at 2:52
  • $\begingroup$ Alright, I've just tried joining a Bezier circle to a mesh circle with the same number of vertexes and it actually seemed to join up correctly! I don't know why though as I know if you put a NURBs circle over a Bezier circle, they don't line up correctly and I remember reading it was due to the inaccurate way Beziers are calculated. Is it good practice to use Beziers for modelling? $\endgroup$ – Sphynx Apr 20 at 3:11

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