New here, so let me know if I do something wrong!

I've been sitting here researching Bezier curves for hours now, and I cannot seem to find the answer to what I would think would be a simple question...

I want to create an s-shaped(ish) curve (i.e. one that doubles back on itself). Where exactly should I be putting the control points?? (And please explain why this is the case in your answer, if you would; I've seen a number of answers to questions on this and sister sites that just give steps to solve the problem without explaining why, and I do way better if I understand why something is the way it is. Thanks!)

Note: I'm not a font designer...or at least, that's not what I'm attempting to do now. That seems to matter, according to this question.

I keep seeing stuff about putting the points at the extrema of the curve...but I'm having some trouble finding it. I've been trying out the Bezier game, and I may be sort of getting the hang of it...but tbh, I'm not very good at it.

This answer (and the comments on it) says that

"Another good habit is to cut s shaped curves at the point where the curvature direction changes."

...which I guess makes sense to me? The comments on the above answer mention a different method:

"I tend to do curvature maximum minimum and Inflection point."

But then this page (sections 6. Keep anchor points at extrema – and handles straight and Edit: 7. Explicit Inflection Points) seems to be saying that the inflection point thing goes along with the part about extrema and keeping the handles straight. Is this the same method?

Specific example:

I'm trying to trace the logo for the TV show "Supernatural" (and yes, I could just do it with the Inkscape trace feature, but that'd defeat the purpose of learning, haha), and the flames around the edges are driving me nuts. I'm fairly certain I at least want points at the tips of each flame and also the places where the flames meet, like this

enter image description here

but then I get stuck. I could put points at extremas, which I think--though I'm not by any means certain!--would look a bit like this

enter image description here

But I'm not at all sure if this is right, because some of the stuff I've seen seems to say it should be the opposite, like this

enter image description here

And then the section of the page I linked above

But then this page (sections 6. Keep anchor points at extrema – and handles straight and Edit: > 7. Explicit Inflection Points) seems to be saying that the inflection point thing goes along with the > part about extrema and keeping the handles straight.

seems to be saying that I want both?? Maybe?? Like this

enter image description here

...but surely that can't be right, because I thought the idea was to have the smallest number of points possible...??

I'm very confused, so any help is much appreciated!!


Note 2: I'm working in GIMP currently, then exporting the path to Inkscape. Cannot for the life of me figure out how to translate the practice I've been getting in the Bezier game to Inkscape, as the Inkscape pen tool appears to work very differently than the one in the game... Feel free to help out with that, too, if you're able/willing :)

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    GIMP is absolutely the wrong tool here. – Scott Dec 19 '20 at 8:42

I wouldn't recommend you use GIMP for work like this. It's just not the right tool for the job. Use a vector image editor instead.

Inkscape's Bézier tool works very similar to the one in the Bézier game, but the functionality of the Shift, Alt, and Ctrl modifier keys is different. The game uses Adobe Illustrator's modifier keys.

  • Holding down Shift, creates a corner node and allows you to drag out a curve handle (this is Alt in the Bézier Game)
  • Holding down Ctrl, snaps line and handle angles to multiples of 15° (this is Shift in the Bézier game, and angle snapping is at multiples of 45°)

You only really need two nodes to form an S shape. If the S shape is more complex you can use more if you want. There are no rules. Do as you please. Obviously having fewer nodes is often more efficient, and will lead to smaller SVG files sizes, but sometimes you just need more nodes. Placing nodes at extremas can be a useful technique for creating nice curves, but it's not written in stone.

Example of a two node S-shaped curve.

enter image description here

  • Hmm...I wonder if somehow my Inkscape is wonky, then, because holding Shift seems to do absolutely nothing most of the time, and then occasionally I get a curve but with no handles that I can see... Also, in the Bezier game I'm pretty sure I was able to click-and-drag pull out handles on the first point I created, and that doesn't seem to happen in Inkscape either. I'm gonna see if there are any updates or anything, but if not, I'm not sure what might be the issue, or if there are free and decent alternatives to Inkscape? – Amy de l'ABC Dec 20 '20 at 4:08
  • (Can't figure out how to/if it's possible to edit previous comment, so adding a new one. Hope that's okay!) Update: Welp, apparently I'm dumb XD Not only was my Inkscape version WAAAAAY out of date, but I think I may have somehow ended up with the Spiro curve tool selected instead of the normal Bezier one. Still may take a bit of getting used to, but much better! Thanks for your help; I'll give it a proper try now :) – Amy de l'ABC Dec 20 '20 at 4:47
  • In Inkscape you can click and drag to pull out handles from the first node, without holding down shift, just as you can with any node. The difference holding down shift is it creates a corner node, from which you can pull out handles. Single clicks at a node also create a corner point. Having the spiro option enabled changes the behaviour of the tool entirely. The are no handles when using that option and Shift just creates corner nodes. – Billy Kerr Dec 20 '20 at 10:45
  • @Amydel'ABC Also note that the spiro option creates a Spiro Spline path effect, and although the underlying paths will have handles at nodes, these are ignored by the path effect. In essence, the effect produces the curves. – Billy Kerr Dec 20 '20 at 11:24
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    It's ok. You don't need to do @ to mention me in comments to an answer I posted. I can see them automatically. To be honest with you, although XD is quite nice, I still prefer Inkscape for drawing. Maybe just practice a bit more. It's worth the effort. – Billy Kerr Dec 20 '20 at 22:50

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