Polar Stroking: New Theory and Methods for Stroking Paths · HackerPapers discussions

Polar Stroking: New Theory and Methods for Stroking Paths — mentioned by user____name

Tue, 11 Nov 2025 00:24:21 GMT

Bezier curves can generate degenerate geometry when flattened and stroke geometry has to handle edge cases. See for instance the illustration on the last page of the Polar Stroking paper: https://arxiv.org/pdf/2007.00308 There are also things like interpretting (conflating) coverage as alpha for analytical antialiasing methods, which lead to visible hairline cracks.

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Polar Stroking: New Theory and Methods for Stroking Paths — mentioned by raphlinus

Mon, 09 Jan 2023 14:40:32 GMT

I would say the most likely reason is that 2D graphics is just plain hard. Jasper's classic essay[1] goes into more detail. That said, I'd really love to see more stuff along the lines of what you describe. I think Vello could render, for example, something that visually looks like Mini Metro or Mini Motorways. I also of course would be a massive fan of using Euler spirals - the only curve that's truly, really simpler is quadratic Béziers, and making those look good in your application would be hard. I'm about to do a lot of Euler spiral math on GPU as part of the stroke rework, which you may…

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Polar Stroking: New Theory and Methods for Stroking Paths — mentioned by polarstroking

Sun, 18 Sep 2022 22:32:02 GMT

https://arxiv.org/abs/2007.00308

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Polar Stroking: New Theory and Methods for Stroking Paths — mentioned by bsder

Wed, 10 Aug 2022 22:01:54 GMT

Mark Kilgard from NVIDIA has been beating this drum for a couple decades. It's not simple. His latest paper is about how to handle stroking of cubic splines: https://arxiv.org/abs/2007.00308 He gives it as a talk, but you have to sign up with NVIDIA: https://developer.nvidia.com/siggraph/2020/video/sig03-vid

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Polar Stroking: New Theory and Methods for Stroking Paths — mentioned by raphlinus

Tue, 18 May 2021 13:43:54 GMT

Also see Polar Stroking[1] which covers similar ground. [1]: https://arxiv.org/abs/2007.00308

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Polar Stroking: New Theory and Methods for Stroking Paths — mentioned by raphlinus

Sat, 20 Feb 2021 02:30:56 GMT

Tangentially, huh? So the underlying operation of finding a parallel "curve" is trivial when the curve is a line, as it's just another line. That doesn't mean the problems is simple, though. One challenge (which I didn't address in the post, nor do I have code yet) is dealing with corners, as there are the usual choices of round, miter, and bevel. Of these, only round represents a true Minkowski sum. The others are generally more commonly used. Btw, see "Polar Stroking" [1] for more details on this. I came very close to linking it. The second detail is the "trimming" as the parallel curve…

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