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by raphlinus·7y ago·view on hn ↗
I'll add curvature combs in a future revision. I'll also point out that you can see a curvature plot of the underlying 2-parameter curve family by playing with beztoy.html in the linked github repo, which is one of the main ways I evaluated this.

Higher degree Béziers illustrate the "curse of too many parameters." Yes, they're very expressive, and yes you can have very high degrees of continuity, but it's also easy to make very wiggly or lumpy curves. I don't know of anyone who uses them, certainly not for font design.

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Class-A automotive surfacing (using Alias, ICEM, Catia, NX) is all done with higher degree Béziers. I use them all the time in SolidWorks for consumer and medical product design engineering.

It’s certainly tricky to figure out how to manage Béziers, but with the right tools and some knowledge of the math, you can do amazing things. Using the sketcher constraint tools in the SolidWorks it’s possible to join higher degree Béziers with G3 tangency (or even higher). I also build approximate offset curves of the same degree using a modified version of Tiller and Hansen’s method (I keep the control polygon legs parallel, but I add constraints to control the offset distance of the curve at n-2 places along the curve).

If I was doing font design, I’d love to have higher degree Béziers. Being able to make a sans-serif ‘S’ with single span curves would be great. Or lining up 3 control points on either end of the top of a lower case ‘n’ with vertical straight lines to have it be G3 would be nice.