It would be great to be able to compare this with Béziers of arbitrary degree. Some people get frustrated with degree 3 Béziers, but you can do great things with degree 5, 6, 7, or even higher - and they're C^infinity internally.
If you could add curvature combs to your demo it would help in evaluating what it can do. I can see from the curve itself that I can get pretty nice results, but occasionally I notice small wobbles that would be more obvious with a curvature plot.
Is it possible with this type of curve to vary the weights of the tangent vectors?
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.
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.
Actually manipulating higher-degree Bézier curves (or B splines, etc.) is a pain in the butt. In theory you can make any possible shape, but in practice it’s very difficult to get it to do what you want using the standard provided user interface.
> weights of the tangent vectors
Is this a synonym for curvature? In theory you could directly specify the curvature at a knot.
Or do you mean something more explicitly like weights in NURBS? Those could also conceivably be added, but IMO the hit to human intuition / intelligible UIs makes it not worth the trouble.
