31–40 of 43 posts
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So. Much. Work. And really well done. I loved the discussion on geometric continuity, starts at around 28 minutes in.
All very calm and cool until "it yeets off into fucking wherever" on C2 continuity. I LOLed at that.
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All very calm and cool until "it yeets off into fucking wherever" on C2 continuity. I LOLed at that.
Haha that one caught me way off guard, yeah. Hilarious, but went from a school-safe video to not in 0.1 seconds.
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Haha that one caught me way off guard, yeah. Hilarious, but went from a school-safe video to not in 0.1 seconds.
I think the criteria for "school safe" should be changed to accommodate something like this. My high-school kid taught me the word "yeet" and they are all familiar with the F-word enough to be cool with tasteful occasional use like this.
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I think the criteria for "school safe" should be changed to accommodate something like this. My high-school kid taught me the word "yeet" and they are all familiar with the F-word enough to be cool with tasteful occasional use like this.
Oh yeah I totally agree; this would make an excellent school video. The swearing might even make the kids more likely to watch. (Actcually my oldest already watches Freya.) My high schoolers throw yeet at me all the time, and they don’t care about swearing at all. Not only is it ubiquitous on TikTok and YouTube, they have a friend with Tourette’s that would make most gangsters blush. Sadly, the school district still…
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Great video. One fun basis for 3rd degree parametric polynomials that Freya skipped is a basis of values through which a polynomial can be interpolated. You can pick any 4 nodes in the interval, but I recommend [0, 0.25, 0.75, 1] for the least erratic behavior. Example: https://observablehq.com/@jrus/bez-cheb – try dragging the blue dots. Or for a higher degree polynomial, choose "Chebyshev nodes": equally spaced poi…
Ooh, the Chebyshev basis is neat. I hadn't seen exactly that before. It reminds me a lot of the "shape control" technique[1] which is also similar to a basis function approach but has a bit of linear solving. Essentially, you get one point (usually at t = 0.5), and also the direction but not magnitudes of the tangents at the endpoints (G1, not C1). This is one of the better-performing existing techniques for offset c…
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Oh yeah I totally agree; this would make an excellent school video. The swearing might even make the kids more likely to watch. (Actcually my oldest already watches Freya.) My high schoolers throw yeet at me all the time, and they don’t care about swearing at all. Not only is it ubiquitous on TikTok and YouTube, they have a friend with Tourette’s that would make most gangsters blush. Sadly, the school district still…
see this is where I can simply ask them to pay the educational license fee for the censored version of the video
Random tangent, but I’m glad you joined the discussion! Maybe you’re sick of curves by now, and I realize you said you left out many topics, but I was curious if you’d considered the quadratic B-spline or any other quadratic curves? I feel like we always talk about linear and cubic and hardly anyone considers quadratics. There are good reasons for that, but I like the order-2 B-spline for it’s continuity and because it’s halfway interpolating in the sense that it interpolates every midpoint of the linear skeleton. It’s slightly smoother than the Catmull-Rom (which is a bit lumpy IMO), and I think the continuity is equally good, right?
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Ooh, the Chebyshev basis is neat. I hadn't seen exactly that before. It reminds me a lot of the "shape control" technique[1] which is also similar to a basis function approach but has a bit of linear solving. Essentially, you get one point (usually at t = 0.5), and also the direction but not magnitudes of the tangents at the endpoints (G1, not C1). This is one of the better-performing existing techniques for offset c…
ah gosh, a collab would be cool but I think you overestimate my knowledge in this area! I have no formal education or even an eighth of the vocabulary let alone mathematical background to contribute much ;-; I've been reading your paper on the spiro splines and a lot of it goes way over my head! I'd have to research every step along the way
(I originally dug into Beziers because I was several levels deep into "Processing.js's text-in-a-box fitting is bad, how can I fix that". Queue learning how OpenType works, how TTF/CFF works, how Beziers work, writing up a code playground tutorial before we really had code playgrounds, and then going "...I can use this for more, can't I?"... And thanks to that I've talked to far smarter people with formal training in both the type design and maths communities. I still consider myself an amateur, but an amateur with expert acquaintances =)
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Ooh, the Chebyshev basis is neat. I hadn't seen exactly that before. It reminds me a lot of the "shape control" technique[1] which is also similar to a basis function approach but has a bit of linear solving. Essentially, you get one point (usually at t = 0.5), and also the direction but not magnitudes of the tangents at the endpoints (G1, not C1). This is one of the better-performing existing techniques for offset c…
ah gosh, a collab would be cool but I think you overestimate my knowledge in this area! I have no formal education or even an eighth of the vocabulary let alone mathematical background to contribute much ;-; I've been reading your paper on the spiro splines and a lot of it goes way over my head! I'd have to research every step along the way
While you’re here, it’s a bit of a tangent, but the introductory part of the video talking about lerp reminded me again that not enough people know about (not quite uniformly) interpolating along a circular arc using two lerps and one division:
For complex numbers a (start), m ("midpoint" on the circle), b (end), and t (parameter in [0,1], or in [-∞, ∞] to cover the whole circle),
circle_interp = (a, m, b, t) =>
lerp(a * (b - m), b * (m - a), t) / lerp(b - m, m - a, t)
Conveniently, this works for points in a straight line (a circle of infinite diameter) and we never need to explicitly construct the center or radius of the circle.
I was astonished to find this, and even more astonished to find it had never been clearly published anywhere (at least not that I could find after a lot of searching).
[This parametrization of the circle can equivalently be rewritten as a rational quadratic Bézier, but this formula is IMO a lot clearer to understand.]
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Ooh, the Chebyshev basis is neat. I hadn't seen exactly that before. It reminds me a lot of the "shape control" technique[1] which is also similar to a basis function approach but has a bit of linear solving. Essentially, you get one point (usually at t = 0.5), and also the direction but not magnitudes of the tangents at the endpoints (G1, not C1). This is one of the better-performing existing techniques for offset c…
ah gosh, a collab would be cool but I think you overestimate my knowledge in this area! I have no formal education or even an eighth of the vocabulary let alone mathematical background to contribute much ;-; I've been reading your paper on the spiro splines and a lot of it goes way over my head! I'd have to research every step along the way