I don't understand the author's reasons for dismissing the Euler spiral / clothoid squircle.
> the center of curvature of the circular portion moves as a function of the smoothing parameter ξ — ideally, it would remain fixed.
Why should it ideally remain fixed?
> More importantly, the power of the arc length s in the terms we’ve kept to produce the plots can be as high as nine. In Figma, continuous paths must be representable by cubic Bézier curves
Why didn't they use multiple segments instead of seemingly just truncating the approximation? They mentioned earlier in the article that "designers would rather deal with fewer Bézier curves at the expense of having a mathematically perfect curvature profile"; is that the only reason?
65•2mo ago
Oops, looks like Figma forgot to remove the alpha on their equations, because they're unreadable in dark mode.
creata•2mo ago
> the center of curvature of the circular portion moves as a function of the smoothing parameter ξ — ideally, it would remain fixed.
Why should it ideally remain fixed?
> More importantly, the power of the arc length s in the terms we’ve kept to produce the plots can be as high as nine. In Figma, continuous paths must be representable by cubic Bézier curves
Why didn't they use multiple segments instead of seemingly just truncating the approximation? They mentioned earlier in the article that "designers would rather deal with fewer Bézier curves at the expense of having a mathematically perfect curvature profile"; is that the only reason?