4 ms·
>I just added a weirdly missing short section on plain rational beziers That's great! Thanks for writing and maintaining this document over the years! Coinci
by delhanty 7y ago
>I just added a weirdly missing short section on plain rational beziers
That's great! Thanks for writing and maintaining this document over the years!
Coincidentally, I was referencing the section on offsetting [0] just last week and read the following,
>There is a small class of polynomials where the square root is also a polynomial, but they're utterly useless to us: any polynomial with unweighted binomial coefficients has a square root that is also a polynomial. ...We can already create offset curves for points, we call them circles, and they have much simpler functions than Bézier curves.
and thought, something like: "That's correct because Bézier curves in the context of this document, SVG, HTML canvas and fonts means polynomial (i.e non-rational) Bézier curves."
But if you're now considering rational Bézier curves as in-scope for the document that changes things doesn't it ? E.g Circles represented as rational Bézier quadratics, and Pythagorean Hodographs [1].
[0] https://pomax.github.io/bezierinfo/#offsetting https://pomax.github.io/bezierinfo/#offsetting
[1] http://demonstrations.wolfram.com/G1HermiteInterpolationWithPythagoreanHodographCubicCurves/ http://demonstrations.wolfram.com/G1HermiteInterpolationWith...
- TheRealPomax 7y agoRational Beziers are no longer polynomials, though. If the basis value used for the division was a constant, then it would be, but instead it's a function of t.