2 ms·

This really shouldn't need the (2013) suffix - it's constantly getting updated, and the most recent update was from only a few days ago. (it's probably about 50

This really shouldn't need the (2013) suffix - it's constantly getting updated, and the most recent update was from only a few days ago. (it's probably about 50 pages longer than it was back in 2013, if not more)

dahart 7y ago
I didn’t know it was under active development, but I use this reference a lot. Thank you! What are you adding these days? You know what’s on my wish list? A simplified uniform B-spline treatment specific to cubic & quadratic curves. Everywhere I look online, the B-spline explanations are crazy long and complicated with recursive summation diagrams and math about knots and non-uniformity and N-degree evaluation all at once. An open uniform cubic B-spline, though, is really simple, and that’s probably all I’d ever use in CG in practice. But it’s difficult to distill from what’s online right now. Converting a cubic B-spline to Bezier, for example, is a simple 4x4 matrix, and recently I needed it and went looking... it took a while to find.
- TheRealPomax 7y ago
  That does sound useful to talk about, could I convince you to hit up the issue tracker to for that as a section request? I just added a weirdly missing short section on plain rational beziers (not b-splines, just single beziers), and I'd like to still add a section on turning hand drawn paths into polybeziers.
  - 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 ago
      Rational 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.
  - dahart 7y ago
    Yes, I’ll request it via the issue tracker. Thanks!!

dahart 7y ago

I didn’t know it was under active development, but I use this reference a lot. Thank you! What are you adding these days? You know what’s on my wish list? A simplified uniform B-spline treatment specific to cubic & quadratic curves. Everywhere I look online, the B-spline explanations are crazy long and complicated with recursive summation diagrams and math about knots and non-uniformity and N-degree evaluation all at once. An open uniform cubic B-spline, though, is really simple, and that’s probably all I’d ever use in CG in practice. But it’s difficult to distill from what’s online right now. Converting a cubic B-spline to Bezier, for example, is a simple 4x4 matrix, and recently I needed it and went looking... it took a while to find.

TheRealPomax 7y ago
That does sound useful to talk about, could I convince you to hit up the issue tracker to for that as a section request? I just added a weirdly missing short section on plain rational beziers (not b-splines, just single beziers), and I'd like to still add a section on turning hand drawn paths into polybeziers.
- 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 ago
    Rational 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.
- dahart 7y ago
  Yes, I’ll request it via the issue tracker. Thanks!!