4 ms·
> strictly 2D (planar curve). A single curve segment is indeed planar, but it might be too strong to say strictly 2D? You can certainly make 3D quadratic curve
by dahart 3y ago
> strictly 2D (planar curve).
A single curve segment is indeed planar, but it might be too strong to say strictly 2D? You can certainly make 3D quadratic curves. I use cubic and quadratic Beziers mostly for fur and hair, and some people do mention to me their concerns about quadrics being planar, but I think it’s not an issue in practice at all. (And quadratics are simpler and have some big advantages over cubics.) When you piece together multiple quadric segments and match tangents properly, it’s a 3D spline and you can’t really even see the planarity, each segment is a different plane. 2 quadratic segments do a pretty good job of approximating 1 cubic segment.
I like thinking about B-splines more that individual segments, and for a B-spline, you can think about the difference between quadratic and cubic as more like a smoothing factor and little else.
- xeonmc 3y agowhat I meant is that any parabola, no matter how you orient it in 3D space, will always fit on a flat piece of paper, because only two vector directions are ever involved in its construction (the starting velocity and the acceleration direction). And a single quadratic bezier is simply a segment of a parabola.
- dahart 3y agoTotally, I understand and agree, I just wanted to rant for a minute about how that might not matter in practice, but obviously it depends on how you’re using the curves and what you need.