Oh Béziers are great and not going anywhere, and I’m not suggesting they should. It’s all about your specific goals. I think B-splines are misunderstood and underutilized, and your comment might be exemplifying that a little. ;) For one, Catmull-Rom is not a B-spline. For two, it’s easy to achieve local control of a B-spline wherever it’s needed (there are two separate ways to do this). For three, and most importantly - note that the goal of the article is to get a smooth join, and the technique in the article is to drop localized control (!) by imposing constraints on both sides of a join point. Using a Bézier for this is more complicated than using a B-spline, for no additional benefit that I can see. Also worth mentioning that uniform B-splines and Béziers are mathematically shape equivalent - it’s trivial to convert between them, so they provide identical levels of control, they’re just slightly different interfaces for the same shape.
Minor edit here to note, it just occurred to me that the curvature constraint affects the curve over a span of 7 control points, whereas editing a B-spline control point affects the curve over a span of 4 control points. B-splines are strictly more localized than Curvature Béziers…
One reason B-splines aren’t well known & used is because seemingly most/all online content launches into the math and discussion of knots. The uniform B-spline doesn’t need knots, and I wish more tutorials would start there rather than intimidating people with the math.
BTW yes you’re right about the ‘scalars’ (the beta parameters) in the G2 curvature matching equation. I haven’t tried this and I don’t know what they do. I was wondering if these might have a relationship to the ‘heuristic’ the Acko article derives? That was kind of my question.
Minor edit here to note, it just occurred to me that the curvature constraint affects the curve over a span of 7 control points, whereas editing a B-spline control point affects the curve over a span of 4 control points. B-splines are strictly more localized than Curvature Béziers…
One reason B-splines aren’t well known & used is because seemingly most/all online content launches into the math and discussion of knots. The uniform B-spline doesn’t need knots, and I wish more tutorials would start there rather than intimidating people with the math.
BTW yes you’re right about the ‘scalars’ (the beta parameters) in the G2 curvature matching equation. I haven’t tried this and I don’t know what they do. I was wondering if these might have a relationship to the ‘heuristic’ the Acko article derives? That was kind of my question.