NURBS

[numerys]

Nurbs support would be great:

https://en.wikipedia.org/wiki/Non-uniform_rational_B-spline

[JustinSDK]

bspline_curve?

[BrettRD]

The 2d case of bspline_curve, like bezier_surface

[JustinSDK]

Encapsulate it into a function?

use <bspline_curve.scad>;
use <function_grapher.scad>;

ctrl_pts = [
    [[0, 0, 20],  [60, 0, -35],   [90, 0, 60],    [200, 0, 5]],
    [[0, 50, 30], [100, 60, -25], [120, 50, 120], [200, 50, 5]],
    [[0, 100, 0], [60, 120, 35],  [90, 100, 60],  [200, 100, 45]],
    [[0, 150, 0], [60, 150, -35], [90, 180, 60],  [200, 150, 45]]
];

thickness = 2;
t_step = 0.05;
degrees = 2;

function bspline_surface(t_step, points, degrees, r_knots, c_knots, r_weights, c_weights) =
    let(
		row_pts = [for(i = [0:len(ctrl_pts) - 1]) 
		    bspline_curve(t_step, degrees, ctrl_pts[i], r_knots, r_weights)
		]
	)
	[
	    for(j = [0:len(row_pts[0]) - 1]) 
		bspline_curve(t_step, degrees,
			[for(i = [0:len(row_pts) - 1]) row_pts[i][j]],
			c_knots, c_weights
		) 
	];
	


function_grapher(bspline_surface(t_step, ctrl_pts, degrees), thickness);

[numerys]

I see, is the "other way around" also possible? In Inkscape and other vector-graphic-software all points which the curve must go through are defined. The shape is changed flexible with tangential routes (angle and size). Maybe such a "Inkscape"-way is possible?

Such like here would be even better.

[BrettRD]

The splines you've pictured are separate bezier curves (not nurbs) which start and stop at common points and have matching tangents.
The first control point in a bezier marks the terminating location, the next control point sets the tangent.
You can make multiple bezier_surfaces continuous by making them share control mesh edges, and by making the control points nearest the edge co-linear between surfaces. Using that, you can stitch an arbitrarily complex smooth curve out of patches of bezier surfaces.

xnurbs takes a very different approach. it uses a constraint solver to build one huge nurbs surface satisfying a list of constraints (your edges), then takes chunks out of the resulting nurbs surface between the constraining edges. The major advantage to this approach is in their marketing material; it can make curves that are aesthetically consistent across the large patch by optimising a single parameter across the patch.

Something like Xnurbs can be built in OpenSCAD and it would use bspline_surface for final render.
It would need a numerical optimiser, a collection of error functions that can compare a surface to user-supplied constraints, and a Jacobian of the error-function in terms of the arguments to bspline_surface.
OpenSCAD 2021.01 included function-literals which should make solvers and optimisers much less painful to implement.

Don't wait around though, if you just want to join a sweeping curve to a few straight edges, a bezier_surface is a great tool for it, and bspline_surface has just eliminated the tedium of stitching spline control point tangents between patches.

[numerys]

Could something like that be build on top of bezier_surface?

[numerys]

Of course in a scripted Openscad way. Non-clicky.