The first thing I wanted to know was the page for the curve itself. Specifically, what constitutes a uniform vs. non-uniform and rational vs. non-rational b-spline. In https://wiki.freecadweb.org/B-Splines#N ... _B-splines:
Now, I want to know whether this is in fact the correct form of non-uniform b-splines by some translation. AFAICT, a non-uniform b-spline only needs to have knots being unequally apart. By setting different weights to poles the spline becomes rational. So,As you can imagine, it can be useful to have B-splines whose Bézier parts have different path lengths. This can be achieved by weighting the different polynomials:
[w_k] is hereby the weight of the [k]-th control point. When the weights are not equal, the B-spline is called non-uniform.
- A b-spline with unequally spaced knots (including multiplicities) but with all poles having equal weights makes a non-uniform non-rational b-spline.
- A b-spline with equally spaced knots (including multiplicities) but with all poles having different weights makes a uniform rational b-spline.
I am trying to find resources that can shed some light on whether there is some equivalence between these. If there is not, this also has some implications in https://wiki.freecadweb.org/B-Splines#C ... the_Weight. For example, the following statement may be wrong:
To create a non-uniform B-spline the weights have to be non-uniform. To achieve that you can either change the radius constraint of the first control point circle
HI Uwe, tagging you since you last updated this page. Could you dig up the source for the formula?uwestoehr wrote: Hi