How to control points of a B-spline breaking it in multi-splines?

[easyw-fc]

Hi,
referring to this thread [new feature] Bspline knots
I learned that

It is always possible to increase the degree of a BSpline curve, while keeping its exact shape.
The algorithm will ( usually ? always ? I'm not sure ) add 1 control point for each degree increase step.
On the other hand, in the general case, there is no way to decrease the degree of the curve AND keep the original shape.

So what I would need in my user case is to break a part a Bspline into sub-splines all of the same degree (in my need 3), but with always the same number of control points (in my need 4 .
This is because I noticed that KiCAD, when importing a DXF file with a complex Bspline, always breaks it in sub-splines, all with degree = 3 and 4 control points.
I'm attaching a Bspline imported from a dxf file in FC and the counter part imported by KiCAD and then re-exported broken in sub-splines.
The question is:
Is it possible to break the first single spline sketch into multi-splines sketch within the degree=3 and with 4 control points by using a python script?

I'm attaching the FC file with the two Sketches and the images of the differences.

6knots-bspline.FCStd

(6.85 KiB) Downloaded 20 times

spline-comparison.png (319.77 KiB) Viewed 1121 times

[Chris_G]

Here is an example :

Code: Select all

import FreeCAD
from FreeCAD import Vector
import Part

# Create and display an example BSpline Curve

poles0 = [Vector (-0.028185, 0.0, 0.0), Vector (1.775631, 5.242338, 0.0), Vector (11.104738, 6.454277, 0.0), Vector (16.065231, 0.338215, 0.0), Vector (10.428308, -3.917662, 0.0), Vector (7.356185, -4.509538, 0.0)]
weights0 = [1.0, 1.0, 1.0, 1.0, 1.0, 1.0]
knots0 = [0.0, 0.3333333333333333, 0.6666666666666666, 1.0]
mults0 = [4, 1, 1, 4]
periodic0 = False
degree0 = 3
rational0 = False
bs = Part.BSplineCurve()
bs.buildFromPolesMultsKnots(poles0, mults0, knots0, periodic0, degree0, weights0, rational0)
obj = FreeCAD.ActiveDocument.addObject("Part::Spline","BSplineCurve")
obj.Shape = bs.toShape()
print("Input curve : %s (degree : %d / nb poles : %d)"%(bs, bs.Degree, bs.NbPoles))

# Set degree
if bs.Degree < 3:
    bs.increaseDegree(3)
elif bs.Degree > 3:
    # degree too high. We need to approximate the curve
    bs = bs.approximateBSpline(0.001,999,3) # (tolerance, maxSegments, maxDegree)

# Generate to a list of bezier curves
bezier_list = bs.toBezier()

# Check the result
for bc in bezier_list:
    print("%s (degree : %d / nb poles : %d)"%(bc, bc.Degree, bc.NbPoles))
    Part.show(bc.toShape())

[chrisb]

Could this be an approach to points and tangents on a B-spline or is the approximation not exact enough?

[easyw-fc]

Here is an example :
...

Hi @Chris,
thanks a lot as always!
Your code fulfills perfectly my user case.
Maurice

[Chris_G]

Could this be an approach to points and tangents on a B-spline or is the approximation not exact enough?

I don't know much about the sketcher internals.
But I don't think this is an approximation problem (you can choose the approx tolerance).