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Threshold for line segments from exploding spline in arcs.

Posted: Mon Dec 18, 2023 10:48 am
by CVH
Splines are said to be exploded (XP) in tangentially connected arcs.
Where the curvature is not so pronounced XP may include line segments in the resulting polyline.

I agree that this is again related to short arcs and/or small radii but that statement won't hold here.
I can fool this a bit with a tighter approximation tolerance resulting in many more and shorter/flatter arc segments.
Even then I might get some line segments and thus corners as these are not tangentially connected.
Fewer line segments, that's true, but certainly a large number of short segments with negative consequences in a later stage.

The whole basic idea was a less tighter tolerance to avoid the so called 'small arcs'.

Example at hand (tolerance = 0.05):
  • Line segment length: 0.09269668
    Estimated arc segment:
    Radius: 2.29026748
    Sweep: 2.31915755°
    Bulge: 0.01011958
    Sagitta: 0.21833748 (9.5% of R)
  • Adjacent arc segment chord length: 0.04545307
    Radius: 2.04767242
    Sweep: 1.27184527°
    Bulge: 0.00554953
    Sagitta: 0.24418725 (11.9% of R)
In any aspect the adjacent arc segment is smaller and shorter than the segment that was returned as straight.
True, based on estimations the first listed segment was probably a fraction 'flatter'.

What is the determination method and threshold value for returning line segments instead of tangentially connected arcs?
Bottom line: Can it be forced to explode splines in polyline including nothing else then arc shapes?

Regards,
CVH