Hi All,

After looking into bug #424, I think I found the source of some oddly slow
blends with the new TP. In some cases, blending between two nearly-tangent
arcs creates a very short blend segment, and therefore a very low velocity
for that segment. I have a fix for this in my github repo, and also in the
official repo under the same name:

https://github.com/robEllenberg/linuxcnc-mirror/tree/feature/tangent-improvement-2.7

If anyone has a G code program that slows down in places with lots of arcs,
it would be worth trying it out with this branch to see if it helps.

Detailed explanation (using the sim_XYZ.ini config, 30 in/sec^2
acceleration, with TP debug flags on):

At line 6-7 in the  G code below, the resulting blend arc ends up having a
length of about 0.0007mm, which restricts the velocity to about 0.7 mm /
sec for a 1kHz servo update. The previous segment's maximum velocity is 20
mm/sec, so this is a big slowdown.

Gcode example:

N1 G90 G21
N2 g0 x0 y0 z0
N3 g1X54.834 Y-52.151 F120000
N4 X55.038 Y-59.286
N5 G3 X58.636 Y-62.782 I3.598 J.103
N6 X58.739 Y-62.781 I0. J3.599
N7 X62.104 Y-60.15 I-.103 J3.598
N8 G1 X62.158 Y-59.927 Z-3.31 F600.
N9 X62.199 Y-59.701 Z-3.324
N10 X62.294 Y-57.044 Z-3.495
N11 G2 X62.121 Y-56.199 I7.25 J1.918
N12 X62.069 Y-55.733 I7.423 J1.073
N13 G1 X62.023 Y-55.583
m30

The trick to fixing this is that the arc segments being blended are nearly
tangent. This means that if we slow down a bit at the intersection, the
acceleration spike from the slight "kink" in the trajectory will be small.
In the above example, if the speed at the intersection is less than about
14.9 mm/sec, the acceleration spike will be only 10% of the machine maximum
at the corner. The TP can do way better by simply slowing down a bit at the
corner, so it doesn't bother creating the blend arc for this case.

Before:* 0.7* mm / sec between line 6 and 7
After: *14.9* mm / sec

Fixing this issue won't massively shorten run times for most programs,
since this is an edge case, but it may get us more consistent cutting
speeds.

Best,
Rob
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