[bugfix 1.1.x] Fix G2/G3 so that slicer rounding error does not require impossible arc

[edwilliams16]

Requirements

Description

This is a back port of a fix to bugfix-2.0.x
It fixes the problem caused by slicer rounding error creating a G2/G3 request for a geometrically impossible arc whose diameter would be less than the distance to the destination point.

Benefits

Fixes #14745

Related Issues

[Roxy-3D]

Thank You Ed!

You aren't going to be able to claim you don't know C if you keep using ternary operators....

[edwilliams16]

@Roxy-3D
I try not to confuse it with the Fortran arithmetic (3-way) if:
IF (expression) negative,zero,positive from the days when goto's were popular.

[Roxy-3D]

Personally... I really dislike ternary operators. But they do have their place.

For the Marlin coding standards, what you have coded is good! But for me, personally, I would prefer looking at something more like:

                      h2 = ( r - 0.5f * d) * (r + 0.5f * d),        // factor to reduce rounding error         
                      if (h2 >= 0.0)
                            h = SQRT(h2);
                      else
                            h = 0.0;

[edwilliams16]

I'd vote for if then else if the true/false expressions were more complicated than they are here.

[Roxy-3D]

I'm not criticizing your code!!! It is fully compliant with the Marlin code base! I'm just expressing a personal preference. I find a multiple line if-then-else easier to read.

[edwilliams16]

I'm not taking it as criticism! As I said if the expressions were not so simple I'd agree with you.
It's a space/clarity trade-off.

[edwilliams16]

@Roxy-3D
I think one of the more obscure uses of the ternary operator occurs just a few lines earlier in the code:
const float e = clockwise ^ (r < 0) ? -1 : 1, // clockwise -1/1, counterclockwise 1/-1
This determines the sign (e) of the arc_offset vector, - if clockwise, + if counter-clockwise BUT with the convention that if the arc-radius r is negative, the direction of rotation is reversed. I guess some slicer must emit only G2's and flip the sign of r rather than using G3's.

clockwise ^ (r < 0) has the correct truth table to achieve this result, as would the equally obscure clockwise != (r < 0)
I was really tempted to change it to something like:

     e = clockwise ? -1 : 1;    // sign of arc
     e *= (r >= 0) ? 1 : -1;     // flip if r < 0

or even
e = (clockwise ? -1 : 1) * ((r >= 0) ? 1 : -1);

but I didn't think it appropriate to change merely on the grounds of clarity (to me). Who knows, the XOR trick could be a common idiom that I was unaware of.

[thinkyhead]

No worries @edwilliams16 — Whatever idiom works best for you. The important thing is that it changes the right bits in the right way at the right time, and the code is not intentionally obfuscatory.