stroke-linejoin="arcs"

Hey guys,

I am a computer graphics researcher and have been looking into the new
"arcs" stroke-linejoin proposal for SVG 2. Is the specification complete?
If so, I can imagine many developers will have trouble sorting out the
missing details. Take at look at 12.5.8 and figure 13 at

http://www.w3.org/TR/SVG2/painting.html#CurvatureCalculation

It seems to me that easiest way to specify the center of the circle is
relative to point P, and not relative to points P1 and P2. This is because
we are offsetting the osculating circles to the path at P (at each side).
The offset circle has the same center as the osculating circle. If the
normals of the path at P are N1 and N2 and the curvatures are k1 and k2,
the center is always at P + N1/k1 and P + N2/k2, regardless of the
stroke-width.

Once the center is fixed, we need the radius. Here, I believe the correct
formula is abs(1/k - 0.5 stroke-width). Look at figure 13. If you increase
the stroke width on and on, at some point P1 will cross the center of
Aoutside. You need the abs() for this case. It is the sign of the curvature
that tells whether we should add or subtract 0.5 stroke-width to the radius
of curvature. The abs() allows us to unify everything in a single case.

There also seems to be missing information on the arcs that make up the
join:

" If the two circles (or circle and line) intersect, the line join region
is defined by the lines that connect P with P1 and P2 and the arcs defined
by the circles (or arc and line) between the closest intersection point to P,
and P1 and P2. "

In the case where both curvatures are positive and both radii of curvature
are smaller than 0.5 stroke-width, the arcs that connect P1 to P4 and P4 to
P2 are CCW (and can easily span more than 180 degrees). In all other cases,
the arcs seem to be CW.

There is an additional interesting corner case. The documentation mentions
the cases where the points do not intersect and when both curvatures are
zero, in which case we should fall back to miterclip. However, when either
curvature is +/- infinite (or very large magnitude), it is better to revert
to round instead.

There seems to be a a typo in "For a line: the curvature is infinite." I
think you mean that the curvature is zero, right?

At any rate, this is just a heads up and a request for clarifications. The
more explicit the documentation is, the fewer confused people like me there
will be.

Kind regards,
Diego