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[Octave-patch-tracker] [patch #9974] [octave forge](mapping) gc2sc scxsc

From: Philip Nienhuis
Subject: [Octave-patch-tracker] [patch #9974] [octave forge](mapping) gc2sc scxsc gcxsc
Date: Wed, 30 Sep 2020 17:43:32 -0400 (EDT)
User-agent: Mozilla/5.0 (Windows NT 6.1; rv:52.0) Gecko/20100101 Firefox/52.0

Follow-up Comment #7, patch #9974 (project octave):

Attached is my version so far, based on yours in comment #6.
I had a bit of trouble vectorizing the two stanzas, but I finally realized
that I tried it with three pair of circles all the time which led cross() to
take the wrong dimension. cross(), like dot() needs unambiguous indication of
which dimensions to work on. From then on it was not too hard.
I've also added a third output indicating the intersection status of each pair
of circles.

Comparing with Matlab, I find some consistent differences.

A perhaps small issue:
Experimenting to get two small circles with just one intersection point gives
for Octave:

>> [u, v, w] = scxsc (0, 0, 1, 0, 2, [1.0000000002340808, 1.0000000002340809]
## (where the first radius lead to disjoint circles, and the second leads to
one intersection point)

but Matlab needs:

>> [u, v] = scxsc ([0 0],[0 0], [1 1], [0 0], [2 2], [0.999998 .999999])
## ditto

Maybe Matlab seems to work with the "flat" circle radius (of the circle in the
plane that intersects the surface) where the Octave version seems to take the
radius over the surface of the sphere? Anyway it's just small differences.

A more profound issue is this:
Consider two circles with centers 90 degrees apart and then check with radii
of 44 and 46 degrees. Only the second should have intersection points.
Octave does:

>> [u, v] = scxsc ([0 0], [0 0], [45 45], [0 0], [90 90], [44  46])
u =
   NaN   NaN
   NaN   NaN

v =
   NaN   NaN
   NaN   NaN

and complains about coinciding circles (which they aren't, their axes are
Matlab does (correctly IMO):

>> [u, v] = scxsc ([0 0], [0 0], [45 45], [0 0], [90 90], [44  46])
u = 
        NaN       NaN
     7.5908   -7.5908
v =
    44.4912   44.4912

Your first and second scxsc versions and mine yield identical results, so I
suppose there's something wrong in the applied math somewhere.

(file #49897)

Additional Item Attachment:

File name: scxsc.m                        Size:8 KB


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