Fix gmt_get_smallcircle for equinox

[Esteban82]

This fixes #8936.

The code was written by Claude after some attemps. This is its explanation:

---

Problem

On the vernal and autumnal equinoxes (~March 20 and ~September 22), all
four solar terminator lines drawn by gmt solar -Tdcna overlap
completely instead of appearing as distinct concentric bands.

Root cause

In gmt_get_smallcircle (src/gmt_map.c), the generating vector X
is computed by finding a starting point xlat along the meridian
through the pole, colat degrees away:

xlat = (plat > 0.0) ? plat - colat : plat + colat;

All four terminator types use colat > 90° (90.833, 96, 102, 108).
On the equinoxes, plat ≈ −0.04° (solar declination near zero), so:

plat + colat = −0.04 + 90.833 = +90.79°  ← invalid latitude
plat + colat = −0.04 + 108    = +107.96° ← invalid latitude

gmt_geo_to_cart receives an out-of-range latitude and produces the
same degenerate vector X for all four terminators regardless of their
different colat values. All four small circles end up identical.

Confirmed with -Vd: the Added extra point coordinates were
byte-for-byte identical for -Td (90.833°) and -Ta (108°) before
the fix.

Fix

When xlat exceeds ±90°, wrap it around the pole by reflecting the
latitude and shifting the longitude by 180°. This places X at the
geometrically equivalent point on the correct side of the pole, at a
valid latitude, preserving the exact angular distance colat from P.

xlon = plon;
if (xlat > 90.0) {
    xlat = 180.0 - xlat;
    xlon += 180.0;
    if (xlon > 180.0) xlon -= 360.0;
} else if (xlat < -90.0) {
    xlat = -180.0 - xlat;
    xlon += 180.0;
    if (xlon > 180.0) xlon -= 360.0;
}

After the fix, -Vd shows four distinct Added extra point coordinates,
one per terminator, confirming each gets a unique generating vector:

Terminator	Radius	Extra point
-Td	90.833°	−180/−89.107 and 180/+89.193
-Tc	96°	−180/−83.941 and 180/+84.027
-Tn	102°	−180/−77.941 and 180/+78.027
-Ta	108°	−180/−71.941 and 180/+72.027

Files changed

• src/gmt_map.c — gmt_get_smallcircle: added pole-wrap guard and
  xlon variable; updated gmt_geo_to_cart call to use xlon instead
  of plon.

[joa-quim]

This line is not correctly indented.

[Esteban82]

I revised the code style.

[joa-quim]

We have test failures

[Esteban82]

Yes, I see that the pssolar_fill.sh and pssolar_fill2.sh are different.

pssolar_fill.sh:

Original:

New:

pssolar_fill2.sh:

Original:

New:

[joa-quim]

Can it be that originals were wrong?

[Esteban82]

Can it be that originals were wrong?

For pssolar_fill.sh, I think so. I am checking for pssolar_fill2.sh.

[joa-quim]

They are both wrong.

[Esteban82]

This is the image from timeanddate:

https://www.timeanddate.com/worldclock/sunearth.html?day=26&month=09&year=2017&hour=12&min=40&sec=0&n=&ntxt=&earth=0

The pssolar_fill2.sh plots the astronomical twilight so it is also wrong.

[mikez]

I checked the earliest version of the pssolar_fill{1,2}.ps files (now in DVC). Even there, 8 years ago, it seems the ps files are wrong. Very weird.

[mikez]

Also, the issue 1155 referred to in the comments and commit is this one from an earlier issue tracker:
https://web.archive.org/web/20200919155701/http://gmt.soest.hawaii.edu/issues/1155

[Esteban82]

Also, the issue 1155 referred to in the comments and commit is this one from an earlier issue tracker: https://web.archive.org/web/20200919155701/http://gmt.soest.hawaii.edu/issues/1155

Thanks for this link. I couldn't find the issue.

[Esteban82]

@joa-quim Do we only need to fix the two failing pssolar tests, or is there anything else failing in this PR?

[joa-quim]

Yes, the two failing PS should be replaced by the new ones obtained when this PR is merged.