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<p>Arnold,</p>
<p>Good to ear from you.<br>
<br>
Yes, <br>
XOR(R1,R2) = Difference (Union(R1, R2), Intersection(R1,R2))<br>
i.e, if we have neither XOR nor MINUS:<br>
XOR(R1,R2) = Intersection (Union(R1, R2),
Not(Intersection(R1,R2)))</p>
<p>But:</p>
<p>1. I wonder why having put the MINUS and not the XOR in the
standard.<br>
When dealing with boolean, the "DIFFERENCE" is the "XOR"<br>
and is more natural (from my biased perspective) than the "MINUS":<br>
For a point p, <br>
A.contains(p) != B.contains(p) <=> (A XOR B).contains(p)<br>
while<br>
A.contains(p) && !B.contains(P) <=> (A MINUS
B).contains(p)</p>
<p>and the MINUS is easier to build from other operations (A AND
NOT(B)),<br>
as stated in the STC-S document, than the XOR ((A OR B) AND NOT(A
AND B)).<br>
I would thus say that implementing the XOR is more important,
especially considering...<br>
</p>
<p>2. ...performances. Again, having a built-in XOR is more
important<br>
than having a MINUS in case we have to emulate the
not-in-the-standard one.<br>
</p>
<p>My personal choice would be to change DIFFERENCE for MINUS and to<br>
add XOR in the STC-S standard.<br>
<br>
You may had good reasons not to do that, please let me know.<br>
</p>
<p><br>
</p>
<p>fx<br>
</p>
<p><br>
</p>
<p><br>
</p>
<p><br>
</p>
<div class="moz-cite-prefix">Le 14/12/2023 à 19:40, Arnold Rots a
écrit :<br>
</div>
<blockquote type="cite"
cite="mid:CAJXToE8kWNyWQ9HP8_+G65-TB3MsCsVPYCfNFnVTn5GqZRMayA@mail.gmail.com">
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<div>FWIW</div>
<div> XOR(R1,R2) = Difference (Union(R1, R2),
Intersection(R1,R2))</div>
<div>
<div>
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<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">On Thu, Dec 14, 2023 at
1:10 PM Arnold Rots <<a href="mailto:arots@cfa.harvard.edu"
moz-do-not-send="true" class="moz-txt-link-freetext">arots@cfa.harvard.edu</a>>
wrote:<br>
</div>
<blockquote class="gmail_quote"
style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
<div dir="ltr">
<div>This discussion sent me down a rabbit hole. So, here is
some historical context.<br>
</div>
<div>I developed STC-S at the request of Jim Gray who was
interested in using it for his indexing scheme in MS
SQLServer.</div>
<div>Indexing spherical coordinates in SQL.<br>
</div>
<div>See: <a href="https://arxiv.org/abs/cs/0701171"
target="_blank" moz-do-not-send="true"
class="moz-txt-link-freetext">https://arxiv.org/abs/cs/0701171</a>
and references therein.</div>
<div><br>
</div>
<div>Tamas Budavari had a parser for SkyQuery that converted
STC-S to a series of half-spaces to describe regions.</div>
<div>But that, of course, worked with HTM, not HealPix.</div>
<div>However, the half-spaces scheme was very clever, since
it allowed describing polynomials not only using great
circles, but also parallels, using the sides, rather than
the vertices; and it discriminated in a natural way
between inside and outside.</div>
<div>It's described in an ADASS 2006 talk, attached.<br>
</div>
<div><br>
</div>
<div>Cheers,</div>
<div><br>
</div>
<div> - Arnold<br>
</div>
<div>
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<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">On Wed, Dec 13, 2023 at
6:49 AM F.-X. Pineau <<a
href="mailto:francois-xavier.pineau@astro.unistra.fr"
target="_blank" moz-do-not-send="true"
class="moz-txt-link-freetext">francois-xavier.pineau@astro.unistra.fr</a>>
wrote:<br>
</div>
<blockquote class="gmail_quote"
style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
<div> <font face="monospace">Dear all,</font><br>
<br>
<font face="monospace">Whatever the future of the STC-S
working draft is, having -- even partial --</font><br>
<font face="monospace">implementations may help the
debate.</font><br>
<br>
<font face="monospace">A few MOCPy users have asked for
a S-MOCs from STC-String feature.</font><br>
<font face="monospace">And it seems that S-MOCs are
considered to replace (at least in some places)</font><font
face="monospace"> STC.<br>
I am curious to know where exactly since MOCs and
STC-S are complementary:</font><br>
<font face="monospace">* STC-S is compact -- as far as
it does not contains unions/intersection of hundreds</font><br>
<font face="monospace"> of shapes -- and precise, but
not indexation oriented</font><br>
<font face="monospace">* MOCs are approximations, not
compact -- except at low resolutions --</font><br>
<font face="monospace"> but fast and indexation
oriented</font><br>
<font face="monospace">I believe that efficient STC-S
queries must rely (internally) on MOCs</font><br>
<font face="monospace">(or other similar mechanisms),
but should not be replaced by MOC queries</font><br>
<font face="monospace">(even if MOC queries are
interesting too and can help in STC-S queries).</font><br>
<br>
<br>
<font face="monospace">## STC-S Parser</font><br>
<br>
<font face="monospace">So, as previously announced, I
implemented a STC-S parser available on both</font><br>
<font face="monospace"> github and <a
href="http://crates.io" target="_blank"
moz-do-not-send="true">crates.io</a>:</font><br>
<font face="monospace">* <a
href="https://github.com/cds-astro/cds-stc-rust"
target="_blank" moz-do-not-send="true"
class="moz-txt-link-freetext">https://github.com/cds-astro/cds-stc-rust</a></font><br>
<font face="monospace">* <a
href="https://crates.io/crates/stc-s"
target="_blank" moz-do-not-send="true"
class="moz-txt-link-freetext">https://crates.io/crates/stc-s</a></font><br>
<font face="monospace">There is still room for
improvement and feeback/comments from people</font><br>
<font face="monospace">with STC experience would be much
appreciated.</font><br>
<br>
<br>
<font face="monospace">## STC-S to S-MOC</font><br>
<br>
<font face="monospace">This email to announced that I
now have also implemented a <b>first version of</b></font><b><br>
</b><font face="monospace"><b>the STC-S to S-MOC feature</b>
in MOCLibRust and in:</font><br>
<font face="monospace">* <b>moc-cli</b>: already
available in pypi and github release</font><br>
<font face="monospace"> + <a
href="https://pypi.org/project/moc-cli/"
target="_blank" moz-do-not-send="true"
class="moz-txt-link-freetext">https://pypi.org/project/moc-cli/</a></font><br>
<font face="monospace"> + <a
href="https://github.com/cds-astro/cds-moc-rust/tree/main/crates/cli"
target="_blank" moz-do-not-send="true"
class="moz-txt-link-freetext">https://github.com/cds-astro/cds-moc-rust/tree/main/crates/cli</a></font><br>
<font face="monospace"> + Example: echo "Circle ICRS
147.6 69.9 0.4" | moc from stcs 14 - fits
stcs.moc.fits --force-u64</font><br>
<font face="monospace">* moc-wasm: already available in
github release</font><br>
<font face="monospace"> + <a
href="https://github.com/cds-astro/cds-moc-rust/tree/main/crates/wasm"
target="_blank" moz-do-not-send="true"
class="moz-txt-link-freetext">https://github.com/cds-astro/cds-moc-rust/tree/main/crates/wasm</a></font><br>
<font face="monospace">* <b>MOCPy</b>: implemented in
the github source code, but not released yet</font><br>
<font face="monospace"> + <a
href="https://github.com/cds-astro/mocpy"
target="_blank" moz-do-not-send="true"
class="moz-txt-link-freetext">https://github.com/cds-astro/mocpy</a></font><br>
<font face="monospace">The feature has been put in place
but now have to be tested more thoroughly.</font><br>
<font face="monospace">So far the limitations are:</font><br>
<font face="monospace">* it <b>supports only
frame=ICRS, flavor=SPHER2 and units=deg</b></font><br>
<font face="monospace">* it wrongly considers the<b>
DIFFERENCE to be a SYMMETRIC DIFFERENCE</b> (XOR)</font><br>
<font face="monospace"> instead of a "MINUS".</font><br>
<font face="monospace"> Note that for a single polygon
whith a hole inside it, the result is the same,</font><br>
<font face="monospace"> except that:</font><br>
<font face="monospace">* it does not adopt the STC
definition of a polygon:</font><br>
<font face="monospace"> + it <b>supports
self-intersecting polygons</b></font><br>
<font face="monospace"> + the polygon interior is (kind
of) the part having the smallest area, i.e.</font><br>
<font face="monospace"> the order of the vertices
does not matter</font><br>
<font face="monospace">We do support nested
UNION/NOT/INTERSECTION/XOR operations.</font><br>
<font face="monospace">To do so, we rely on BMOCs
implemented in the CDS HEALPix Rust library. </font><br>
<font face="monospace">BMOCs are S-MOCs storing in each
cell a boolean flag telling if the cell is for </font><br>
<font face="monospace">sure fully inside the geometrical
shape or not.</font><br>
<font face="monospace">For example, the NOT operation
removes all cells having the boolean set to 'true'</font><br>
<font face="monospace">but preserves the cells having
the boolean set to 'false' (and add missing cells</font><br>
<font face="monospace">setting their flag to 'true').</font><br>
<font face="monospace">BMOCs have so far two drawback:</font><br>
<font face="monospace">* operations on BMOCs has not yet
been thoroughly tested</font><br>
<font face="monospace">* operations on BMOCs are -- at
least in the current implementation -- much slower </font><br>
<font face="monospace"> than operations on MOCs</font><br>
<font face="monospace">In the future, we may first
detect the operations in a STC-String to switch</font><br>
<font face="monospace">between MOCs (neither NOT or
DIFFERENCE operations) and BMOCs.</font><br>
<font face="monospace">Except that BMOCs have also one
big advantage: they can be spitted into 2 sub-MOCs</font><br>
<font face="monospace">* one fully inside the STC region
(no additional test needed, e.g. when retrieving
sources)</font><br>
<font face="monospace">* one "edges" MOC: additional
tests needed to determine if a source in this MOC</font><font
face="monospace"><br>
is in or out of the STC region.</font><br>
<font face="monospace"><br>
<b>If you have example of STC-String, especially with
operations (Alberto?), <br>
please send them to us so we can add them to our
tests.</b><br>
<br>
Even if STC-S is dropped in the future, it should not
be that complex to<br>
adapt to another standard like DALI "shape".<br>
(Although STC-S is complex, it is quite complete and
self-consistent since it contains<br>
information such as the frame: the two sides of a
medal).<br>
<br>
<br>
## About polygons:<br>
<br>
We support self-intersecting polygons.<br>
<br>
Although it is useless when describing footprints, I
do think it makes sense<br>
when you let a user create a polygon by clicking in
interfaces such as<br>
Aladin/Aladin Lite or TOPCAT.<br>
In addition, the existing algorithm to deal with
self-intersecting polygons is<br>
simple (at least in the plane, with some complications
on the sphere)<br>
and fast (see <a
href="https://wrfranklin.org/Research/Short_Notes/pnpoly.html"
target="_blank" moz-do-not-send="true"
class="moz-txt-link-freetext">https://wrfranklin.org/Research/Short_Notes/pnpoly.html</a>).<br>
<br>
The best option to define the interior/exterior of a
self-intersecting polygon<br>
may be to provide a control point, provided it is not
a vertex and is not part<br>
of an edge. (It's on of the several options that has
been implemented in the<br>
CDS Healpix Lib).<br>
The control point can be automatically computed from
the current standard for<br>
non-intersecting polygons:<br>
* for convex polygons: we can use the gravity center
(or its opposite) by testing it<br>
with the current convention (if the gravity center
is (0, 0, 0),<br>
remove recursively one vertex, starting from the
first one).<br>
* concave polygons: by testing the gravity center of 3
successive non-aligned vertices,<br>
iterating till one lies inside the polygon by the
current standard (also ensuring<br>
the point is not a vertex or on an edge).<br>
* self-intersecting: the control point would have to
be provided, i.e. after the last<br>
vertex (unless we all agree on a same algorithm,
using the NOT operation to define<br>
the complement polygon).<br>
<br>
Alberto:<br>
If I understand correctly, a polygon with a hole is
the intersection<br>
of a CCW polygon with a (smaller) CW polygon, right?<br>
Why not having used the difference between two CCW
polygons?<br>
Is it because the difference in STC-S is not a
symmetric difference and hence<br>
you cannot use the logical XOR operation in a database
expression?<br>
(<b>That may advocate to replace the DIFFERENCE by/ or
at least to add a<br>
SYMMETRIC DIFFERENCE in STC :)</b> ).<br>
<br>
<br>
fx<br>
<br>
<br>
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