[For the following function, we have to think hard whether going through
the tangential plane is what we'd like to do; it should go in with
a bunch of other astrometric functions]

\subsubsection{ivo\_apply\_pm(long, lat, pmlong, pmlat, epochDist)}

Returns a POINT for the position an object at \texttt{ra},
\texttt{dec} will be at after \texttt{epochDist} Julian years if its proper
motion is \texttt{prma}, \texttt{pmdec}.  Positions must be in degrees,
proper motions are expected in degrees/year. The proper motions must be
given in the tangential plane (i.e., the simple derivative has been
``divided by $cos(\delta)$'').

Note that this is an operation of spherical geometry, i.e., the function
would work as well with non-equatorial coordinates \emph{and} proper
motions.  However, you cannot, of course, mix galactic coordinates with
equatorial proper motions.

\begin{description}
\item[Parameters]

\begin{args}
	\arg long (REAL) -- longitude of the spherical position, in degrees.
	\arg lat (REAL) -- latitude of the spherical position, in degrees.
	\arg pmlong (REAL) -- proper motion in longitude in the
	tangential plane (i.e., the simple derivative has been divided by
	cos(lat)), in degrees per time unit.
	\arg pmlat (REAL) -- proper motion in latitude, in degrees per time
	unit.
	\arg epochDist (REAL) -- propagate the object this many time units.
\end{args}

\item[Return type] \texttt{POINT}

\item[Source] This document.
\end{description}

\begin{examples}
\example \verb|ivo_apply_pm(30, 15, 0, 0.1, 20)|
\becomes \verb|[30, 16.9991882802]|
\done as a 2-array with \xmlel{xtype}=\emph{point}; note that the
latitude here is not 17 because of the gnomonic projection.

\example \verb|ivo_apply_pm(30, 60, 0.1, 0, 20)|
\becomes \verb|[33.993520433, 59.93965025567]|
\done as a 2-array with \xmlel{xtype}=\emph{point}; note that the motion
along the longitude is a lot longer than time times proper motion
because of latitude effects.
\end{examples}

Note that this is a minimal, restricted form of ``applying proper
motions''.  A full, physically valid treatment requires an object's
distance and radial velocity to reconstruct the actual space motion.
Later versions of this specification may include extensions to this
function supporting this.

The five-parameter function discussed here should be implemented using
calculations in the tangential plane; the result of the function should
be $$G\big((\mu_l, \mu_b), (l, b)\big),$$ where $G(\vec d, \vec p)$ is the
gnomonic projection of the tangential plane coordinate $\vec d$ and the
tangent point $\vec b$, $l$ and $b$ are \verb|long| and \verb|lat|,
repectively, and $\mu_l$ and $\mu_b$ are \verb|pmlong| and \verb|pmlat|,
respectively.




[This function may be a good idea in a world with interval-valued
columns; as long as we don't have many of those, it's probably
dispensable]

\subsubsection{ivo\_interval\_has(value, interval)}

The function returns 1 if the interval \texttt{interval} contains
\texttt{val}, 0 otherwise. Both limits are always included in
\texttt{interval}.

\begin{description}
\item[Parameters]

\begin{args}
	\arg value (NUMERIC) -- a value to test for interval membership.
	\arg interval (INTERVAL) -- the interval to test against.  There are no
	guarantees that whatever is put here can be a part of a select list or
	that any other operation is possible on it (i.e., the implementation
	of the UDF does not mean that some sort of interval is available as a
	type in the underlying database engine).
\end{args}

\item[Return type] \texttt{INTEGER}

\item[Source] Originally proposed by the roadmap for STC discovery
\citep{note:regstc}; standardised in this document.
\end{description}