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<H2><A NAME="SECTION000466000000000000000"> </A><A NAME="xref_SLA_DTPV2C"> </A><A NAME="SLA_DTPV2C"> </A>
<BR>
SLA_DTPV2C - Plate centre from <IMG WIDTH="26" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
SRC="img90.gif"
ALT="$\xi,\eta$"> and <I>x</I>,<I>y</I>,<I>z</I>
</H2>
<DL>
<DT><STRONG>ACTION:</STRONG>
<DD>From the tangent plane coordinates of a star of known
direction cosines, determine the direction cosines
of the tangent point (double precision)
<P> <DT><STRONG>CALL:</STRONG>
<DD><TT>CALL sla_DTPV2C (XI, ETA, V, V01, V02, N)</TT>
<P> </DL>
<P> <DL>
<DT><STRONG>GIVEN:</STRONG>
<DD>
<BR>
<TABLE CELLPADDING=3>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>XI,ETA</EM></TD>
<TH ALIGN="LEFT"><B>D</B></TH>
<TD ALIGN="LEFT" NOWRAP>tangent plane coordinates of star (radians)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>V</EM></TD>
<TD ALIGN="LEFT"><B>D(3)</B></TD>
<TD ALIGN="LEFT" NOWRAP>direction cosines of star</TD>
</TR>
</TABLE></DL>
<P> <DL>
<DT><STRONG>RETURNED:</STRONG>
<DD>
<BR>
<TABLE CELLPADDING=3>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>V01</EM></TD>
<TH ALIGN="LEFT"><B>D(3)</B></TH>
<TD ALIGN="LEFT" NOWRAP>direction cosines of tangent point, solution 1</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>V01</EM></TD>
<TD ALIGN="LEFT"><B>D(3)</B></TD>
<TD ALIGN="LEFT" NOWRAP>direction cosines of tangent point, solution 2</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>N</EM></TD>
<TD ALIGN="LEFT"><B>I</B></TD>
<TD ALIGN="LEFT" NOWRAP>number of solutions:</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM></EM></TD>
<TD ALIGN="LEFT"><B></B></TD>
<TD ALIGN="LEFT" NOWRAP> 0 = no solutions returned (note 2)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM></EM></TD>
<TD ALIGN="LEFT"><B></B></TD>
<TD ALIGN="LEFT" NOWRAP> 1 = only the first solution is useful (note 3)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM></EM></TD>
<TD ALIGN="LEFT"><B></B></TD>
<TD ALIGN="LEFT" NOWRAP> 2 = there are two useful solutions (note 3)</TD>
</TR>
</TABLE></DL>
<P> <DL>
<DT><STRONG>NOTES:</STRONG>
<DD><DL COMPACT>
<DT>1.
<DD>The vector V must be of unit length or the result will be wrong.
<DT>2.
<DD>Cases where there is no solution can only arise near the poles.
For example, it is clearly impossible for a star at the pole
itself to have a non-zero XI value.
<DT>3.
<DD>Also near the poles, cases can arise where there are two useful
solutions. The argument N indicates whether the second of the
two solutions returned is useful.
N=1
indicates only one useful solution, the usual case; under these
circumstances, the second solution can be regarded as valid if
the vector V02 is interpreted as the ``over-the-pole'' case.
<DT>4.
<DD>The projection is called the <I>gnomonic</I> projection; the
Cartesian coordinates <IMG WIDTH="41" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img85.gif"
ALT="$[\,\xi,\eta\,]$"> are called
<I>standard coordinates.</I> The latter
are in units of the distance from the tangent plane to the projection
point, <I>i.e.</I> radians near the origin.
<DT>5.
<DD>This routine is the Cartesian equivalent of the routine sla_DTPS2C.
</DL></DL>
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<ADDRESS>
<I>SLALIB --- Positional Astronomy Library<BR>Starlink User Note 67<BR>P. T. Wallace<BR>12 October 1999<BR>E-mail:ptw@star.rl.ac.uk</I>
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