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+<H2><A NAME="SECTION0004173000000000000000">&#160;</A><A NAME="xref_SLA_TPV2C">&#160;</A><A NAME="SLA_TPV2C">&#160;</A>
+<BR>
+SLA_TPV2C - 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 (single precision)
+<P>    <DT><STRONG>CALL:</STRONG>
+<DD><TT>CALL sla_TPV2C (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>R</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>R(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>R(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>R(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_TPS2C.
+ </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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