STC-1_33-Erratum-1 < IVOA

---+ STC-1.33 Erratum 1:

Author: DM WG

Date last changed: 2018-11-16

<span style="background-color: transparent;">Date accepted:</span>
---++ Rationale

This erratum is to correct an error reported at the IVOA interop in Victoria, BC: May 2018

   * <a target="_blank" href="http://wiki.ivoa.net/internal/IVOA/InterOpMayy2018DAL/ivoa_201805_micol_polygons.pdf">POLYGON with different orientations issue</a>
---++ Erratum Content
<div title="Page 6">

The formula in Section 4.5.1.4 (pg 30: Region.Polygon) states:
<div title="Page 30">

"The summation is over determinants of matrices formed by the position vectors x<em>i</em> of successive vertices; x<em>n+1</em> = x<em>1</em>. In spherical space (left-handed coordinates) the area is:

<span style="background-color: transparent;">A = - SUM[ &alpha;(i) ] &ndash; (n-2) *pi</span>

</div> <div title="Page 30">

&alpha;<em>i</em> are the polygon&rsquo;s angles at the vertices. Reverse the sign for right-handed <span style="background-color: transparent;">coordinates."</span>

</div>

<span style="background-color: transparent;">but..</span>

<br /> A = (RA,DEC)[0] = (90, 0)

<span style="background-color: transparent;">B = (RA,DEC)[1] = (0, 0)</span>

<span style="background-color: transparent;"> </span><span style="background-color: transparent;">C = (RA,DEC)[2] = (0, 90)</span>

The three angles of the polygon are all 90 deg, or pi/2 rad by construction. <span style="background-color: transparent;">A in the above case is: -3 * pi/2 &ndash;pi = -5/2 pi</span>

<span style="background-color: transparent;">One expects an area of pi/2.</span>

The correct formula is:

A = <strong>+</strong>SUM[ &alpha;(i) ] &ndash; (n-2) *pi

</div>

---++ Impact Assessment
---++ Notes

   * We need to confirm that the example has considered the 'left-handed' vs 'right-handed' qualifiers from the text.
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Topic revision: r2 - 2018-11-18 - MarkCresitelloDittmar