STC-1_33-Erratum-1 < IVOA

---+ STC-1.33 Erratum 1:

Author: DM WG

Date last changed: 2019-02-04

<span style="background-color: transparent;">Date accepted: 2019-04-16</span>
---++ Rationale

This erratum is to correct an issue related to POLYGON with different orientations <a target="_blank" href="http://wiki.ivoa.net/internal/IVOA/InterOpMayy2018DAL/ivoa_201805_micol_polygons.pdf">reported</a> at the IVOA interop in Victoria, BC: May 2018

<div title="Page 6">

cite (from <a href="http://www.ivoa.net/Documents/REC/DM/STC-20071030.pdf" title="STC1.33">STC-1.33</a>):

<em>"The summation is over determinants of matrices formed by the position vectors xi of successive vertices; xn+1 = x1. In spherical space (left-handed coordinates) the area is:</em><em><br />A = - SUM[ &alpha;(i) ] &ndash; (n-2) *pi</em><em>&alpha;i are the polygon&rsquo;s angles at the vertices. Reverse the sign for right-handed coordinates."</em>
</div>

---++ Erratum Content
<div title="Page 6">
---++++ Original Wording
   * 4.5.1.4 page 30 <br />A = - SUM[ &alpha;(i) ] &ndash; (n-2) *pi
</div>
---++++ New Wording
   * 4.5.1.4 page 30 <br />A = <span style="color: crimson;" class="WYSIWYG_COLOR">+</span> SUM[ &alpha;(i) ] &ndash; (n-2) *pi
---++ Impact Assessment

Software using the wrong formula must be updated
---++ Example

A = (RA,DEC)[0] = (90, 0)<br />B = (RA,DEC)[1] = (0, 0) <br />C = (RA,DEC)[2] = (0, 90) <br />The image below shows gaphically that triangle (CCW as seen from inside the sphere, but CW as seen from outside the sphere).

<img alt="" src="%ATTACHURL%/ABC.png" style="width: 300px;" />

The three angles of the polygon are all 90 deg, or pi/2 rad by construction. The area is indeed: +3 * pi/2 -pi = pi/2 (1/8 of the entire sky)

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This topic: IVOA > WebHome > IvoaDataModel > STC > STC-1_33-Errata > STC-1_33-Erratum-1
Topic revision: r7 - 2019-05-08 - MarkCresitelloDittmar