International Virtual Observatory Alliance

Difference: STC-1_33-Erratum-1 (4 vs. 5)

Revision 52019-02-05 - LaurentMichel

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 STC-1.33 Erratum 1: 

Author: DM WG
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+  name="STC-1_33-Errata"
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+Date last changed: 2018-11-16
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+Date last changed: 2019-02-04
 Date accepted:
 Rationale
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+This erratum is to correct an error reported at the IVOA interop in Victoria, BC: May 2018
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+This erratum is to correct an issue related to POLYGON with different orientations reported at the IVOA interop in Victoria, BC: May 2018
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+ POLYGON with different orientations issue
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+cite:
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+cite (from STC-S):
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+The formula in Section 4.5.1.4 (pg 30: Region.Polygon) states
"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:
A = - SUM[ α(i) ] – (n-2) *piαi are the polygon’s angles at the vertices. Reverse the sign for right-handed coordinates."
but.
A = (RA,DEC)[0] = (90, 0)
B = (RA,DEC)[1] = (0, 0)
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+"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:
A = - SUM[ α(i) ] – (n-2) *piαi are the polygon’s angles at the vertices. Reverse the sign for right-handed coordinates."
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+ C = (RA,DEC)[2] = (0, 90) 

The three angles of the polygon are all 90 deg, or pi/2 rad by construction. A in the above case is: -3 * pi/2 –pi = -5/2 pi One expects an area of pi/2.
The correct formula is:
A = +SUM[ α(i) ] – (n-2) *pi
  Erratum Content 

 Original Wording 
 
 4.5.1.4 page 30 
A = - SUM[ α(i) ] – (n-2) *pi
 

 New Wording 
 
 4.5.1.4 page 30 
A = + SUM[ α(i) ] – (n-2) *pi
 
 Impact Assessment 

Software using the wrong formula must be updated
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+ Notes
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+ Example
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+ We need to confirm that the example has considered the 'left-handed' vs 'right-handed' qualifiers from the text.
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+A = (RA,DEC)[0] = (90, 0)
B = (RA,DEC)[1] = (0, 0) 
C = (RA,DEC)[2] = (0, 90) 
The image below shows gaphically that triangle (CCW as seen from inside the sphere, but CW as seen from outside the sphere).
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+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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