STC-1.33 Erratum 1:

Author: DM WG

Date last changed: 2018-11-16

Date accepted:


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

Erratum Content

The formula in Section (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) *pi

αi are the polygon’s angles at the vertices. Reverse the sign for right-handed coordinates."


A = (RA,DEC)[0] = (90, 0)

B = (RA,DEC)[1] = (0, 0)

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

Impact Assessment


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