STC-1.33 Erratum 1:Author: DM WG Date last changed: 2019-02-04 Date accepted:RationaleThis 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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"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." Erratum ContentNew Wording
Impact AssessmentSoftware using the wrong formula must be updatedExampleA = (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). 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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