STC-1.33 Erratum 1:Author: DM WG Date last changed: 2019-02-04 | ||||||||
Changed: | ||||||||
< < | Date accepted: | |||||||
> > | Date accepted: 2019-04-16 | |||||||
RationaleThis erratum is to correct an issue related to POLYGON with different orientations reported at the IVOA interop in Victoria, BC: May 2018
cite (from STC-1.33):
"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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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 | ||||||||
Changed: | ||||||||
< < | cite (from STC-S): | |||||||
> > | cite (from STC-1.33): | |||||||
"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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STC-1.33 Erratum 1:Author: DM WG | ||||||||
Changed: | ||||||||
< < | Date last changed: 2018-11-16 | |||||||
> > | Date last changed: 2019-02-04 | |||||||
Date accepted:
Rationale | ||||||||
Changed: | ||||||||
< < | This erratum is to correct an error reported at the IVOA interop in Victoria, BC: May 2018 | |||||||
> > | This erratum is to correct an issue related to POLYGON with different orientations reported at the IVOA interop in Victoria, BC: May 2018 | |||||||
Deleted: | ||||||||
< < | ||||||||
Changed: | ||||||||
< < | cite: | |||||||
> > | cite (from STC-S): | |||||||
Changed: | ||||||||
< < | 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) | |||||||
> > | "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." | |||||||
Deleted: | ||||||||
< < | 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 ContentNew Wording
Impact AssessmentSoftware using the wrong formula must be updated | ||||||||
Changed: | ||||||||
< < | Notes | |||||||
> > | Example | |||||||
Changed: | ||||||||
< < |
| |||||||
> > | 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). | |||||||
Added: | ||||||||
> > |
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)
| |||||||
STC-1.33 Erratum 1:Author: DM WG Date last changed: 2018-11-16 Date accepted:RationaleThis erratum is to correct an error reported at the IVOA interop in Victoria, BC: May 2018
cite: | ||||||||
Changed: | ||||||||
< < | 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) | |||||||
> > | 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) | |||||||
Added: | ||||||||
> > | C = (RA,DEC)[2] = (0, 90) | |||||||
Changed: | ||||||||
< < | 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 | |||||||
> > | 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 | |||||||
Added: | ||||||||
> > | ||||||||
Erratum ContentNew Wording
Impact AssessmentSoftware using the wrong formula must be updatedNotes
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STC-1.33 Erratum 1:Author: DM WG Date last changed: 2018-11-16 Date accepted:RationaleThis erratum is to correct an error reported at the IVOA interop in Victoria, BC: May 2018 | ||||||||
Changed: | ||||||||
< < | Erratum Content | |||||||
> > | ||||||||
Changed: | ||||||||
< < | The formula in Section 4.5.1.4 (pg 30: Region.Polygon) states: | |||||||
> > | cite: | |||||||
Deleted: | ||||||||
< < | ||||||||
Changed: | ||||||||
< < | "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: | |||||||
> > | 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) | |||||||
Changed: | ||||||||
< < | A = - SUM[ α(i) ] – (n-2) *pi | |||||||
> > | 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 | |||||||
Deleted: | ||||||||
< < |
αi are the polygon’s angles at the vertices. Reverse the sign for right-handed coordinates." | |||||||
Changed: | ||||||||
< < |
but..
A = (RA,DEC)[0] = (90, 0) | |||||||
> > | Erratum Content | |||||||
Deleted: | ||||||||
< < | 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 | |||||||
Changed: | ||||||||
< < | ||||||||
> > | New Wording | |||||||
Added: | ||||||||
> > |
| |||||||
Impact Assessment | ||||||||
Added: | ||||||||
> > | Software using the wrong formula must be updated | |||||||
Notes
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STC-1.33 Erratum 1:Author: DM WG Date last changed: 2018-11-16 Date accepted:RationaleThis erratum is to correct an error reported at the IVOA interop in Victoria, BC: May 2018 | ||||||||
Added: | ||||||||
> > | ||||||||
Erratum Content | ||||||||
Changed: | ||||||||
< < | The formula in 4.5.1.4 states: | |||||||
> > | The formula in Section 4.5.1.4 (pg 30: Region.Polygon) states: | |||||||
Added: | ||||||||
> > | ||||||||
Changed: | ||||||||
< < | “A = - SUM[ A(i) ] – (n-2) *pi“ | |||||||
> > | "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: | |||||||
Changed: | ||||||||
< < | but: A = (RA,DEC)[0] = (90, 0) | |||||||
> > | A = - SUM[ α(i) ] – (n-2) *pi | |||||||
Changed: | ||||||||
< < | B = (RA,DEC)[1] = (0, 0) | |||||||
> > | ||||||||
Changed: | ||||||||
< < | C = (RA,DEC)[2] = (0, 90) | |||||||
> > | αi are the polygon’s angles at the vertices. Reverse the sign for right-handed coordinates." | |||||||
Changed: | ||||||||
< < | The three angles of the polygon are all 90 deg, or pi/2 rad by construction. | |||||||
> > | ||||||||
Changed: | ||||||||
< < | A in the above case is: -3 * pi/2 –pi = -5/2 pi | |||||||
> > | but.. | |||||||
Changed: | ||||||||
< < | One expects an area of pi/2. | |||||||
> > | A = (RA,DEC)[0] = (90, 0) | |||||||
Added: | ||||||||
> > | 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: | ||||||||
Changed: | ||||||||
< < | A = +SUM[ A(i) ] – (n-2) *pi | |||||||
> > | A = +SUM[ α(i) ] – (n-2) *pi | |||||||
Added: | ||||||||
> > | ||||||||
Impact AssessmentNotes | ||||||||
Added: | ||||||||
> > |
| |||||||
STC-1.33 Erratum 1:Author: DM WG Date last changed: 2018-11-16 Date accepted:RationaleThis erratum is to correct an error reported at the IVOA interop in Victoria, BC: May 2018Erratum Content
The formula in 4.5.1.4 states:
“A = - SUM[ A(i) ] – (n-2) *pi“
but:
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[ A(i) ] – (n-2) *pi Impact AssessmentNotes |