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). ![]()
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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). ![]()
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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: | ||||||||
> > |
![]()
| |||||||
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 |