# STC-1.33 Erratum 1:

Author: DM WG

Date last changed: 2019-02-04

Date accepted:

## Rationale

This 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-S):

"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."

## 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

## Example

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).

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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png ABC.png manage 50.7 K 2019-02-05 - 08:07 LaurentMichel
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Topic revision: r5 - 2019-02-05 - LaurentMichel

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