Fix the equation for the spherical triangle area

[massile]

Hello 👋 ,

I think I found an error in the equation of the spherical triangle area in terms of the cross and dot products of the vertices (https://pbr-book.org/4ed/Geometry_and_Transformations/Spherical_Geometry#eq:triangle-solid-angle-better)

According to the source code, reverting back to the tangeant from the area, we should get

tan(A/2) = (a . (b x c)) / (1 + (a . b) + (a . c) + (b . c))

while the equation shown is (cf screenshot below)

tan(A/2) = (A . (b x b)) / (1 + (a . b) + (a . c) + (b . c))

The following articles seem to agree with the equation I found as well:

• https://www.jstor.org/stable/2691141
• https://www.johndcook.com/blog/2021/11/29/area-of-spherical-triangle/

[mmp]

Thanks!!