## Sweep of a solid angle

Practical and theoretical implementation discussion.
sriravic
Posts: 20
Joined: Fri Jun 22, 2012 6:48 pm

### Sweep of a solid angle

Hello All

I'm stuck with a problem that basically boils down to analytically computing the total sweep of the solid angle subtended at a point. Assume that there is a quad that moves along a direction vector say u, and for each position on the direction u, I would like to compute the solid angle subtended by the quad at a fixed point. Can someone point out if there are any existing methods or possible locations for where I can find a solution?

dr_eck
Posts: 45
Joined: Mon Dec 05, 2011 7:35 pm

### Re: Sweep of a solid angle

To find the solid angle subtended by a surface, begin by projecting it onto a sphere centered on your point. The projected area can be formed by intersecting lines from the point to each of the vertices of your quad with the sphere. The projected area can then be calculated by breaking the quad into a couple spherical triangles and using some spherical trigonometry. Or perhaps you can find a formula that allows you to calculate the area directly from the projected quad.

The solid angle is 4 * pi * (the projected area of the surface) / (the area of the sphere)

koiava
Posts: 45
Joined: Thu Apr 24, 2014 8:18 am
Location: Munich, Germany
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### Re: Sweep of a solid angle

You can directly calculate solid angle of spherical rectangle without triangulation.
https://www.solidangle.com/research/egs ... tangle.pdf
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