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### Sweep of a solid angle

Posted: Mon Feb 22, 2016 6:18 pm
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?

### Re: Sweep of a solid angle

Posted: Wed Feb 24, 2016 6:59 pm
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)

### Re: Sweep of a solid angle

Posted: Thu Feb 25, 2016 1:19 pm
You can directly calculate solid angle of spherical rectangle without triangulation.
https://www.solidangle.com/research/egs ... tangle.pdf