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I am looking for the generalized formula how to find the solid angle for a closed curve in $R^3$ then to generalize it for $R^n$. Thanks for answers and papers or books references and links that are related to the subject.

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I am trying to express the general formula of the projection area ($S$) on the unit sphere as shown in the picture above.

For example how to find the solid angle for the special case?

A curve defined :

$x=3+\cos(t)$

$y=3+\sin(t)$

$z=3$

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