Solid angle created from irregular polygon (over a sphere)
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I have an $n$-polygon on a sphere ($ngeqslant3$). In this example the vertices are $C,D,E,F,G,H,I,J,K$. Which solid angle alpha generate this polygon respect origin of the sphere? For $C,D,E,F,G,H,I,J,K$ are know coordinate Cartesian or polar.
I am searching for a "closed solution" without integrals, and when is the solid angle generated from polygon $KJIHGFEDC$ being $β=4π-α$?
polygons solid-angle
edited Jan 6 at 15:03
Saad
20.4k92452
asked Jan 6 at 14:42
Mario RossiMario Rossi
1
$endgroup$
add a comment |
$begingroup$
I have an $n$-polygon on a sphere ($ngeqslant3$). In this example the vertices are $C,D,E,F,G,H,I,J,K$. Which solid angle alpha generate this polygon respect origin of the sphere? For $C,D,E,F,G,H,I,J,K$ are know coordinate Cartesian or polar.
I am searching for a "closed solution" without integrals, and when is the solid angle generated from polygon $KJIHGFEDC$ being $β=4π-α$?
polygons solid-angle
edited Jan 6 at 15:03
Saad
20.4k92452
asked Jan 6 at 14:42
Mario RossiMario Rossi
1
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$begingroup$
Do you have co-ordinates for the points?
$endgroup$
– stuart stevenson
Jan 6 at 14:46
$begingroup$
Yes, I apologize for my bad English
$endgroup$
– Mario Rossi
Jan 6 at 14:51
1
$begingroup$
You might want to read up on spherical excess. See, for example en.wikipedia.org/wiki/…
$endgroup$
– random
Jan 6 at 15:15
add a comment |
$begingroup$
I have an $n$-polygon on a sphere ($ngeqslant3$). In this example the vertices are $C,D,E,F,G,H,I,J,K$. Which solid angle alpha generate this polygon respect origin of the sphere? For $C,D,E,F,G,H,I,J,K$ are know coordinate Cartesian or polar.
I am searching for a "closed solution" without integrals, and when is the solid angle generated from polygon $KJIHGFEDC$ being $β=4π-α$?
polygons solid-angle
edited Jan 6 at 15:03
Saad
20.4k92452
asked Jan 6 at 14:42
Mario RossiMario Rossi
1
$endgroup$
I have an $n$-polygon on a sphere ($ngeqslant3$). In this example the vertices are $C,D,E,F,G,H,I,J,K$. Which solid angle alpha generate this polygon respect origin of the sphere? For $C,D,E,F,G,H,I,J,K$ are know coordinate Cartesian or polar.
I am searching for a "closed solution" without integrals, and when is the solid angle generated from polygon $KJIHGFEDC$ being $β=4π-α$?
polygons solid-angle
polygons solid-angle
edited Jan 6 at 15:03
Saad
20.4k92452
asked Jan 6 at 14:42
Mario RossiMario Rossi
1
edited Jan 6 at 15:03
Saad
20.4k92452
asked Jan 6 at 14:42
Mario RossiMario Rossi
1
edited Jan 6 at 15:03
Saad
20.4k92452
edited Jan 6 at 15:03
Saad
20.4k92452
edited Jan 6 at 15:03
Saad
20.4k92452
20.4k92452
asked Jan 6 at 14:42
Mario RossiMario Rossi
1
asked Jan 6 at 14:42
Mario RossiMario Rossi
1
asked Jan 6 at 14:42
Mario RossiMario Rossi
1
1
$begingroup$
Do you have co-ordinates for the points?
$endgroup$
– stuart stevenson
Jan 6 at 14:46
$begingroup$
Yes, I apologize for my bad English
$endgroup$
– Mario Rossi
Jan 6 at 14:51
1
$begingroup$
You might want to read up on spherical excess. See, for example en.wikipedia.org/wiki/…
$endgroup$
– random
Jan 6 at 15:15
add a comment |
$begingroup$
Do you have co-ordinates for the points?
$endgroup$
– stuart stevenson
Jan 6 at 14:46
$begingroup$
Yes, I apologize for my bad English
$endgroup$
– Mario Rossi
Jan 6 at 14:51
1
$begingroup$
You might want to read up on spherical excess. See, for example en.wikipedia.org/wiki/…
$endgroup$
– random
Jan 6 at 15:15
$begingroup$
Do you have co-ordinates for the points?
$endgroup$
– stuart stevenson
Jan 6 at 14:46
$begingroup$
Do you have co-ordinates for the points?
$endgroup$
– stuart stevenson
Jan 6 at 14:46
$begingroup$
Yes, I apologize for my bad English
$endgroup$
– Mario Rossi
Jan 6 at 14:51
$begingroup$
Yes, I apologize for my bad English
$endgroup$
– Mario Rossi
Jan 6 at 14:51
1
1
$begingroup$
You might want to read up on spherical excess. See, for example en.wikipedia.org/wiki/…
$endgroup$
– random
Jan 6 at 15:15
$begingroup$
You might want to read up on spherical excess. See, for example en.wikipedia.org/wiki/…
$endgroup$
– random
Jan 6 at 15:15
add a comment |
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$begingroup$
Do you have co-ordinates for the points?
$endgroup$
– stuart stevenson
Jan 6 at 14:46
$begingroup$
Yes, I apologize for my bad English
$endgroup$
– Mario Rossi
Jan 6 at 14:51
1
$begingroup$
You might want to read up on spherical excess. See, for example en.wikipedia.org/wiki/…
$endgroup$
– random
Jan 6 at 15:15