Solid angle definition from an ellipsoid surface
0
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Let assume there is a unit sphere inside a oblate spheroid with minor axis 1 and major axis b. What is the surface area in the oblate spheroid surface produced from extending the subtended solid angle $omega$ in the sphere?
geometry
asked Jan 10 at 1:39
Jose E CalderonJose E Calderon
1014
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show 1 more comment
0
$begingroup$
Let assume there is a unit sphere inside a oblate spheroid with minor axis 1 and major axis b. What is the surface area in the oblate spheroid surface produced from extending the subtended solid angle $omega$ in the sphere?
geometry
asked Jan 10 at 1:39
Jose E CalderonJose E Calderon
1014
$endgroup$
2
$begingroup$
It’s obviously going to depend on the location and shape of the patch of the sphere that comprises that solid angle.
$endgroup$
– amd
Jan 10 at 3:11
$begingroup$
Exactly, but is there a particular technique to described the relationship?
$endgroup$
– Jose E Calderon
Jan 10 at 8:52
$begingroup$
You could try inverting the computation of solid angle for a patch of the ellipsoid: project from the unit sphere onto the ellipsoid and compute the resulting surface integral.
$endgroup$
– amd
Jan 10 at 9:13
$begingroup$
@amd Thanks for pointing this out! It is Spheroid. Have corrected question. To be more specific- a Oblate Spheroid.
$endgroup$
– Jose E Calderon
Jan 10 at 9:29
$begingroup$
you can well reduce the problem to 2D
$endgroup$
– G Cab
Jan 10 at 9:38
|
show 1 more comment
0
0
0
$begingroup$
Let assume there is a unit sphere inside a oblate spheroid with minor axis 1 and major axis b. What is the surface area in the oblate spheroid surface produced from extending the subtended solid angle $omega$ in the sphere?
geometry
asked Jan 10 at 1:39
Jose E CalderonJose E Calderon
1014
$endgroup$
Let assume there is a unit sphere inside a oblate spheroid with minor axis 1 and major axis b. What is the surface area in the oblate spheroid surface produced from extending the subtended solid angle $omega$ in the sphere?
geometry
geometry
asked Jan 10 at 1:39
Jose E CalderonJose E Calderon
1014
asked Jan 10 at 1:39
Jose E CalderonJose E Calderon
1014
edited Jan 10 at 9:27
Jose E Calderon
asked Jan 10 at 1:39
Jose E CalderonJose E Calderon
1014
asked Jan 10 at 1:39
Jose E CalderonJose E Calderon
1014
asked Jan 10 at 1:39
Jose E CalderonJose E Calderon
1014
1014
2
$begingroup$
It’s obviously going to depend on the location and shape of the patch of the sphere that comprises that solid angle.
$endgroup$
– amd
Jan 10 at 3:11
$begingroup$
Exactly, but is there a particular technique to described the relationship?
$endgroup$
– Jose E Calderon
Jan 10 at 8:52
$begingroup$
You could try inverting the computation of solid angle for a patch of the ellipsoid: project from the unit sphere onto the ellipsoid and compute the resulting surface integral.
$endgroup$
– amd
Jan 10 at 9:13
$begingroup$
@amd Thanks for pointing this out! It is Spheroid. Have corrected question. To be more specific- a Oblate Spheroid.
$endgroup$
– Jose E Calderon
Jan 10 at 9:29
$begingroup$
you can well reduce the problem to 2D
$endgroup$
– G Cab
Jan 10 at 9:38
|
show 1 more comment
2
$begingroup$
It’s obviously going to depend on the location and shape of the patch of the sphere that comprises that solid angle.
$endgroup$
– amd
Jan 10 at 3:11
$begingroup$
Exactly, but is there a particular technique to described the relationship?
$endgroup$
– Jose E Calderon
Jan 10 at 8:52
$begingroup$
You could try inverting the computation of solid angle for a patch of the ellipsoid: project from the unit sphere onto the ellipsoid and compute the resulting surface integral.
$endgroup$
– amd
Jan 10 at 9:13
$begingroup$
@amd Thanks for pointing this out! It is Spheroid. Have corrected question. To be more specific- a Oblate Spheroid.
$endgroup$
– Jose E Calderon
Jan 10 at 9:29
$begingroup$
you can well reduce the problem to 2D
$endgroup$
– G Cab
Jan 10 at 9:38
2
2
$begingroup$
It’s obviously going to depend on the location and shape of the patch of the sphere that comprises that solid angle.
$endgroup$
– amd
Jan 10 at 3:11
$begingroup$
It’s obviously going to depend on the location and shape of the patch of the sphere that comprises that solid angle.
$endgroup$
– amd
Jan 10 at 3:11
$begingroup$
Exactly, but is there a particular technique to described the relationship?
$endgroup$
– Jose E Calderon
Jan 10 at 8:52
$begingroup$
Exactly, but is there a particular technique to described the relationship?
$endgroup$
– Jose E Calderon
Jan 10 at 8:52
$begingroup$
You could try inverting the computation of solid angle for a patch of the ellipsoid: project from the unit sphere onto the ellipsoid and compute the resulting surface integral.
$endgroup$
– amd
Jan 10 at 9:13
$begingroup$
You could try inverting the computation of solid angle for a patch of the ellipsoid: project from the unit sphere onto the ellipsoid and compute the resulting surface integral.
$endgroup$
– amd
Jan 10 at 9:13
$begingroup$
@amd Thanks for pointing this out! It is Spheroid. Have corrected question. To be more specific- a Oblate Spheroid.
$endgroup$
– Jose E Calderon
Jan 10 at 9:29
$begingroup$
@amd Thanks for pointing this out! It is Spheroid. Have corrected question. To be more specific- a Oblate Spheroid.
$endgroup$
– Jose E Calderon
Jan 10 at 9:29
$begingroup$
you can well reduce the problem to 2D
$endgroup$
– G Cab
Jan 10 at 9:38
$begingroup$
you can well reduce the problem to 2D
$endgroup$
– G Cab
Jan 10 at 9:38
|
show 1 more comment
0
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2
$begingroup$
It’s obviously going to depend on the location and shape of the patch of the sphere that comprises that solid angle.
$endgroup$
– amd
Jan 10 at 3:11
$begingroup$
Exactly, but is there a particular technique to described the relationship?
$endgroup$
– Jose E Calderon
Jan 10 at 8:52
$begingroup$
You could try inverting the computation of solid angle for a patch of the ellipsoid: project from the unit sphere onto the ellipsoid and compute the resulting surface integral.
$endgroup$
– amd
Jan 10 at 9:13
$begingroup$
@amd Thanks for pointing this out! It is Spheroid. Have corrected question. To be more specific- a Oblate Spheroid.
$endgroup$
– Jose E Calderon
Jan 10 at 9:29
$begingroup$
you can well reduce the problem to 2D
$endgroup$
– G Cab
Jan 10 at 9:38