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SolidAngle
gives the solid angle at the point p and spanned by the vectors u1,…,ud.
Details
- SolidAngle is also known as planar angle or spherical angle.
- SolidAngle is typically used to measure the amount of the field of view from a point that an object covers.
- SolidAngle[p,{u1,…,ud}] is the measure of the intersection of the d-dimensional unit sphere Sphere[p] and the conic hull generated by the vectors u1,…,ud.
- SolidAngle[p,reg] is the measure of the intersection of the unit sphere centered at p and half‐lines from p through points of the region reg.
Examples
open allclose allBasic Examples (1)Summary of the most common use cases
The solid angle at the point {1/2,1/2,0} and spanned by the vectors {0,0,1}, {0,1,1}, {1,1,1} and {1,0,1}:
https://wolfram.com/xid/0rsrlh9bq-6ftdz9
https://wolfram.com/xid/0rsrlh9bq-jg3w5h
Scope (2)Survey of the scope of standard use cases
Use SolidAngle to find the angle at the point and spanned by the vectors:
https://wolfram.com/xid/0rsrlh9bq-eedb1a
https://wolfram.com/xid/0rsrlh9bq-tu6z5d
The solid angle subtended by the Cone[{{1,1,1},{0,0,0}}]:
https://wolfram.com/xid/0rsrlh9bq-ekr9nh
https://wolfram.com/xid/0rsrlh9bq-s1v5zp
Properties & Relations (5)Properties of the function, and connections to other functions
SolidAngle[{0,0},{u1,u2}] is the planar angle between the half‐lines from the point p in the direction of u1 and u2:
https://wolfram.com/xid/0rsrlh9bq-0uz03d
https://wolfram.com/xid/0rsrlh9bq-1kxdnt
https://wolfram.com/xid/0rsrlh9bq-chwid9
SolidAngle[{0,0,0},{u1,u2,u3}] is the surface area of the triangle on the unit sphere with corner points :
https://wolfram.com/xid/0rsrlh9bq-rtxsgy
In 2D, SolidAngle[p,Line[{q1,q2}] is equivalent to PlanarAngle[{q1,p,q2}]:
https://wolfram.com/xid/0rsrlh9bq-1vwyjn
In 3D, SolidAngle[p,reg] is the surface area of the intersection of the unit sphere centered at p that lies in the infinite cone with vertex p and enclosing reg:
https://wolfram.com/xid/0rsrlh9bq-7tk6g7
https://wolfram.com/xid/0rsrlh9bq-q8x2gg
SolidAngle[p,{u1,…,ud}] is equivalent to PolyhedronAngle[ℛ,p], where u1,…,ud are vectors adjacent to the point p in a polyhedron ℛ:
https://wolfram.com/xid/0rsrlh9bq-r7mz30
https://wolfram.com/xid/0rsrlh9bq-m1appj
https://wolfram.com/xid/0rsrlh9bq-4c1k1y
https://wolfram.com/xid/0rsrlh9bq-gk4ig3
https://wolfram.com/xid/0rsrlh9bq-4fbqkd
https://wolfram.com/xid/0rsrlh9bq-xxzp0h
Wolfram Research (2019), SolidAngle, Wolfram Language function, https://reference.wolfram.com/language/ref/SolidAngle.html.
Text
Wolfram Research (2019), SolidAngle, Wolfram Language function, https://reference.wolfram.com/language/ref/SolidAngle.html.
Wolfram Research (2019), SolidAngle, Wolfram Language function, https://reference.wolfram.com/language/ref/SolidAngle.html.
CMS
Wolfram Language. 2019. "SolidAngle." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SolidAngle.html.
Wolfram Language. 2019. "SolidAngle." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SolidAngle.html.
APA
Wolfram Language. (2019). SolidAngle. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SolidAngle.html
Wolfram Language. (2019). SolidAngle. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SolidAngle.html
BibTeX
@misc{reference.wolfram_2024_solidangle, author="Wolfram Research", title="{SolidAngle}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/SolidAngle.html}", note=[Accessed: 10-January-2025
]}
BibLaTeX
@online{reference.wolfram_2024_solidangle, organization={Wolfram Research}, title={SolidAngle}, year={2019}, url={https://reference.wolfram.com/language/ref/SolidAngle.html}, note=[Accessed: 10-January-2025
]}