solid angle
Let an agent explain solid angle, relay definitions, units, calculations and uses from physics, metrology and graphics sources, describe the named related concepts and flag loosely filed aliases, and distinguish solid angle from plane angle, field of view as a linear angle, luminous intensity and square degrees used in astronomy.
Research draft, second pass
A second pass drafted this model: the structure a model of this thing needs, and what is known about it in the world. The line under this one says how the second half was obtained - researched against sources, or recalled without web access, in which case nothing here was read anywhere and every claim is a lead to verify. Unreviewed either way.
written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify
Researched by: Claude
Purpose and description
Let an agent explain solid angle, relay definitions, units, calculations and uses from physics, metrology and graphics sources, describe the named related concepts and flag loosely filed aliases, and distinguish solid angle from plane angle, field of view as a linear angle, luminous intensity and square degrees used in astronomy.
A measure of the field of view from a point, the three-dimensional analogue of a plane angle, equal to the area of the projection of an object onto a unit sphere around the observer, measured in steradians, with a full sphere subtending 4 pi steradians, about 12.57, used in radiometry, photometry, antenna theory and astronomy; related concepts the registry aliases name include field of view, field of regard, camera field of view and field of view in video games, which are often given as plane angles, viewing frustums in computer graphics, and trihedra, figures formed by three planes meeting at a point, which appear loosely filed.
What it is for: Measuring angular extent in three dimensions.
It can be explain definition and units; relay calculations; describe related field-of-view concepts; flag loosely filed aliases.
Distinguishing features
Dimensionless SI derived quantity
Measured on unit sphere
Radiometry use
Field-of-view link
What it looks like
Not a physical object; visualised as a cone from a point to a surface.
Physical character
SI unit: steradian unit - sr
full sphere: 4 pi sr - about 12.566
square degrees in a sphere: about 41,253 deg2
How it is recognised
Three-dimensional angular extent
Field of view, field of regard, trihedron, camera field of view, field of view in video games, viewing frustum
Plane angles are two-dimensional; field of view is often in degrees; luminous intensity is candela per steradian; square degrees are an astronomy unit
Related models
is a kind of - in registry terms, dimensionless
is measured in -
is related to -
is contrasted with - plane angle
In practice
Families and kinds
solid angles of cones and polygons
fields of view
viewing frustums
square degree measures
Standards and regulation
SI Brochure
ISO 80000-3
Failure modes and hazards
Confusing solid and plane angles
Mixing square degrees and steradians
Loosely filed geometry aliases
Also called
Where this came from
wikidata · CC0 1.0
Drafted structure
Bundle to layer to finding to question, as the second pass will find it: 4 bundles · 8 layers · 8 findings · 16 questions.
Understand What a solid angle is.
Definition.
Definition
Definition.
Definition
Definition.
- What is a solid angle, and how does it differ from plane angles, field of view in degrees, luminous intensity and square degrees? definition
- Is the question about physics, astronomy, cameras or games? boundary
Concepts
Named concepts.
Concepts
Concepts.
- What are field of view, field of regard, viewing frustums and trihedra, and how do they relate? definition
- Which entry fits the specific concept? action
Mathematics Calculation.
Science.
Steradian
Steradian.
Steradian
Steradian.
- How is the steradian defined, and why does a sphere have 4 pi steradians? measurement
- Which references are standard? provenance
Cones
Cone formula.
Cones
Cones.
- How is the solid angle of a cone with a given half-angle calculated? measurement
- Which sources are cited? provenance
Applications Applications.
Science.
Radiometry
Radiometry and photometry.
Radiometry
Radiometry.
- How do radiance and luminous intensity use steradians? provenance
- Which entry fits candela? action
Astronomy
Sky surveys.
Astronomy
Astronomy.
- How do astronomers express survey areas in square degrees? measurement
- Which entry fits square degree? action
Context Imaging and games.
Context.
Cameras
Camera field of view.
Cameras
Cameras.
- How do focal length and sensor size determine camera field of view? measurement
- Which entry fits angle of view? action
Frustum
Viewing frustum.
Frustum
Frustum.
- What is a viewing frustum in 3D graphics, and how does game FOV work? provenance
- Which entry fits viewing frustum? action
What the second pass must settle
- The registry alias trihedron should be moved to geometry entries
- Should field of view be a separate entry?
- How should radiometry references be linked?