azimuth
Enable an agent to recognise, interpret, compare and use azimuth values while preserving the reference direction, geometric frame and conventions that give them meaning.
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.
recalled by Codex without web access - no source was read
Researched by: Codex
Purpose and description
Enable an agent to recognise, interpret, compare and use azimuth values while preserving the reference direction, geometric frame and conventions that give them meaning.
Azimuth is an angular coordinate specifying a direction about a reference axis, measured in a reference plane from a stated reference direction according to a stated rotational convention.
It can be Interpret an azimuth as a direction in a declared frame.; Compute azimuth from a target direction when its projection and reference frame are valid.; Normalise angular notation and calculate circular differences.; Convert between reference conventions when the required frame relationships and corrections are available.; Assess whether an azimuth is sufficiently defined and precise for a pointing or comparison task.; Identify when additional elevation, distance or orientation information is required..
Distinguishing features
An azimuth specifies a direction around an axis; it does not by itself specify distance or a complete three-dimensional direction.
In a local horizontal frame, azimuth resolves direction within the horizontal plane, whereas elevation resolves departure from that plane.
A numeric angle qualifies as an interpretable azimuth only when its reference direction and rotation convention are known.
Heading describes where an object's forward axis points, while target azimuth describes a selected direction; they coincide only when those directions coincide.
Azimuth commonly overlaps with bearing terminology, so the model must identify whether a bearing uses a full-circle azimuth convention or a quadrant notation.
Scope
+ The origin, target direction, reference plane and axis defining an azimuth
+ Zero direction, positive rotation sense, angular units and value range
+ True, magnetic, grid and other explicitly defined reference directions
+ Observed, computed and commanded azimuth values with their validity conditions
+ Circular comparison, reference conversion and cases where azimuth is undefined
- Elevation, altitude and zenith angle as independently modelled angular quantities
- Complete position, pose or orientation models
- Surveying instruments, compasses and antenna mechanisms as physical devices
- Routes, trajectories and geodesic solutions beyond their associated azimuths
- Magnetic-field and map-projection models used to establish reference corrections
Characteristics
- Angular value
- Degrees, radians or another declared angular unit Provides the magnitude while preventing unit-dependent interpretation errors.
- Geometric frame
- Origin, reference plane, axis and frame identifier Determines the geometry in which the angle has meaning.
- Target direction
- Target point, direction vector, line tangent or designated object axis Distinguishes sightline azimuth, heading, path direction and other uses.
- Zero reference
- True north, magnetic north, grid north, named coordinate axis or other declared direction Values using different zero references cannot be compared directly.
- Positive rotation convention
- Declared positive rotation sense with viewing direction or handedness Clockwise and counterclockwise descriptions are ambiguous without a viewing convention.
- Angular representation
- Declared interval and endpoint policy; wrapped or unwrapped Separates circular direction from accumulated rotation and handles the interval boundary.
- Definition and validity state
- Defined, undefined, indeterminate or invalid for the intended use Prevents missing geometry or singular directions from being treated as valid zero angles.
- Uncertainty
- Angular uncertainty with stated interpretation, or unknown Supports decisions about pointing, comparison and tolerance without assuming precision.
- Context of applicability
- Location, time, reference model, observation or computation record as applicable Some reference directions and corrections depend on where and when the azimuth applies.
Where this came from
wikidata · CC0 1.0
Drafted structure
Bundle to layer to finding to question, as the second pass will find it: 5 bundles · 9 layers · 15 findings · 23 questions.
Direction geometry Establishes what direction the azimuth locates and the geometry supporting that relation.
An angle alone cannot identify an azimuth without an origin, axis, plane and target direction.
Origin and frame
Identifies the geometric setting in which azimuth is evaluated.
Azimuth frame
Record the origin, axis and perpendicular reference plane, including whether the frame is local horizontal or another declared coordinate frame.
- At what origin and around which axis is this azimuth defined? definition
- What establishes the reference plane, and how is it related to the surrounding coordinate system? provenance
Direction referent
Distinguishes the direction being described from the object or position that supplies it.
Projected target direction
Identify the sightline, vector, tangent or object axis whose projection into the reference plane determines azimuth.
- Does this azimuth refer to a target sightline, a forward axis, a path tangent or another direction? definition
- Is that direction projected into the reference plane, and is the projection nonzero? measurement
Angular conventions Captures the choices that turn a geometric direction into a numeric azimuth.
The same direction can receive different azimuth values under different zero, rotation and notation conventions.
Zero and rotation
Makes the angular origin and positive sense explicit.
Reference direction convention
Record the zero direction and positive rotation sense without assuming that every discipline uses north and clockwise rotation.
- Which direction is assigned zero, and what convention or authority establishes it? provenance
- In which sense does the angle increase, viewed from which side of the reference plane? definition
Notation and periodicity
Controls units, interval boundaries and the distinction between direction and accumulated rotation.
Circular value representation
Preserve the angular unit, canonical interval and whether whole turns are discarded or retained for an operational purpose.
- What units, interval and endpoint rules govern the recorded value? measurement
- Does a value beyond one turn encode rotation history, or should it be normalised to a direction? boundary
Reference alignment Supports justified comparisons and transformations between azimuths.
A numeric difference can reflect a reference mismatch rather than a difference in physical direction.
North reference conversion
Handles true, magnetic and grid references with explicit contextual corrections.
Reference correction evidence
Record the source, applicability and sign convention of any correction used to align north references.
- Which source and location or time context establish the required magnetic or grid correction? provenance
- How is the correction's sign defined and checked against the source and destination azimuth conventions? action
Comparison and reversal
Separates circular comparison within one frame from transformations between origins or frames.
Comparable directions
Require compatible frames before calculating circular differences; distinguish reversing a vector at one origin from finding a return direction at another origin.
- Are both azimuths expressed in the same frame and convention, or what transformation is required first? boundary
- Does the requested reverse azimuth mean a half-turn at the same origin or a direction evaluated in the destination's local frame? action
Determination and usability Connects azimuth values to their derivation, uncertainty and permissible use.
An agent must distinguish a usable directional estimate from a singular, unsupported or insufficiently precise value.
Determination evidence
Records how the azimuth was obtained and what limits its precision.
Azimuth derivation
Distinguish an observation, coordinate-derived result, nominal direction and commanded value, preserving relevant inputs and uncertainty.
- Was this azimuth measured, computed, specified or commanded, and what evidence supports it? provenance
- What angular uncertainty follows from the inputs, reference alignment and determination method? measurement
Singularities and action
Identifies undefined geometry and checks whether a value supports the intended decision.
Azimuth validity gate
Treat zero in-plane projection or an undefined reference direction as a validity problem; evaluate near-singular sensitivity and task tolerances before use.
- Is the direction parallel to the azimuth axis, nearly parallel to it, or evaluated where the chosen zero reference is undefined? boundary
- Given the uncertainty and validity state, may the agent use this azimuth for the intended pointing or comparison action? action
Evidence and external alignment What the world already says about this thing, gathered so the model can be checked against it.
A model that cannot be lined up against existing standards, identifiers and practice cannot be adopted by anyone who already uses them.
Reported evidence
Findings from the breadth pass, kept separate from the structural claims.
Check these first
Recalled without web access and unsourced; every item is a lead to verify.
- This describes the angular-coordinate sense; no narrower registry sense was supplied.
- North-origin clockwise measurement is common in navigation and surveying, but mathematical and astronomical conventions must be checked explicitly.
- Astronomical and geodetic azimuth use different local reference constructions, involving the gravity vertical and reference-ellipsoid normal respectively; precision work must distinguish them.
- Which of these check these first hold for the sense of azimuth this model covers, and on what evidence? provenance
Kinds and varieties
Recalled without web access and unsourced; every item is a lead to verify.
- True-north azimuth
- Magnetic azimuth
- Grid azimuth
- Astronomical azimuth
- Geodetic azimuth
- Which of these kinds and varieties hold for the sense of azimuth this model covers, and on what evidence? provenance
Real-world use
Recalled without web access and unsourced; every item is a lead to verify.
- Expressing navigation headings and directions to landmarks.
- Specifying survey lines and geodetic directions.
- Locating celestial objects in a horizontal coordinate system.
- Orienting antennas, telescopes and solar panels.
- Describing directions in radar and tracking systems.
- Which of these real-world use hold for the sense of azimuth this model covers, and on what evidence? provenance
Typical measurements
Recalled without web access and unsourced; every item is a lead to verify.
- Azimuth angle - 0 inclusive to 360 exclusive for a complete turn; signed representations also occur - degree
- Azimuth angle in mathematical computation - 0 inclusive to 2π exclusive, or a signed interval spanning one turn - radian
- Which of these typical measurements hold for the sense of azimuth this model covers, and on what evidence? provenance
Failure modes and hazards
Recalled without web access and unsourced; every item is a lead to verify.
- Confusing true north, magnetic north and grid north produces systematic direction errors.
- Mixing reference directions or clockwise and counterclockwise conventions gives incompatible angles.
- Treating the 0°/360° boundary as an ordinary numerical discontinuity corrupts averaging, interpolation and control.
- Azimuth is undefined when the direction has zero projection onto the reference plane, as at the zenith in horizontal coordinates.
- Using an outdated magnetic declination correction can misdirect navigation or instrument alignment.
- Which of these failure modes and hazards hold for the sense of azimuth this model covers, and on what evidence? provenance
Regional variation
Recalled without web access and unsourced; every item is a lead to verify.
- Magnetic declination varies with location and time, so magnetic and true azimuth differ by a locally dependent correction.
- Grid north depends on the map projection and position; conversion between grid and true azimuth requires the applicable convergence correction.
- Which of these regional variation hold for the sense of azimuth this model covers, and on what evidence? provenance
Neighbouring kinds and how to tell them apart
Recalled without web access and unsourced; every item is a lead to verify.
- bearing - Bearing is a broader directional term that can denote an azimuth or a quadrant-based direction; azimuth specifies an angular coordinate around a reference axis.
- elevation angle - Elevation measures the angle above or below the reference plane, while azimuth specifies direction around its normal axis.
- heading - Heading describes where a vehicle or object points; azimuth can describe any direction, including one unrelated to its orientation.
- zenith angle - Zenith angle measures angular distance from the upward vertical, whereas azimuth measures direction around that vertical.
- longitude - Longitude locates a position relative to a reference meridian; local azimuth specifies a direction at an observation point.
- Which of these neighbouring kinds and how to tell them apart hold for the sense of azimuth this model covers, and on what evidence? provenance
What the second pass must settle
- Does vr.tr.azimuth intend to cover general spherical-coordinate azimuth as well as geographic and astronomical horizontal azimuth?
- Which authoritative conventions should govern zero direction, rotation sense and notation in each supported application domain?
- How should the registry relate azimuth to bearing, heading and position angle while preserving their overlapping but distinct uses?
- Which uncertainty representations and near-singularity thresholds are appropriate for the intended operational tasks?
- Which existing Vercy models already own coordinate frames, magnetic corrections and geodesic direction calculations, and how should this model reference them?