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geodetic-coordinate-bounds

Abstract math for geodetic coordinate constraints: valid ranges, wrap semantics, and coordinate type distinctions. USE FOR: validating latitude ∈ [−90°, +90°] and longitude ∈ (−180°, +180°]; understanding why latitude is clamped but longitude wraps; difference between geodetic and geocentric latitude; ellipsoidal height vs. orthometric (MSL) height; antimeridian handling; normalizing out-of-range coordinates. DO NOT USE FOR: reference ellipsoid parameters (use reference-ellipsoids); datum transformations (use helmert-datum-transformation); coordinate system conversions (use coordinate-system-conversions).

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NetFabric/NetFabric.Numerics36 stars(GitHub 36 + cccskills 0)

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Files included (3)

SKILL.md3.1 KB
references/formulas.md2.0 KB
references/numerical-stability.md2.1 KB

SKILL.md (original)

Review the instructions the agent will receive before you install.

Geodetic Coordinate Bounds

Valid Ranges

Coordinate	Range	Boundary type
Latitude φ	[−90°, +90°]	Closed both ends (poles are valid points)
Longitude λ	(−180°, +180°]	Open at −180° (the antimeridian is a single line)
Ellipsoidal height h	(−∞, +∞)	No geometric bound (can be below ellipsoid)

Why Latitude is Clamped, Not Wrapped

The poles are distinct point-entities: there is no "86°N wraps to 94°N". Latitude has physical poles at ±90°.

Values outside [−90°, +90°] indicate an input error — clamp or reject.

Why Longitude Wraps

Longitude is a circular coordinate: 180°E and 180°W are the same meridian (antimeridian). Wrap formula: λ = ((λ + 180°) mod 360°) − 180° → maps to (−180°, +180°].

−180° is excluded to prevent both −180° and +180° representing the antimeridian. +180° is included as the canonical form for the antimeridian.

Geodetic vs. Geocentric Latitude

Type	Symbol	Definition
Geodetic	φ	Angle of ellipsoid normal to equatorial plane
Geocentric	φ'	Angle of radius vector to equatorial plane
Reduced (parametric)	β	Auxiliary latitude for ellipse parameterization

For WGS84: φ − φ' ≤ 11.5 arcmin at 45°.

Conversion (geodetic → geocentric):

tan φ' = (1 − e²) · tan φ = (b/a)² · tan φ

Antimeridian Handling

A geographic polygon crossing the antimeridian requires special treatment:

Do NOT test if all longitudes are < 180° (a segment from 170°E to −170°E crosses the antimeridian)
Detect crossing: |λ₂ − λ₁| > 180°
Split the polygon at the antimeridian for Cartesian bounding box calculations

Height Types

Type	Reference surface	Use
Ellipsoidal height h	Reference ellipsoid (WGS84)	GPS, geometric geodesy
Orthometric height H	Geoid (mean sea level)	Topographic, engineering
Relationship	h = H + N (N = geoid undulation)	N varies by location (−107 to +85 m)

Reference Files

File	Load When
references/formulas.md	Longitude wrap formula, geodetic→geocentric derivation, height conversion
references/numerical-stability.md	Floating-point boundary tests, antimeridian edge cases, pole singularity

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Install

Install with a command

npx skills add https://github.com/NetFabric/NetFabric.Numerics --skill geodetic-coordinate-bounds

Paste it into your terminal and run it (requires Node.js). You can choose which agents to install it for, such as Claude Code or Codex.

Ask your agent

Please install the following Agent Skill.
https://github.com/NetFabric/NetFabric.Numerics/tree/main/.agents/skills/geodetic-coordinate-bounds

First review SKILL.md and the bundled files and confirm there is nothing suspicious (such as sending data externally or reading credentials). Then place it in ~/.claude/skills/geodetic-coordinate-bounds/ for Claude Code, or ~/.agents/skills/geodetic-coordinate-bounds/ for Codex.

Send this text to Claude Code or Codex as is. It checks the contents before installing.

View source on GitHub

Repository: NetFabric/NetFabric.Numerics
Stars: 36
Forks: 1
Category: Other
License: MIT
Original language: English
Last updated: Aug 10, 2026

A skill is a set of instructions and scripts for an agent. cccskills does not guarantee that skills are safe. Review the contents before you install.