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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).

日本語の概要は準備中です。原文の説明を表示しています。

NetFabric/NetFabric.Numericsスター 36(GitHub 36 + cccskills 0)

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  • references/formulas.md2.0 KB
  • references/numerical-stability.md2.1 KB

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Geodetic Coordinate Bounds

Valid Ranges

CoordinateRangeBoundary 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

TypeSymbolDefinition
GeodeticφAngle of ellipsoid normal to equatorial plane
Geocentricφ'Angle of radius vector to equatorial plane
Reduced (parametric)βAuxiliary 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

TypeReference surfaceUse
Ellipsoidal height hReference ellipsoid (WGS84)GPS, geometric geodesy
Orthometric height HGeoid (mean sea level)Topographic, engineering
Relationshiph = H + N (N = geoid undulation)N varies by location (−107 to +85 m)

Reference Files

FileLoad When
references/formulas.mdLongitude wrap formula, geodetic→geocentric derivation, height conversion
references/numerical-stability.mdFloating-point boundary tests, antimeridian edge cases, pole singularity

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