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