Vincenty's formulae¶
Vincenty's formulae are two related iterative methods used in geodesy to calculate the distance between two points on the surface of a spheroid, developed by Thaddeus Vincenty (1975a).
Core Idea¶
Vincenty's formulae is treated here as the recurring cross-domain formal modeling identity summarized by this source-grounded definition: Vincenty's formulae are two related iterative methods used in geodesy to calculate the distance between two points on the surface of a spheroid, developed by Thaddeus Vincenty (1975a). Vincenty's formulae are two related iterative methods used in geodesy to calculate the distance between two points on the surface of a spheroid, developed by Thaddeus Vincenty (1975a). They are based on the assumption that the figure of the Earth is an oblate spheroid, and hence are more accurate than.
Scope of Application¶
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Direct problem. If the standard 2-argument arctangent atan2 function is used, then these values are usually handled correctly.
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Background. Finally, simple iterative techniques were used to solve the implicit equations in the direct and inverse methods; even though these are slow (and in the case of the inverse method it.
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Documented setting. Vincenty's formulae are two related iterative methods used in geodesy to calculate the distance between two points on the surface of a spheroid, developed by Thaddeus Vincenty (1975a).
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Background. The expressions were put in Horner (or nested) form, since this allows polynomials to be evaluated using only a single temporary register.
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Nearly antipodal points. Depending on how the inverse method is implemented, the algorithm might return the correct result (19936288.579 m), an incorrect result, or an error indicator.
Clarity¶
A clear use of Vincenty's formulae names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is Vincenty's formulae are two related iterative methods used in geodesy to calculate the distance between two points on the surface of a spheroid, developed by Thaddeus Vincenty (1975a).
Manages Complexity¶
Vincenty's formulae compresses multiple cross-domain formal modeling details into a stable diagnostic relation. The source shows both the central mechanism—legendre showed that an ellipsoidal geodesic can be exactly mapped to a great circle on the auxiliary sphere by mapping the geographic latitude to reduced latitude and setting the azimuth of the great circle equal to that of the geodesic.—and the practical consequence—this requires about 130 iterations to.
Abstract Reasoning¶
- Type the carrier. Identify the cross-domain formal modeling entities to which the claim applies.
- State the relation. Use the source-grounded identity: Vincenty's formulae are two related iterative methods used in geodesy to calculate the distance between two points on the surface of a spheroid, developed by Thaddeus Vincenty (1975a).
- Check operation and conditions. The longitude on the ellipsoid and the distance along the geodesic are then given in terms of the longitude on the sphere and the arc length along the great circle by simple.
Knowledge Transfer¶
Within the home domain. Knowledge about Vincenty's formulae transfers literally when a new case preserves the same carrier type, relation, and recognition test. If the standard 2-argument arctangent atan2 function is used, then these values are usually handled correctly. Finally, simple iterative techniques were used to solve the implicit equations in the direct and inverse methods; even though these are slow (and in the case of the inverse method it sometimes does not converge), they result in the least increase in code size.
Relationships to Other Abstractions¶
Current abstraction Vincenty's formulae Domain-specific
Parents (1) — more general patterns this builds on
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Vincenty's formulae is a kind of Algorithm Prime
Vincenty's formulae is a domain-specific instance of algorithm under its frozen identity. The complete catalog already supplies this broader identity.
Hierarchy paths (2) — routes to 2 parentless roots
- Vincenty's formulae → Algorithm → Function (Mapping)
Neighborhood in Abstraction Space¶
Vincenty's formulae sits in a moderately populated region (48th percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.
Family — Geometric Figures & Constructions (32 abstractions)
Nearest neighbors
- Albers Equal-Area Conic Projection — 0.88
- Gnomonic Projection — 0.86
- Oblate Spheroidal Coordinates — 0.86
- Ellipse — 0.86
- Laplace expansion (potential) — 0.86
Computed from structural-signature embeddings · 2026-10-08