Three-point resection
The coordinates of an occupied station from the angles it turned between three known points, by Tienstra's method, with a warning when the station is near the danger circle.
Experimental: not yet fully verified. How results are checked
The station is at northing 500 ft, easting 1,350 ft.
- Easting
- Distance from the danger circle
Provenance
- Computed by
- survey.cogo.resection 1.0.0, core 0.1.0
- Model
- Tienstra: with the triangle's angles A′, B′, C′ and the station's opposite angles α = ∠BPC, β = ∠CPA, γ = ∠APB, P = (K₁A + K₂B + K₃C)/(K₁ + K₂ + K₃), Kᵢ = 1/(cot of the triangle angle − cot of the station angle) (Ghilani & Wolf 2021, ch. 11)
- Accuracy
- Exact for the geometry; unstable near the circle through the three points, where every station on it sees the same angles
- Notes
- 1 shown with the answer
- Cites
- Ghilani, C. D., and Wolf, P. R., Pearson, Elementary Surveying: An Introduction to Geomatics
Something look off?
How we got thisFormula, worked example, sources, and proof
Model: Tienstra: with the triangle's angles A′, B′, C′ and the station's opposite angles α = ∠BPC, β = ∠CPA, γ = ∠APB, P = (K₁A + K₂B + K₃C)/(K₁ + K₂ + K₃), Kᵢ = 1/(cot of the triangle angle − cot of the station angle) (Ghilani & Wolf 2021, ch. 11)
Accuracy: Exact for the geometry; unstable near the circle through the three points, where every station on it sees the same angles
Worked example: A station south of three control points. Source: Angles computed from a station at (500, 1350). It is golden test vector v001, and every build checks the tool still gives its answer within its tolerance.
You enter
- Angle A to B
- 37.85442542467041 deg
- Angle B to C
- 34.00749241973227 deg
- Control points A, B, C
- 1000 ft, 1000 ft 1500 ft, 1400 ft 1100 ft, 1800 ft
You get
- Northing
- 500 ft
- Easting
- 1,350 ft
- Distance from the danger circle
- 0.4697
Review: Not yet independently reviewed by a licensed surveyor.
Last verified: 2026-09-23, when a maintainer last confirmed this tool's sources at the issuer. See the sources ledger.
Status: version 1.0.0, core 0.1.0. See this tool in the verification report.
Changes
- 2026-09-23, fixed: Survey tools cite Ghilani and Wolf's Elementary Surveying, 16th edition (2021), but their method notes said "Ghilani & Wolf 2018". The notes now give 2021, the edition cited. No results change. Changelog
Checked against: 5 golden test vectors (download the test vectors, each with its source and tolerance). See how results are checked and every source.
Sources
- Elementary Surveying: An Introduction to Geomatics, Ghilani, C. D., and Wolf, P. R., Pearson, 16th edition. Chapter 11 (coordinate geometry: intersections and three-point resection).
Experimental means this tool has not yet met the stable bar: at least 20 golden vectors, differential tests, and an independent worked example.