Tienstra Resection

Status: Research brief below. Replace this entire body with finished MDX when research is complete. Update description in frontmatter.

Paired tool: /tools/calculators/tienstra-resection

AI research prompt

You are writing a Learn article for Surveying Core. Produce a single MDX-ready document (article body only). Published at /learn/tools/tienstra-resection, paired with the Tienstra Resection Calculator at /tools/calculators/tienstra-resection.

Audience

• Engineering surveyors who need to fix an unknown point by angles only (no distance to control)
• Students studying intersection and resection methods
• Field crews setting up total stations at unknown points near control

Platform conventions (must match the tool)

The calculator implements three-point Tienstra resection:

• Three known control points A, B, C supplied in that order (E/N coordinates)
• Unknown station P; observed angles at P: α = ∠APB, β = ∠BPC, γ = ∠CPA
• Constraint: α + β + γ = 360° (full horizon observation)
• Output: weighted coordinate of P (E, N) using cotangent form — article should explain the method conceptually and give the formula structure without requiring the reader to code it
• Azimuth convention elsewhere on the platform: grid north, clockwise

Scope — must cover

1. Problem definition: resection vs intersection; when Tienstra applies (three control points visible, horizontal angles measured at unknown point)
2. History and naming (Tienstra / three-point resection) — brief, cited
3. Geometric configuration: order of points A-B-C; importance of well-conditioned triangle (avoid near-collinear control, small angles)
4. The danger circle (collins / danger circle concept): explain why some configurations fail or are ambiguous — surveyor-facing language, diagram described in text if no figure
5. Angle observation practice: circle left/right, horizon closure to 360°, instrument height and target height at high level
6. Step-by-step solution narrative aligned with the tool inputs
7. Worked example with realistic E/N control coordinates and observed angles (e.g. α=118.4550°, β=104.3820°, γ=137.1630°) — show computed P and sanity check
8. Checks: plot bearings from P to A,B,C; compare to observed geometry; mention alternative methods (Collins point, reverse polar) briefly
9. Link to calculator in intro and conclusion

Out of scope

• Trigonometric height resection / vertical angles for height
• Four-point resection and least-squares adjustment of multiple observations
• Full total station operating manual
• Legal admissibility of resection-only control

Quality bar

• Cite primary sources (standard surveying computation texts, peer-reviewed or authoritative resection references)
• No filler; include danger circle explanation (this is a differentiator for quality content)
• One complete numeric example end-to-end
• Limitations subsection: angles sum ≠ 360°, poor geometry, near-180° angles causing numerical instability
• WCAG-friendly ## / ### heading hierarchy

Deliverable format

Return MDX body only. Suggested outline:

1. Introduction (tool link)
2. What is resection?
3. Tienstra three-point method
4. Control geometry and the danger circle
5. Field observations
6. Computation walkthrough
7. Worked example
8. Checking your result
9. Limitations and alternatives
10. References
11. Next steps (tool link)

Target length: 1,500–2,200 words.