--- title: "Intersection vs resection, three point method" subject: "Surveying II" chapter: 5 key: "semester_4/surveying_ii:intersection-vs-resection-three-point" source: https://www.bctengineer.com/q/semester_4/surveying_ii/intersection-vs-resection-three-point site: BCT Engineering --- # Intersection vs resection, three point method Surveying II · Chapter 5: Orientation - Asked in: 2074 Bhadra, 4 marks - Video: [3 Point Resection Calculations](https://www.youtube.com/watch?v=pKzn2VWMkow) — Rami Tamimi | Professional Surveyor - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/surveying_ii/intersection-vs-resection-three-point - Whole chapter: https://www.bctengineer.com/md/semester_4/surveying_ii/chapter-5 ## Question What is the difference between intersection and resection? Explain three point resection method to determine the unknown co-ordinate of a point. ## Short answer Intersection places instrument at known stations to observe unknown; resection places it at unknown station to observe at least three known points. Three-point method: from coordinates compute sides AB, BC, angle B; with measured angles α=APB, β=BPC, find S=360°-(α+β+B), k=BC·sinα/(AB·sinβ), solve x,y and AP. ## Answer #### Difference between intersection and resection **Intersection** is the method of finding the coordinates of an unknown point P by measuring the horizontal angles to P from two (or more) stations of known coordinates. The instrument is set up at the known stations, not at P. **Resection** is the method of finding the coordinates of an unknown station P by measuring the horizontal angles at P to three (or two) stations of known coordinates. The instrument is set up only at the unknown point. | Point | Intersection | Resection | |---|---|---| | Instrument station | At the known stations | At the unknown station | | Observed angles | Angles at the known ends of a base to the unknown point | Angles at the unknown point to the known stations | | Minimum known points | Two (a base line) | Three (two for the two-point problem with extra station) | | Use | Inaccessible point, triangulation, detail points | Fixing a station where it is not possible to set up on known points | | Field work | Instrument is set at two or more stations | Only one set-up | | Check | A third station gives a check | Observing a fourth station gives a check | #### Three-point resection method The coordinates of three known stations A, B, C are given; the angles $\alpha = \angle APB$ and $\beta = \angle BPC$ are measured at the unknown point P. 1. Compute the sides $c = AB$, $a = BC$ and the angle $B$ at the middle station from the coordinates. 2. $S = x + y = 360^\circ - (\alpha + \beta + B)$, where $x = \angle PAB$ and $y = \angle PCB$. 3. $k = \dfrac{a\sin\alpha}{c\sin\beta}$ and $\tan\dfrac{x-y}{2} = \dfrac{k-1}{k+1}\tan\dfrac{S}{2}$; hence $x$ and $y$. 4. $AP = \dfrac{c\sin(180^\circ - \alpha - x)}{\sin\alpha}$, the bearing of AP = bearing of AB $\pm x$, and $E_P = E_A + AP\sin\theta,\; N_P = N_A + AP\cos\theta$. 5. Check by computing P from C. A graphical (tracing paper) solution also exists, and Tienstra's formula gives the coordinates directly as the weighted mean of the three stations. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is the key difference between intersection and resection? A. Intersection sets the instrument at the unknown point; resection at known points B. Intersection observes angles from known stations to the unknown point; resection observes angles at the unknown point to known stations C. Intersection needs three known points; resection needs one D. There is no difference Answer: B. In intersection the instrument stands on known stations; in resection it stands only on the unknown station. (Key point: Where the instrument is set) 2. How many known stations does the basic resection (three-point problem) use? A. One B. Two with a base line C. Three D. Five Answer: C. Three-point resection uses three known stations; intersection needs two (a base line). (Key point: Minimum known stations) 3. In the three-point method with x = angle PAB and y = angle PCB, S = x + y equals: A. 180° - (alpha + beta) B. 360° - (alpha + beta + B) C. alpha + beta + B D. 360° - B Answer: B. The angles of quadrilateral PABC add to 360°, so x + y = 360° - (alpha + beta + B). (Key point: Sum of unknown angles) 4. Which relation gives (x - y)/2? A. tan((x-y)/2) = (k-1)/(k+1) x tan(S/2) B. tan((x-y)/2) = k x tan(S) C. sin((x-y)/2) = k D. tan((x-y)/2) = (k+1)/(k-1) Answer: A. From sin x / sin y = k, the sum-difference identity gives tan((x-y)/2) = ((k-1)/(k+1)) tan(S/2), with k = a sin(alpha)/(c sin(beta)). (Key point: Solving for x - y) ## Related in Surveying II - [Resection, two point problem, intersection](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aresection-two-point-problem-ab-p) — Surveying II, chapter 5 - [Derive three point analytical resection](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Athree-point-analytical-resection-derivation) — Surveying II, chapter 5, asked 2× - [Define intersection and resection, derive](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aintersection-resection-define-derive) — Surveying II, chapter 5 - [Three point analytical resection, average coordinates of O](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Athree-point-resection-p-w-d) — Surveying II, chapter 5 - [Resection point O inside triangle N, P, G](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aresection-nag-triangle-2078c) — Surveying II, chapter 5 - [Two point resection method](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atwo-point-resection-method-describe) — Surveying II, chapter 5 ## Related in other subjects - [Resection by three point problem](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Athree-point-resection-sketches) — Surveying I, chapter 6 - [Intersection versus resection in plane tabling](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aintersection-vs-resection-plane-table) — Surveying I, chapter 6 - [Magnetic difference of [Co(NH₃)₆]³⁺ and [CoF₆]³⁻](https://www.bctengineer.com/question.md?key=semester_2%2Fengineering_chemistry%3Aco-nh3-cof6) — Engineering Chemistry, chapter 6 - [Two-point resection in plane tabling](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atwo-point-resection-plane-table) — Surveying I, chapter 6