What is the key difference between intersection and resection?

Intersection observes angles from known stations to the unknown point; resection observes angles at the unknown point to known stations

Intersection sets the instrument at the unknown point; resection at known points

Intersection needs three known points; resection needs one

Which relation gives (x - y)/2?

tan((x-y)/2) = (k-1)/(k+1) x tan(S/2)

2074 Bhadra · 4 marks

Intersection vs resection, three point method

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.

What is the difference between intersection and resection? Explain three point resection method to determine the unknown co-ordinate of a point.

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.

Compute the sides $c = AB$ , $a = BC$ and the angle $B$ at the middle station from the coordinates.
$S = x + y = 360^\circ - (\alpha + \beta + B)$ , where $x = \angle PAB$ and $y = \angle PCB$ .
$k = \dfrac{a\sin\alpha}{c\sin\beta}$ and $\tan\dfrac{x-y}{2} = \dfrac{k-1}{k+1}\tan\dfrac{S}{2}$ ; hence $x$ and $y$ .
$AP = \dfrac{c\sin(180^\circ - \alpha - x)}{\sin\alpha}$ , the bearing of AP = bearing of AB $\pm x$ , and $E_P = E_A + AP\sin\theta,\; N_P = N_A + AP\cos\theta$ .
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.

✓ Answer checked by Claude Opus 5.5 (high effort)

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