Q26. The two-point problem and three-point problem are methods of:
📚 Detailed Explanation: Two-Point & Three-Point Problems as Combined Orientation & Resection
The two-point and three-point problems are special field situations encountered in plane table surveying where the instrument is set up at an unknown station. Solving these problems requires simultaneously determining both the correct table orientation and the station’s position on the sheet — neither can be solved in isolation from the other.
When the plane table is set up at an unknown point, the table is not yet oriented (you do not know which way to rotate it) and the station is not yet plotted (you do not know where on the sheet you are). The two-point and three-point problems solve both issues together in one integrated procedure:
• Orientation is achieved when the table is correctly rotated so that plotted lines are parallel to ground lines.
• Resection is achieved when the station’s position is fixed on the sheet by the convergence of rays from known control points.
Neither can be done without the other at an unknown station — they are co-dependent. This is why the correct answer is “orientation and resection” together.
Two-Point vs Three-Point Problem
| Feature | Two-point problem | Three-point problem (Lehmann/Bessel) |
|---|---|---|
| Known plotted points used | 2 | 3 |
| Core technique | Auxiliary ray method + back-sight from auxiliary station | Trial-and-error using triangle of error (Lehmann) or tracing paper (Bessel) |
| Field effort | Must move to an auxiliary known station | All work from one station; no movement needed |
| Accuracy | Lower (fewer constraints) | Higher (three constraints + self-checking triangle) |
| Danger circle applies? | No | Yes — avoid placing instrument on great circle |
Why the Other Options Are Wrong
A — Resection only: Resection fixes the station position, but without correct orientation the resection rays are drawn in wrong directions and the fix is meaningless. Orientation must be achieved simultaneously. Saying “resection only” understates what these methods accomplish.
B — Orientation only: Similarly, orientation alone (rotating the table to the correct direction) does not fix the station’s position on the sheet. Both problems do more than just orient the table — they also fix the plotted position. Option B is equally incomplete.
D — None of these: Clearly incorrect; both problems are well-defined graphical surveying techniques that have been used in plane table practice for over a century.
Key Concepts for Students
- Remember the pairing: unknown station = orientation + resection together: Whenever the instrument is at an unknown position, both operations must be performed simultaneously. The two-point and three-point problems are the systematic procedures for doing exactly this — they are not just resection (finding position) or just orientation (rotating the table), but both at once.
- Three-point preferred in practice: The three-point problem uses one more known point, providing a cross-check via the triangle of error. This makes it the standard method for high-quality work. The two-point problem is used when only two control points are visible from the new station, requiring a visit to an auxiliary station as compensation for the missing third point.
- Exam tip — Option C vs Option A: This question commonly catches students who remember “resection” but forget that orientation is inseparable from it at an unknown station. Always select the complete answer (“orientation and resection”) rather than the partial one (“resection only”).