Plane Table Resection – When Is the Three-Point “Fix” Most Reliable? While fixing a plane-table station by the three-point problem with three known points plotted on the sheet, the quality of the fix is best under which geometric condition?

Introduction:
The three-point problem determines the position and orientation of a plane table by sighting three well-defined points whose plan locations are already plotted. The reliability of the 'fix' depends on the geometry formed by the points relative to the unknown station.

Given Data / Assumptions:

• Three well-spaced, non-collinear control points are visible.
• The station to be fixed lies within the triangle of these points (preferred).
• The 'middle' point refers to the point that lies between the other two when viewed from the plane-table station.

Concept / Approach:

A well-conditioned triangle with the station near its interior reduces angular intersection sensitivity. Classical plane-table guidance states that the fix improves when the middle point is the nearest, yielding better angular spread and smaller intersection errors on the table. Collinearity or extreme skinny triangles degrade accuracy severely.

Step-by-Step Solution:

Verification / Alternative check:

Textbook rules for good resection condition lists include: station inside the control triangle, good spread of rays, and middle point nearest to the station to strengthen the solution.

Why Other Options Are Wrong:

Making the middle point farthest tends to flatten angular spread; choosing a side point as nearest skews geometry; collinear points give no unique solution.

Common Pitfalls:

Placing the plane table outside the control triangle; using poorly separated control points; ignoring identification of the middle point in the field.

Final Answer:

The middle (intermediate) control point is nearest to the plane-table station