Surveying fundamentals — when is earth’s curvature considered? The type of land surveying in which the curvature of the Earth is explicitly taken into account is called:

Introduction / Context:
Surveying methods are grouped by the scale of work and the required accuracy. Over large areas, assuming a flat Earth introduces unacceptable error; therefore, spherical or ellipsoidal geometry must be considered.

Given Data / Assumptions:

• Large-area mapping and control are required.
• High positional accuracy is needed (often tied to national datums).
• Angular and linear measurements may span tens to hundreds of kilometres.

Concept / Approach:
Geodetic surveying accounts for the Earth’s curvature and uses an ellipsoidal model with geodetic coordinates, triangulation/trilateration networks, and satellite-based observations. Plane surveying treats the surface as a plane and is adequate only for small areas where curvature effects are negligible.

Step-by-Step Solution:
Identify scale: regional/national → curvature matters.Use geodetic methods and datums (e.g., ellipsoid, geoid separations).Apply appropriate corrections (spheroidal excess, projection scale factors).

Verification / Alternative check:
Modern GNSS control is geodetic by nature, inherently reflecting Earth curvature and reference ellipsoids.

Why Other Options Are Wrong:
Plane surveying is limited to small areas. “Preliminary,” “topographical,” and “route” describe purpose rather than the geometric model; they may be executed as plane or geodetic depending on extent.

Common Pitfalls:

• Applying plane-coordinate methods over large extents without projection corrections.
• Mixing geodetic and ground distances without scale adjustments.

Final Answer:
Geodetic surveying