Identify the named image point defined by a geometric bisector On an aerial photograph, the point where the bisector of the angle between the vertical (plumb) line through the optical centre and the plate perpendicular meets the photo plane is called the:

Introduction / Context:
Tilted photographs introduce three special image points—principal point, plumb (nadir) point, and isocentre—that help describe how the optical axis and the vertical relate within the image. Correctly naming these points is essential for tilt corrections and interior orientation in photogrammetry.

Given Data / Assumptions:

• The camera is tilted with respect to the vertical (not a perfectly vertical photograph).
• The optical centre (perspective centre) and the image plane are defined.
• The plumb line is the vertical through the perspective centre projected onto the image plane.

Concept / Approach:

The isocentre is the point on the photograph where the bisector of the angle between the principal line (perpendicular from the perspective centre to the plate) and the plumb line meets the image plane. It lies midway (angularly) between the principal point and the plumb (nadir) point along the direction of tilt. This contrasts with the principal point (foot of the perpendicular from the optical centre) and the plumb point (image of the vertical direction). The perspective centre itself does not lie on the photo plane.

Step-by-Step Solution:

Verification / Alternative check:

Standard tilt-geometry diagrams show the isocentre lying on the line joining the principal point and the nadir point, typically at a characteristic distance related to tilt (for small tilts, approximately halfway between).

Why Other Options Are Wrong:

• Principal point: defined by the perpendicular, not the bisector.
• Plumb point: projection of the vertical alone.
• Perspective centre: a space point, not on the image plane.

Common Pitfalls:

Assuming the principal and plumb points coincide; they coincide only when there is no tilt. Misnaming the isocentre as “principal point” is a frequent error in quick quizzes.

Final Answer:

Isocentre