Vertical aerial photography — effects and properties on a true vertical Which statements about a truly vertical aerial photograph and relief displacement are correct?
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AOn a true vertical photo, the principal point coincides with the plumb point
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BThe top of a hill plots farther from the principal point than its foot (for positive relief)
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CThe hilltop is shown at a larger image scale than a nearby valley floor
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DRelief displacement on a true vertical is directly proportional to both radial distance from the principal point and the point’s elevation above datum
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EAll of the above
Answer
Correct Answer: All of the above
Explanation
Introduction / Context:Vertical aerial photographs are central to photogrammetry and mapping. Understanding principal, plumb, and isocentres and the nature of relief displacement is essential for accurate plotting and height interpretation.
Given Data / Assumptions:
- Truly vertical exposure (tilt ≈ 0).
- Positive relief features (hills) and lower areas (valleys).
- Central projection geometry.
Concept / Approach:
On a true vertical, the optical axis is vertical; hence the principal point equals the plumb point (and the isocentre). Relief displacement radiates from the principal point; higher points are displaced outward, appearing farther from the principal point and at a slightly larger image scale than lower points at the same radial direction.
Step-by-Step Solution:
(a) True vertical → principal point = plumb point.(b) Positive relief → outward displacement → hilltop farther from P than its foot.(c) Larger radial distance at same nominal scale → locally larger effective scale.(d) Displacement magnitude d ≈ r * h / H → proportional to radial distance r and elevation h.Verification / Alternative check:
Relief displacement formula derives from similar triangles in central projection; mapping texts present the proportionality d = (r * h) / H for small relief relative to flying height H.
Why Other Options Are Wrong:
- Each individual statement accurately describes vertical photo geometry; thus the combined option is correct.
Common Pitfalls:
- Confusing true verticals with tilted photos where principal, plumb, and isocentre do not coincide.
Final Answer:
All of the above.