Perspective effects on horizontal photographs (central projection) For photographs formed by central (perspective) projection, which statements are true for “horizontal photographs” considered as perspective views?

Introduction / Context:
Central projection introduces perspective effects. Understanding which sets of lines appear parallel and which converge helps interpret imagery, locate vanishing points, and perform rectification when planimetric measurements are required.

Given Data / Assumptions:

• A camera forms images by central projection.
• “Horizontal photograph” here means the image plane is nominally vertical to the viewing direction, producing a perspective view of a horizontal scene.
• We discuss geometric tendencies, ignoring lens distortion and terrain undulations.

Concept / Approach:
In perspective projection, sets of lines that are parallel in space but not parallel to the image plane generally appear to converge toward a vanishing point. However, lines in object space that are themselves parallel to the image plane project as parallel lines. These principles explain why road edges meet at a vanishing point in photographs while lines lying in planes parallel to the image remain parallel.

Step-by-Step Solution:
Assess (a): Perspective projection makes many parallel sets appear non-parallel → true.Assess (b): Classic example—receding road edges converge → true.Assess (c): When an object’s line set is parallel to the image plane, projectors intersect the plane without angular divergence → lines remain parallel → true.Therefore, “All of the above”.

Verification / Alternative check:
Projective geometry textbooks derive vanishing points from directions not parallel to the image plane; empirical inspection of photographs confirms these behaviours.

Why Other Options Are Wrong:
Each of (a)–(c) is correct under central projection; hence (d) is the inclusive correct choice. “None of these” is inappropriate.

Common Pitfalls:
Confusing orthographic (parallel) projection with perspective projection; only the latter produces vanishing points.

Final Answer:
All of the above