Field of view is tied to the final image
Use the horizontal field of view for the lens setting and crop that will produce the photographs. The planner derives vertical field of view from the aspect ratio using a rectilinear-camera model. Strong fisheye distortion or an unknown digital crop requires a test measurement; the approximation does not model those lens behaviors.
Distance fits a bounding sphere
The sphere radius is half the three-dimensional diagonal of the measured envelope. The smaller camera field of view and the chosen frame-fill margin determine a conservative distance. A minimum focus clearance can push the camera farther away. Ring heights and horizontal radii then follow from that distance and the ring’s elevation angle.
Overlap is visual evidence, not only an angle
The planner limits angular steps to 15 degrees and reduces them further for tighter overlap requests. This sampling rule is a starting heuristic. A box, a concave sculpture and a smooth cylinder expose different surfaces at the same angle. Inspect neighboring images for shared landmarks and add photographs where the geometry hides them.