Smart Phone Panoramas

Geometry Level 5

Many smart phones today are able to take panorama shots, by sweeping the camera from one direction to another.\

Assuming ideal pinhole optics and that the camera works like a slit scan, all straight lines of the object become what family of curves?

Assume that, mathematically speaking, all points of the object are projected onto the surface of a cylinder, by means of rays that all pass through a common point on the axis of the cylinder. Then the surface of the cylinder is unrolled flat to create the final image.

1 Conic curves in general, depending on orientation of straight lines in object

2 Parabolic curves only

3 Circular and elliptical curves only

4 Hyperbolic curves only

5 Trigonometric curves in general, depending on orientation of straight lines in object

6 Sinusoidal curves only (or Cosinusoidal if you prefer--they differ only by phase)

7 Cosecant curves only (or Secant if you prefer--they differ only by phase)

8 Not limited to conic or trigonometric curves

If either 2, 3, or 4 is true, do not choose 1. If either 6 or 7 is true, do not choose 5.

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