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If I have any 3D object, for example a car...

  • I place my camera in a fixed position that never changes.
  • I rotate the object in increments of 1°.
  • I take a photo with every rotation incrementation.

By the end of this I would have a photo of the object in every possible position, how many photos do I have.

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up vote 2 down vote accepted

$360$ as there are that many degrees in one rotation. This assumes you rotate only in one plane, which seems to be what you are saying. If you rotate in two axes, you are asking how many points on the sphere have both latitude and longitude integral. You have a range of $-89$ to $+89$ degrees in latitude, $179$ points. For each there are $360$ points in longitude, plus the two poles. $179 \cdot 360 + 2=64442$. However, the points are not equidistributed. Near the poles, one degree of longitude is only $\cos \lambda$ times as long as a degree at the equator or a degree of latitude.

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