Geometrical similarities of the Orlov and Tuy sampling criteria and a numerical algorithm for assessing sampling completeness

Tuy and others have derived a sufficiency condition for complete sampling using a cone-beam geometry. Herein, we express Tuyʹs cone-beam condition in the language and geometry of Orlovʹs condition for parallel-beam collimation. One may determine from this condition what volume is completely sampled. This inversion has been implemented in software. The software determines a lower bound on the completely sampled volume for arbitrary orbits.