Many scientific datasets (for example, simulations and reconstructions in astrophysics and geophysics) are spheres or sections of spheres and naturally fit into spherical coordinates.When tracing rays through naturally spherical domains (for example, for visualization), converting to Cartesian coordinates introduces aberrations.Therefore, we seek an algorithm to natively cast rays through spherical coordinates, and without performing calculations that would amount to in-place conversion to Cartesian.Three things make this work:1. An alternative coordinate system which is isomorphic to spherical coordinates but has useful properties along straight lines.2. Constantly referring back to the equation of the line a ray is a segment of, to control propagation of errors.3. Using the shape of the cells to restrict where the ray might exit a cell so that we can (in some cases) select the next zone by process of elimination.This method applies also to cylindrical coordinates (or even more simply, 2-d polar coordinates).
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