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Wilson, R.E., 1975: Eclipses by an elliptical torus. Astron. J., 80, 719-722, doi:10.1086/111804.
The geometry of a torus having elliptical meridian sections is discussed in regard to its eclipsing properties when viewed at arbitrary inclinations. Eclipses involving the hole horizon as well as the outer horizon are considered. Various special cases of such a torus include those of a thin ring or disk, an ellipsoid of revolution, and a section of a right circular cylinder. Thus the relations given here may be used in place of a number of special schemes used previously for these particular cases, as well as for the case of a general torus of finite thickness. A simple method is given by means of which one can decide if an arbitrary point in space is or is not eclipsed by the torus. Leading up to this procedure, a general horizon condition is derived and the basic equations of the problem are listed, as are quadrant rules for the surface coordinates of the torus. Certain basic equations might be used to derive analytic eclipse functions for special cases, such as eclipses of limb-darkened spheres, although this has not been done in the present paper. Major simplifications are made possible by the definition oof an auxiliary ellipsoid, points on which are mapped in one-to-one correspondence into surface points of the torus. Finally, some dicussion of practical computational problems is given, and a FORTRAN subroutine, TORUS, is briefly described.
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