INTERSECTION OF A RAY WITH A SURFACE OF THIRD OR FOURTH DEGREE.
Los Alamos Scientific Lab., N. Mex. Indiana Univ., Bloomington. Dept. of Physics (US), E Cashwell, Christopher N Everett · 1969
It has become desirable to include, in the geometric subroutine of Monte Carlo programs, a procedure for finding the intersections of a line of flight with a toroidal surface.Such problems, for surfaces of third or fourth degree, depend in an obvious way on the solution of cubic or quartic equations.Although the latter subject is centuries old, we give here, without apology, a careful exposition of its details, required for machine computation, and not to be found elsewhere.A routine is then derived for solution of the required torus-intersection problem.