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I need calculate ray (line) intersection with torus for my ray-tracing program (I know, its to graphics, but i need math behind it).

I can solve equation of order $x^4$, but thats too way slow (Cardano's method). So is there better way, how to calculate this ?

My torus has center $[0,0,0]$ and $R$, $r$ diameters Line (Ray) is point and its direction vector

Thanks

  • 0
    Is applying an explicit formula for the solutions of a 4th-degree polynomial too slow, or are you depressing the polynomial to solve it? [Here is an explicit formula for the solutions of a general 4th-degree polynomial](http://math.stackexchange.com/questions/785/is-there-a-general-formula-for-solving-4th-degree-equations/786#786).2010-10-25
  • 0
    Cross-posted to MO: http://mathoverflow.net/questions/43552/anuloid-torus-x-line-intersection2010-10-25

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