A straight line in 3 space can be described as A + Bt, where A is a position, B a direction, and t a scalar parameter. CAD surfaces can be represented in terms of polynomial functions of two variables (u and v) with the highest degree term being [itex]u^nv^n[/itex]. The intersections can then be obtained as roots of a polynomial in t. I have seen proofs that for n = 2 or n = 3, the polynomial in t is of 8th or 18th degree respectively [itex](2n^2)[/itex].(adsbygoogle = window.adsbygoogle || []).push({});

Question: Does this relationship [itex](2n^2)[/itex] hold for n > 3?

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# Intersection of line and surface

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