Intersection of line and surface

mathman
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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 u^nv^n. 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 (2n^2).

Question: Does this relationship (2n^2) hold for n > 3?
 
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I do not have a proof but it looks like the general formula.

It also works for n=1.
 

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