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Intersection of line and surface

  1. May 29, 2015 #1

    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 [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].

    Question: Does this relationship [itex](2n^2)[/itex] hold for n > 3?
     
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  3. May 29, 2015 #2

    mfb

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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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