Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Intersection of line and surface

  1. May 29, 2015 #1


    User Avatar
    Science Advisor

    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?
  2. jcsd
  3. May 29, 2015 #2


    User Avatar
    2017 Award

    Staff: Mentor

    I do not have a proof but it looks like the general formula.

    It also works for n=1.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook