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Math Help - line-surface intersection

  1. #1
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    line-surface intersection

    I'm trying to figure out how to find the intersection of a line and a surface in 3-space. For example, what if I had the equation for a line in parametric form:

    x = 1 + t
    y = -2 + t
    z = 1 - 2t

    and a surface (of an ellipsoid) in parametric form:

    x = 2*cos(u)*cos(v)
    y = 2*cos(u)*sin(v)
    z = sin(u)

    where -pi/2<u<pi/2 and -pi<v<pi

    How would I go about finding the intersection point?
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: line-surface intersection

    Verify that x^2+y^2+4z^2=4 and solve the quadratic equation (1-t)^2+(-2+t)^2+4(1-2t)^2=4.
    Last edited by FernandoRevilla; September 24th 2012 at 03:09 AM.
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