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Line to Surface intersection

  1. May 2, 2012 #1
    Im new to the forum, so I didnt know where to post this.

    (x is cross-product, . is dot-product and * is multiplication)

    Consider point P with linear velocity Pv.

    Consider points A and B that define the edge AB of a square with C as center.

    Consider that C has linear velocity Cv and angular velocity Cw.

    Av = Cv + Cw x (A-C)
    Bv = Cv + Cw x (B-C)

    (Considering this is 2D, you can see Cw as (0,0,angle) and all linear velocities as (Vx,Vy,0) )

    Now, lets add time as a variable.

    P(t) = P(0) + Pv*t
    A(t) = A(0) + Av*t
    B(t) = B(0) + Bv*t

    (consider velocities to be constant)

    Now the fun begins:

    A(t) + k*[ B(t) - A(t) ] is a point along the edge AB where 0 ≤ k ≤ 1

    Which means:

    A(0) + Av*t + k*[ B(0) + Bv*t - A(0) - Av*t ]

    So far so good, but what happens if we want to know when P(t) intersects AB(t)?

    P(0) + Pv*t = A(0) + Av*t + k*[ B(0) + Bv*t - A(0) - Av*t ]

    or

    A(0) + k*B(0) - k*A(0) - P(0) = t
    (Pv - Av - k*Bv + k*Av)

    or

    P(0) + Pv*t - A(0) - Av*t = k
    B(0) + Bv*t - A(0) - Av*t

    Finally, I should state that all variables are known except k and t.

    The objective is to know t and k that satisfy the equation BUT then discard any pair (t,k) where k doesn't satisfy 0 ≤ k ≤ 1.

    Can anyone help me find a solution or better way to solve this problem? Or is this impossible?

    Thanks in advance!
     
  2. jcsd
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