1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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 ]


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


    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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted