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    Re: Closest point of approach.
    From: Peter Hakel
    Date: 2012 Jan 2, 16:44 -0800
    Hello Amrin,

    Following up on the response from Andres Ruiz, please see the attached PDF file.  Individual "action steps" are highlighted with bullets.  This is the algorithm encoded into the cpa.xls spreadsheet that I posted earlier for the 2-D case, but it works just as well in 3-D.  I left the specification of angles deliberately vague, since I actually don't know how pilots define those relative to their own aircraft.  It's a bit of a chore to carry out this procedure explicitly, but if it is encoded into a programmable electronic device, the results come out instantaneously.

    The elegant solution using planar trigonometry posted a few days by Gary LaPook for 2-D would in fact work in 3-D as well, since a point (your aircraft) and a straight line (the other aircraft) on which the point does not lie (hopefully!!) define a plane  (see the attached cartoon).  You'd just have to take extra care with those angles.

    Peter Hakel

    From: Amrin Shahziya <ammushaz@gmail.com>
    To: NavList@fer3.com
    Sent: Monday, January 2, 2012 1:04 AM
    Subject: [NavList] Re: Closest point of approach.

    please explain this in 3d space
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