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Math Help - Calculating the intersecting points of a line on two squares

  1. #1
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    Calculating the intersecting points of a line on two squares

    Hi guys,
    I've got an interesting math problem that I'm struggling to solve. It's a little complicated to explain, but essentially it is this:


    Given a point P that is contained by the convex hull of the squares A & B (A & B do not overlap).
    A line intersects A at point PA, B at point PB, and point P; such that the ratio [distance from PA to P] : [distance P to PB] must be as large as possible (PA to P being larger).

    Calculate points PA and PB.


    I'm not really sure how to calculate this, but if anyone could point me in the right direction I would be very grateful!
    Thanks in advance!
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  2. #2
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    Re: Calculating the intersecting points of a line on two squares

    Hey Saifa.

    This sounds like a standard optimization problem where you are maximizing distance. The first thing you should do is convert the problem to a set of equations and inequalities.

    Do you have a definition for lines A and B in terms of all the points?
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  3. #3
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    Re: Calculating the intersecting points of a line on two squares

    Hi Chiro,

    Nope, I don't know any equations for the polygons or lines.
    I just have a list of 4 points for the two squares and I know the x and y coordinate of all points.

    so if I use the line equation:

    ax + by + c = 0

    given that it goes through the point:

    PX, PY

    Can I calculate any line that goes through P and work out the best gradient later?

    I have no clue on what to do after this point, would I represent a square as an equation?
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