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Math Help - [SOLVED] Tricky Problem

  1. #1
    mark007
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    [SOLVED] Tricky Problem

    Hi all,

    I am attempting to work out a time when two moving objects will collide. My simple example takes two simple circles, moving about a 2d world, with the movement of each circle being either linear, or something slightly more than simply linear.

    I need to figure out when (if ever) these two circles "touch", without having to iteratively go through thousands of times checking each. I suppose what I would hope to get at the end of the calculation would be

    -no solutions (they never could touch given their current paths).
    -they only touch once
    -they touch many times (of course with paths that may be circular themselves or similar).

    I really would appreciate any insight into this problem.

    Regards,
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by mark007 View Post
    Hi all,

    I am attempting to work out a time when two moving objects will collide. My simple example takes two simple circles, moving about a 2d world, with the movement of each circle being either linear, or something slightly more than simply linear.

    I need to figure out when (if ever) these two circles "touch", without having to iteratively go through thousands of times checking each. I suppose what I would hope to get at the end of the calculation would be

    -no solutions (they never could touch given their current paths).
    -they only touch once
    -they touch many times (of course with paths that may be circular themselves or similar).

    I really would appreciate any insight into this problem.

    Regards,
    Of course, you will have to specify how they are moving before we can intelligently answer this question without writing a paper on it.

    -Dan
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by mark007 View Post
    Hi all,

    I am attempting to work out a time when two moving objects will collide. My simple example takes two simple circles, moving about a 2d world, with the movement of each circle being either linear, or something slightly more than simply linear.

    I need to figure out when (if ever) these two circles "touch", without having to iteratively go through thousands of times checking each. I suppose what I would hope to get at the end of the calculation would be

    -no solutions (they never could touch given their current paths).
    -they only touch once
    -they touch many times (of course with paths that may be circular themselves or similar).

    I really would appreciate any insight into this problem.

    Regards,
    You have a pair of trajectories as a function of time x_1(t),\  x_2(t) and you are
    interested in the solution set |x_1(t)-x_2(t)|=r_1+r_2, where r_1 and r_2 are
    the radi of the two circles.

    You need to identify if this has any solutions.

    RonL
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