# Math Help - [SOLVED] Tricky Problem

1. ## [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,

2. Originally Posted by mark007
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

3. Originally Posted by mark007
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